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references are at the bottom of this page. When this file is printed (rarely), I append to the end:
The aberration of light (also referred to as astronomical aberration or stellar aberration) is an astronomical phenomenon which produces an apparent motion of celestial objects about their locations dependent on the velocity of the observer. Aberration causes objects to appear to be angled or tilted towards the direction of motion of the observer compared to when the observer is stationary. The change in angle is typically very small, on the order of v/c where c is the speed of light and v the velocity of the observer. In the case of "stellar" or "annual" aberration, the apparent position of a star to an observer on Earth varies periodically over the course of a year as the Earth's velocity changes as it revolves around the Sun, by a maximum angle of approximately 20 arcseconds in right ascension or declination.
Aberration, wikipUnits: 'Joule sec' (THINK what that must mean! weird) J*s is energy multiplied by time but it is also momentum * distance, or angular momentum. Planck's Constant (local).
temp changes but
one of the 2 types of thermodynamic processes in a carnot cycle,
the other is isothermal'. See thermodynamic 'processes'.
refs: XAM p52, Adiabatic_process, wikip
PT1_Q56 adiabatic expansion. What varies when an ideal gas expands freely in
a perfectly rigid and insulated cylinder?
This adiabatic process involves no gain/loss of heat. Only the internal energy changes.
no distinguished point that serves as an origin. no vector can be uniquely associated to a point. (so an AS can't support a mag field (?)). can't add two points of the space. Subtraction to make displacement vector ok. wikip, informal description
.symb rho = 1.225 kg/m³. Serway p153.
from Arabic "al-jabr" meaning "restoration". Muhammad ibn Musa al_Khwarizmi 780-850 his book "The Compendious Book on Calculation by Completion and Balancing".
Algebra, wikip my Algebra book
"magnetic field induced around a closed loop is proportional to
the electric current plus displacement current (rate of change of electric field)
that the loop encloses." His original statement didn't contain mention of what
later was called the 'displacement current'.
alt formulation. (line integral of B.dl)
Related: Maxwells_equations, local notes
In the following: L is angular momentum, a conserved quantity,resistance to changing rotation speed L does not have to be aligned with axis of rotation (full treatment requires a tensor) I believe L is a pseudo vector I is moment of Inertia. It's like mass in the (linear) momentum eqn but its role here is to (also) handle the distribution of mass wrt the spin axis. Basically the sum of all masses times their (r=distance to axis)². m is mass, kg but in 'm²' and 'm/s', it's meters r is radius, m v is velocity, tangential w is ω, > 0 for ccw rotation. Its units are really 1/s
ω has to be perpendicular to the motion
Or for objects which are small relative to the distance from the
turning axis (planet), their L can be
L = r χ mv # vector cross product. Serway p315.
Since torque = dL/dt, L can be considered Torque-seconds
T (N•m) = I angAccel; so T/I = angular acceleration
see wikip, Angular Mom for: A 'pseudo vector' when in 3D. L = (I=r² m) (ω=(r χ v) / r², angular velocity) Angular momentum units can be interpreted as torque-seconds, work-seconds, or energy-seconds. L does not have to be aligned w/ turn axis. Can require a tensor. point particle: Rvec χ Pvec pseudo vector; torque = dL/dt SOON: ref! 161115 notes from the old diagram: conservation of Angular Momentum I.b * ω.b = I.a * ω.a (I.b = m Rb²) * om.b = (I.a = m Ra²) * om.aMore work on this topic in pub/radiusOfgyration.html
In short: - the cathode is usually negative - but some applications switch this. - CRT is an example - Always: the anode has the opposite polarity of the cathode. - in 'normal use', when a device is 'running off' a battery, the cathode is positive and the anode is neg. This arrangement is called 'galvanic' - when charging a battery, doing electro-plating, or driving several types of chemical reactions, the polarities of the anode/cathode are reversed. This arrangement is called 'electrolytic'. "In chemistry, a cathode is the electrode of an electrochemical cell at which reduction occurs." ?? WHOA! "electrochemical" means the solution/cell is being run like a battery charger. (that is, electrons are flowing into the cathode (traditional 'current' flowing out...) and these just-arrived electrons are being 'accepted' by the solution.) Cathode, wikip
eg: 4, 15, 26, 37, 48, … (with common difference 11). (wikip)
arctangent function. avail in excel and python. didnt see in typ web search.
python: start Idle34, import math, math.atan2(yVal,xVal) * 57.3 # answer in degrees
Note that the horizontal axis represents electron density.
Diagram taken from wikipedia's page on the ionosphere.
binding E, SOON
hadron: composite particles, strong force
members: baryon (3 quarks), meson (1 quark, 1 anti) baryon made of 3 quarks. eg proton, neutron spins: ½ proton: neutron: free neutrons decay with a half-life of about 611 seconds meson made fm 1 quark, 1 antiquark. eg: pion, kaon spins: 0 pion: decays in 26ns ; 'pion' = pi meson. members: π^{0}, π^{+}, π^{-} kaon: stats:
boson: force carriers, not matter
members: gluon,photon,Z boson,W boson,Higgs spins: integers stats: bose-einstein (aka 'bosonic' (?) ) gauge bosons are force carriers. photon (electromagnetism) 3 W's and Z of the weak force 8 gluons of the strong force
fermion: all quarks and leptons. assoc'd w/ matter
members: protons, SOON spins: half-integers stats: Fermi-Dirac Pauli Exclusion P: true types: b/c of quarks, protons are fermions
lepton: no strong F, beta decay, neutrinos no chg
members: electron,muon,tau; & neutrino versions of previous 3 muons & taus only seen after high E collisions. spins: 1/2 integer. forces, and their relative strengths: gravitation 0, weak 25, E&M 36, strong force 38 antiparticle: true ref: wikip
quark
members: up,down,charm,strange,top,bottom. spin theorem the "integer" of spin is 'hBar'! chemistry file has blob of info typed in 180301
1897 Thompson discovers the electron 1904 Thompson promoted his "Plum Pudding model" model. 1909 Rutherford discovered the nucleus PT1_Q22 Rutherford Scattering.Planetary model vs Thomson's Plum Pudding... PT1_Q22 1911 Rutherford advanced the Planetary model Rutherford_model, wikip 1913 Bohr (and Rutherford) developed a very good model of the Hydrogen atom, able to answer questions of spectra. Bohr_model, wikip 1932 valence shell model. Atomic_orbital, wikip
all gases have same # molecules/mole. 6.02¤23/mole. N subCapA
prjt ballistics exists to collect equation info. The projectile path is a parabola. For a shot where the target and launch are at the same elevation, the max height of the path is at x,y=(½ distance, ¼ distance). refs: TODO add to sciCalcs, update bad links (teach/ gone...) prjt catapultCA SAFE. bean bags. small, cheap, 30' range. 1802xx prjt catapult405 AGGRESSIVE. clean up, merge. motivor.rb. PRINTs, 1506xx prjt teach/robotics has old diagram. think I have better 1602xx teach/robotics/trajectory.png old diagram. think I have better 1602xx prjt robotFirst made ballistic.py, gd graphs. 171011 archived prjt 2014for throwing pet treats. powered by tape measure 1409xx
balance a 'beam', 'see-saw', 'teeter totter' XAM_Q14, p29; XAM 172 ref12, item 26:m_{1} x_{1} =m_{2} x_{2} (torques cancel).
"SI derived unit of radioactivity",1 Bq == 1 nuclear decay per second . Units 'per second' or 1/s wikip Sievert
1738. Bernoulli's Law.
The venturi is frequently the example but the principle applies to wings too..
XAM p7 notes that the 'equation of continuity' v1 A1 = v2 A2 where A's are cross sections
in a pipe or venturi.
wikip
image of a double tackle. from wikipedia. Block_and_tackle, wikip
Written as a lower case 'k' (fgh likes 'kB', wiki uses 'Kb'. b/c there are lots of k's !)kB = R / NA = (R=8.314 J/(K•mol) / (NA=6.02¤23/mol) = 1.38¤-23 J/K (used in 2 contexts, one "times Avogadro's constant" (to remove the division in the above paragraph, leaving it as just 'R', the gas constant. Preferred units seem to be J/K or Joules per degree K (absolute).) Used in ideal gas law, below wikip on Boltzmann_constant Serway p543.
object_{o} will float if overall_density of object < density of fluid ρ_{o} < ρ_{f} => mass_{o} / vol < mass_{f} / vol sciCalcs PT3_Q21 Mb = M0 ( 1 - pf/p0 ) where M0 is vacuum mass of object, Mb is bouyant mass, pf is the density of the fluid, p0 is the density of the object
Brewster's angle (also known as the polarization angle) is an angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection.
When unpolarized light is incident at this angle, the light that is reflected from the surface is therefore perfectly polarized. This special angle of incidence is named after the Scottish physicist Sir David Brewster (1781–1868).
ref: Phys Eqn. item 49 or so
In 1827, while looking through a microscope at particles trapped in cavities inside pollen grains in water, Robert Brown noted that the particles moved through the water; but he was not able to determine the mechanisms that caused this motion. Atoms and molecules had long been theorized as the constituents of matter, and Albert Einstein published a paper in 1905 that explained in precise detail how the motion that Brown had observed was a result of the pollen being moved by individual water molecules, making one of Einstein's first big contributions to science.
wikip1 BTU = 1060 Joules. 1 kwh = 3400 BTUs = 3604000 J, 3.6¤6 1 gallon of gas = 12500 BTUs = 13250000 J, 1.3¤7 25mpg is 5000 BTUs / mile Serway p554. Joule is a better choice of units than BTUs
A material's resistance to being squished. It's the inverse of compressibility
and used, for example, in calculating the speed of sound in a medium.
speedOfWave = sqrt(B=Bulk Modulus=volumeCompressibility / densityOfMedium) looks wrong. SOON
ref'd in feynman, book 2, pg 19-3
wikip1 cal= 4.184 J, the energy needed to raise 1 gram water fm 15.5C to 16.5C, Serway p554. Serway p554 "the mechanical equivalent of heat" 1824. 1 Cal = 1 kCal = 1000 cal. // nutrition calorie. Cal (with the capital C). 1887 10¤7 ergs = 0.239 cal = kwh / 3.6¤6 // cal= kwh/3600000 x 4.184 0.239 cal = kwh/3600000 0.239 cal / 3600000 cal/kwh = 1 kWh 860400 cal = 1 kWh 1 cal = 4.184 * wh/3600 // wh/3600 = watt-second == Joule = 4.184 * watt-seconds marathoner burns 100 kCal per mile. human body can store 2000 kCal => old runners 'hit wall' at 20 miles. walking burns 1/8 kwh per mile. whpm=125 ! def cal2boilWater(gallons,tInit_F) : # derivation, code '''To boil 'gallons' of tInit_F (Farenheit) degree water requires''' delDegC = 117.7 - 5/9 * tInit_F gramsPerGallon = 3785 cal = gramsPerGallon * gallons * delDegC
Another view is: 1 amp * 1 sec (gives 1 Coulomb) generates 1 F (only in a 1 F cap (?). think not...)
The human body has a capacitance of about 150 pF (wikip on Plasma_globe).
Parallel plate capacitance: C = eSubR * e0 * A / d,
where eSubR is a 0->1 scale for e0, 'd' is the separation distance, 'A' is the area of the plates. I assume all SI units. e0 units are Farads/meter. // 8.85¤-12 F/m uF micro ¤-6 nF nano ¤-9 pF pico ¤-12 ?F femto ¤-15 no such capacitor value (?) supercapacitors Serway, vol 2, chap 26, page 723 discusses/diagrams parallel plate cap. PT1_Q82 tips for fast calcs of parallel and series caps. C1 || C2 (add like R's in series) = C1 + C2 C1 && C2 (add like R's in parallel) = 1 / (1/C1 + 1/C2) = C1 * C2 / C1 + C2 For > 2 parts: // eg 3c12 = c1 * c2 / (c1 + c2) thenc123 = c12 * c3 / (c12 + c3) dielectric, local notes wikip covers many related topics, eg 'stray cap' tuning cap, Legendre!
X(subC) = 1 / (ω C) XAM p93
energy stored is
ref21, p19: Capacitance,
Also the 'constant' is really freq dependent, ie. not constant.
Sum the reciprocals of all the caps. Then invert the sum to get final C.
Series of caps make a 'final C' lower than starting values.
Consider 4 10uF caps. Cfinal =
= 1 / (1/10 + 1/10 + 1/10 + 1/10)
= 1 / (4/10) = 10/4 = 2.5 uF
2 heat reservoirs,2 isothermal, 2 adiabatic French physicist Sadi Carnot, 1824 XAM p52, Serway p618 work done is area w/in PV lines. 1. isotherm Th. absorb heat, Vol++ P- 2. adiabatic expand. T,P fall, Vol+ P-- 3. Isotherm Tc. release heat. Vol-- P+ 4. adiabatic compress. P up, Vol- P++ Carnot cycleefficiency = [ (Q_{H} - Q_{C})/Q_{H} ] * 100 where Q_{H} is Heat In, Q_{C} is Heat Out, and W is Work provided.W = (Q_{H} - Q_{C}) wikip
PVC catapult, seen online. ?instructables? prjt 'cat45'
centripetal force on car tires in a turn is m v²/r Serway p140. XAM p17, p142, XAM_Q08
_mass_ center (not just spatial center)
Center of mass, center of gravity
Serway P174. TODO. don't understand last step.
charge on 1 proton or 1 electron is 1.602¤-19 C, where C is Coulomb
if P const, T,V proportional see Gas Laws
chord(θ) = radius * (2 sin(θ / 2) )
Period,T = 2π r / v uniform motion. Serway p85 See centripetal acceleration, α = v²/r // v is the vel of the tangent line at the edge
see isopropyl wikip
notes on making CO2 photosynthesis notes. local. CO2 entry in chemistry page baking_soda = Sodium bicarbonate, NaHCO3 baking_powder = baking soda + some stuff
have built a 3 stage unit from purchased kit parts. needs testing. Possibly useful for project eFields wikip
wrtn 'α'.
momentum = mv, always conserved. elastic KE also conserved. KE in each dim (x,y,z) conserved. "An elastic collision is an encounter between two bodies in which the total kinetic energy of the two bodies after the encounter is equal to their total kinetic energy before the encounter". wikip inelastic. KE not conserved. usually heat produced. often bodies coupled as resultA basketball-tennis ball collision was a part of PT1_Q24. So I googled 'collision basketball and tennis ball physics'. lots of pages on this.
basketball hits floor at 10mph, bounces upwards at 10 (ok! pretend!). It meets the little tennis ball. They collide at 20mph. Relative to the basketball, the tennis ball leaves the collision with an energy of 20mph plus its speed. So it rockets up at 30mph.
Ok, someone check all the momenta, KEs ... SOON
from rocket balls
k t A deltaT t=time,secs, A=area,sq cm, deltaT is in degrees C or K H = -------------- d_cm k is the Therm Conduc, a property of the mat'lXAM p44. See Law of Thermal Conductivity
conformal (map): angle preserving on a small scale.
entities which share some simple but special relationship: examples: - the other root of a quadratic - for a complex number a+bi, it's a-bi - for a point on a sphere, it's the oppositie point, joined by a line thru the center.
See uncertainty principle
See wikip
6.24150934¤18 charges per Coulomb; 1/1.602¤-19 = .624¤19 or 6.24¤18 _reciprocals_ 1 Amp = Coulomb/sec,1 Coulomb = 1 Amp-sec
1.602¤-19 C is a _quantum_ of charge.
TODO: buy! example: Sparkfun's LTC4150, $13 Sparkfun LTC4150 pdf I think the design is clever b/c the sense resistor is independent of the actual circuit - meaning it should work in a wide range of environments.
Coulomb's Law. Force (repulsive)F = (Ke/Kd) (Q1 Q2 / r²) ; Q's==charges, result N Newtons K_{e}¤9 or, more accurately, 8.988¤9 = 1 / (4π e0) ; Coulomb's Constant='electrostatic constant',K_{e}. K_{d} here is my term for the dielectric constant of the medium (==1 for vacuum, nearly 1 for air) 1784. chap24, p1, kindle loc 6288, ref09 # alternative view (?): wikip, vac perm
The angle of incidence where the exit angle becomes 90°. TIR, Total Internal Reflection, occurs for angles greater than or equal to the critical angle.PT1_Q19, graphic; PT2_Q46, text, eqnscritical angle = arcsin(n_{2} / n_{1}) , where n_{2} must < n_{1}; Example: rays rising into air (n_{2}=1.0) from water(n_{1}=1.333), the critical angle would be arcsin(1 / 1.333) = arcsin( 0.75 ) = 48.6 degrees Angles are measured wrt the 'vertical' (perpendicular to boundary) Viewed through Snell's Law, n_{1} sin(θ1) = n_{2} sin(θ2 == 90° )
The magnitude = r.len * F.len * sin(angle)
( usually written
The vector can be formed w/ this magnitude and the unit vector found w/ right hand rule
length of A χ B, denoted |A χ B|, gives the
(wiki) tip of middle finger to elbow.
cuneiform tablets 1 of the writing methods (hieroglyphics the other). clay tablets. Babylon. 2500 BC (? guesses...)
a vector operator that describes the
The curl operator will, for now, be ©. 180310
The direction of the curl is the axis of rotation, as determined by the right-hand rule, and the magnitude of the curl is the magnitude of rotation. If the vector field represents the flow velocity of a moving fluid, then the curl is the circulation density of the fluid. A vector field whose curl is zero is called irrotational. The curl is a form of differentiation for vector fields. The corresponding form of the fundamental theorem of calculus is Stokes' theorem, which relates the surface integral of the curl of a vector field to the line integral of the vector field around the boundary curve.
The alternative terminology rotor or rotational and alternative notations are often used.
Unlike the gradient and divergence, curl does not generalize as simply to other dimensions; some generalizations are possible, but only in three dimensions is the geometrically defined curl of a vector field again a vector field. This is a similar phenomenon as in the 3 dimensional cross product, and the connection is reflected in the notation Del Cross for the curl.
The name "curl" was first suggested by James Clerk Maxwell in 1871.
curl, wikip
vacuum energy, wikip wikip
The MOND theory proposed changes to the universal gravitation law. MOdified Newtonian Dynamics
dark matter, wikip
Dawes Limit comes down to the following calculation:
D is lens diameter in centimeters,
R is the resolving power, in arcseconds.
yes, these aren't SI units.
logarithmic measure of sound energy or electrical signal amplitude, referenced to some standard value. As in wiki article, these units are used for
field | 20 log10(F/F0) | Fld=10^(Lf/20db) * Fld0 |
power | 10x log10(ratio) | 10dB for 10x power ratio |
root-power |
paramagnetic
PT1_Q99
material which increases the capacitance of a cap by reducing the
internal E field by polarization. That is the dielectric makes a bit of
an opposing field thus reducing the base field. The dielectric's field
opposes that of the cap's plates.
The dielectric is said to be a bit of an insulator too.
"Opposes the field charges on the plate". PT1_Q73
A very short table of dielectric constants. see wikip for more.
vacuum | 1.0000 | _ | |
air | 1.0006 | _ | |
paraffin | 2.2 | rimstar | only attempt gave ~1.0 |
min oil | 2.3 | wikip | _ |
pure water | ~ 80. | my 'distilled' gave 2.8 ! |
A dielectric (or dielectric material) is an electrical insulator that can be polarized by an applied electric field. When a dielectric is placed in an electric field, electric charges do not flow through the material as they do in an electrical conductor but only slightly shift from their average equilibrium positions causing dielectric polarization. Because of dielectric polarization, positive charges are displaced in the direction of the field and negative charges shift in the opposite direction. This creates an internal electric field that reduces the overall field within the dielectric itself. If a dielectric is composed of weakly bonded molecules, those molecules not only become polarized, but also reorient so that their symmetry axes align to the field.
wikip was the main ref vv_permittivity has a note about this. electric field has related material
d sin θ = m.int lambda θ Max(m) = arcsin(m.int lambda / d - sin(incidentAngle) order 'm' (m 0 not interesting...) , d is distance between grating rulings. A spot lights up if all the incoming rays constuctively 'interfere' with each other. That occurs if the distances travelled for all the rays is a multiple of the incoming wavelength. wikip khan
(dimensional analysis is also called 'factor-label' or 'unit-factor'. ref schaum's chem book kindle) When a conversion is 'affine' like Farenheit-to-Celsius, a function can be provided. see R factor mi mi 3600 s 1 mi -- = -- x ---- -- x ---- -- hr s 1 hr 1621 m note that such units terms start w/ a simple expression (equiv to 1 !) 1 hr = 3600 sec and can form 2 units terms. 1st divide both sides by 3600 ; next divide both by 1 1 hr 3600 s ------ = 1 ------ = 1 3600 s 1 hr AND 'you can alway multiply anything (any term etc) by 1' justification... wikip the use of '-' for a multiplication symbol. supposed to be a flying period.
0.7854 D² = circle area. 0.7854 L * W = ellipse area. (π/4) 0.5236 D³ = sphere volume (π/6) area of a sphere = 4 π r² cross product gives area of parallelogram and/or triangle.
unit "per meter", reciprocal of focal length in meters. A unit of measurement of the optical power of a lens or curved mirror. For example, a 3-diopter lens brings parallel rays of light to focus at 1/3 metre. A flat window has an optical power of zero diopters, and does not converge or diverge light. Eye glasses at 1.25 diopters focus at 4/5 meter = 31.5 inches 1.75 diopters focus at 22.5 inches
PT2_Q68: -ve N-region, +ve P-region, conductor, insulator, resistance SOON
Notice that there is a very small margin between the resistivity of the conductors such as silver and gold, compared to a much larger margin for the resistivity of the insulators between glass and quartz.
Note also that the resistivity of all materials at any one time also depends upon their ambient temperature because metals are also good conductors of heat.
Silicon's outermost shell could contain 8 electrons but neutral Si has 4. This ?promotes its lattice structure and provides electrons under certain circumstances. The P and N doping (1 per 10^7) shifts the diode material's tendencies (+/-).
Some thing or volume has an opposing difference, + vs -, either electric or magnetic. Hence, di - pole. Important to the dipole concept is its "moment", a vector quantity representing the strength and spatial distribution.
The dipole doesn't have to be a magnet or a blob of electric charge. It can be a magnetic area created by a current flowing thru a loop.
Polar compounds like hydrogen fluoride (HF), can have a significant dipole moment.
From an article at northwestern.edu:
"A
b² - 4ac is 0 iff eqn has 1 real root > 0 iff eqn has 2 real roots < 0 if eqn has imaginary root The wiki article mentions polynomials of higher than degree 2 and their discriminants. quadratic discusses quadratic eqn, factoring wikip
2. mechanical waves (not light) spread over time. Serway p450, btm.
(A pretty but not so useful eqn if you're actually trying to find AngleOut as a function of AngleIn // and the indices of refraction...)
SOON. relate to Snell's so I can remember it.
an offset current added to Maxwell to
Ampere's eqn XAM p81
See Maxwells_equations, very last equation box.
a vector operator that measures the magnitude of a vector field's source or sink at a given point, in terms of a signed scalar. More technically, the divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point.
For example, consider air as it is heated or cooled. The relevant vector field for this example is the velocity of the moving air at a point. If air is heated in a region it will expand in all directions such that the velocity field points outward from that region. Therefore the divergence of the velocity field in that region would have a positive value, as the region is a source. If the air cools and contracts, the divergence is negative and the region is called a sink.
Divergence, wikipf' = f * ( v+vo / (v-vs) ) where: v = speed of wave through air vo = observer speed, vs = source speed. WITH RESPECT TO MEDIUM v = 1533m/s, vo=9m/s, vs=8m/s. f' = 1415 Hz rules for choosing signs examples/dopplerMusic.py explores speeds, speed needed to shift music notes XAM p69, XAM p149,XAM_Q35 Serway p496-499,p483 PT1_Q29: 2dufus' ea w/ freq gen. duf1 walks to duf2. what hz heard by duf1 (all such 'peaks') fu/v where v is speed of sound; u is walking speed, f is freq of emitted sound A hears the sound of his own source, which frequency is f. He also hears the sound of the moving source carried by B. The apparent frequency of the source with B is f(1+u/v). The beat frequency therefore is f(1+u/v)-f = fu/v. PT1_Q47: Fr = Fs * c / (c - 2u) where u is meteor's speed. Fs 10Ghz. Fr 12.5 SOON review
operation on vectors, aka 'scalar product'. 2 methods: a º b = Sum (a[i] * b[i]) a º b = ||a|| ||b|| cos(θ) vector op An example of using the dot product to construct vector components can be found in the class functions in fieldDraw.py wikip
Tests often ask for the wavelength.
(show: slanted lines are each Integer * wavelength. TODO)
PT1_Q04 test question. PT1_Q48 ? Young's experiment (white light(?) in, colored peaks(?)) wave-particle duality. wavelength = xd/(nL) // more readable as "x/n d/L" b/cwikipd/L is slope x dist from central pk, d dist between slits, n order of the fringe. L dist, slits to screen sciCalcs PT1_Q04, PT1_Q50 PT3_Q91 is really about gratings
e is the base of the natural log system, 'ln'.
The letter 'e' was chosen b/c it's the 1st letter of Euler !
amazing properties shown at left! oooh !
book "Why E=MC²" Maxwell's eqns used measurements of 'E' and 'B' fields (from Faraday(?)) in producing a wave propagation velocity which happens to be C !
earth: mass =6¤24 kg , radius = 6.371¤6 m (6 3/8 ¤6 ),density 5.5 * water Serway p5. eccentricity of orbit: 0.017, Serway p368 // Halley's Comet 0.97 76 y period problem: what angle/day at perihelion,aphelion at what calendar days. (earth: jan 3 is roughly perihelion, july 3-4 aphelion) earth's mag field 0.25 - 0.65 gauss (wikip). ~0.49 Gauss in WC, 10000Gauss/Tesla North magnetic pole location is 78.5N, 103.4W. moving towards siberia ~35 miles/year ! The GEOmagnetic N pole is where the large dipole field seems to locate the mag N pole. 2017: Lat. 80.5°N, 80.5°S; Long. 72.8°W, 107.2°E wikip. GEO moves v slowly.
ellipse x²/a² + y²/b² = r²,For the variability of earth's orbit caused by Jupiter, see uaf.edu.ecc = sqrt(1 - b²/a²) . 0 < ecc < 1. where a=semi-major axis, b=semi-minor. axes are center to edge ecc * semi-major axis = linear eccentricity == distance fm foci to center (wikip) ellipse, wikip for circle x²+y²=r², e is 0, equiv to ellipse w/ a=b Other ecc's are better defined by the end-to-end cones (conic sections). parabola e is 1; hyperbola e > 1. Eccentricity, wikip Orbital eccentricities: 0.0167 Earth 0.0549 moon 0.0934 Mars. eccentric enuf to help Kepler. 0.21 Mercury , the largest of the 8 planets. 0.25 Pluto. actually a little less than .25 0.97 Halleys Comet
I'm too slow... etc calc power dissipation, DC:P = I² R A/C values. look for website which summarizes. SOON PT1_Q26 ++.
V(t) = NAB ω sin(ω t), N = #turns, A=coil area, B= mag field strength, V == induced voltage in an electric generator. Serway vol2, pg 881 The ω next to the NAB comes from the chain rule while differentiating -cos(ω t) XAM p85 has similar generator equation. text not as helpful. PT1_Q78
" ~~~ watch ~~~ the ~~~ units, ~~~ Luke". Obiwan... F = k_{e} q_{1} q_{2} / r² # units: N, Newtons, Coulomb's Law The electric field, E, a vector field E = k_{e} SUM ( q_{i} / r_{i}² ); # units: N/C, Newtons/Coulomb Knowing 'E', the force for a particular charge can be calculated as F = qE # units: N, Newtons, again Note that N/C == V/m == Volts/meter == kg m / (s³ * A) V, volts is surprisingly different than E above. V is a scalar field with a1/r calc .
It acts like gravitational PE in that all that seems to matter is distance above a value chosen to be 0 ("ground"). Some material seemed to ignore (even) the sign, treating -v the same as +v.
The 1/r aspect is visible in the units of V: note the 'm; in N•m/C while E's units are just N/C. Nominally V's units are J/C which equals N•m/C.
J/C comes from W=VQ or V=W/Q
Also, it's worthwhile to fold in the dielectric constant of the medium so the larger process is visible. I'm using K_{d} below to represent a dielectric constant.
Replace k_{e} with k_{e}/K_{d}
Lastly, the equations can be written in a very readable shorthand F = k_{e} q_{1} q_{2} / r² # or F = k_{e}/K_{d} q_{1} q_{2} / r² # with a dielectric, K_{d} Notes, links to related info: 'van de graffs work best in low humidity' implies conductivity of air increases w/ humidity. electric field project, electric field sciCalcs electric field, wikip plasma, gsci Electromagnetism, wikip
TODO
"point in the direction that a positive test charge would accelerate if placed upon the line." the physics classroom
Atmospheric_electricity, wikip St Elmo's Fire requires 1k to 30kv per cm. lower end of V range works w/ pointy ends. N&sub2; glows blue
ping pong balls circling bowl Recall that electric fields stronger at pointy pieces. Arc, St Elmo's Fire, corona. Radius the corners. Youtube 2inch balls are styrofoam? Aaron Fay, Youtube "3 ways to charge things 1. friction: rub balloon against shirt. electrons on balloon won't migrate (not conductive). e- to the balloon, shirt less e- 2. charge by contact: van de graff. little sparks. or put hand on globe. He has a metal globe on a stick, apparently connected to earth ground. 'discharge wand' 3. induction: fine pieces of conductive metal hang inside how to make an electroscope in an erlenmyer flask: Youtube erlenmyer flask has plate on top. vinyl rub w/ hands charges the vinyl." Crash Course Phys #25, PBS Digital Studios, Youtube 2 pieces scotchtape ripped off table will repel each other. both are neg then stick 1 tape to table and the 2nd atop the 1st. then rip off top off btm tape, then lift btm off table. now they attract glass rod, rub w/ cloth; cloth becomes neg; glass + // charge by friction fur against amber. ancient greeks. amber would pull hair and feathers touching 2 rods equalizes the charge between them. charge by contact. // hand doesn't count ? if the 2nd rod doesn't touch the 1st but is close enuf to feel the field, its charges will be redistributed such that the end nearer the fully charged rod will have an opposite charge. It is "polarized". charge by induction charges w/o contact. 'grounding' a charged rod will leak e- and leave rod + (?) measuring the 'q', charge. unit is -1.602e-19 Coulombs // => 6.24e18 e- per C F = Ke q1 q2 / r² ; Ke = 9¤9 N m²/C² for air
eFlux. units V * m Dot product of the electric field and the normal vector to a surface (an area).
conserved. Is a scalar thus simpler than dealing with the field all the time. Serway, vol2, p692
EM_radiation, wikip has cool, moving image of changing E and B fields in light. EMwave3Dfromside.gif, wikip
Youtube "Most good electrometers have input impedance's of 200 teraohms ( = 2¤14 Ω) The average electronic VOM has 10 megohms ( = 1¤7 Ω)" the project
mass 9.11¤^{-31} kg proton mass is 1.67¤-27
1 eV = 1.602176620¤-19 J (Joules) = E (Joules) gained/lost by 1 electron moving across e-field of 1 volt. = 1 J/C sqrt(2 h a / µ0 e0) where: h is planck's constant a is the fine structure constant (from spectroscopy?) wikip eV: Mev (== J = Energy) is used as mass b/c E = M C² so Mev/C² is really the mass. It's inaccurate to say a mass is '10 MeV'; it's "10 Mev/C²" (kg). SOON. check units 1 eV/c2 is 1.783¤-36 kg so1 Mev is 1.793¤-30 kg ~= 2 electrons eV: MeV momentum unit when the true, measured energy, in MeV is divided by C, a speed. That changes the scale but the units are those of momentum. eV is determined experimentally.
"...a human being is represented as a capacitor of 100 picofarads (100e^{-12}) F, charged to a voltage of 4000 to 35000 volts. When touching an object this energy is discharged in less than a microsecond. While the total energy is small, on the order of millijoules..."
wikip, static electricityPE = (q1 q2)/r Ref "Physics" plastic "std demo of es is prob 83 in CSET Physics Exam Guide" = plastic comb + dry hair = lg pos chg. Comb brought close to sml bit of uncharged paper which is initially lifted to the comb. What happens next? PT1_Q39: stationary eDipole in a larger eField feels torque, no impetus to move. PT2_Q83: just wanted calc. 2 protons, 3um apart.
Elements. compendium of geometry. gathered, refined by Euclid. ref26. Have his book somewhere (tablet(?)). Impressive proof of the distributive property.SOON.ref?
The shape of an ellipse is determined by the ratio of minor to major. The size of an ellipse is controlled by scaling 'a' 'b', letting other params be 'whatever'.
ecc: eccentricity = sqrt(1 - (minor/major)² ).
ecc 0 is a circle while near 1 is a skinny ellipse.
foci, locating:
The semi-major and semi-minor axis lengths are measured from the Origin, the center of the ellipse.
"linear eccentricity" == Origin to focus distance
As I see it, there are 2 approaches to scaling/defining an ellipse: - 'math' considers the major-to-minor axis ratio. - 'orbit' starts with eccentricity and derives the ratio of 'a' and 'b'.
This ellipse shows an orbit in which the aphelion is 3.85 times the perihelion; the same number but totally different meaning. If Rb, the perihelion, is scaled to 1, the aphelion becomes 3.85. The major axis is now 4.85 . If we knew the minor axis, we'd have the 'a', 'b' coefficients to generate the ellipse (except for 'r', the scale factor).
The second focus will be Rb shy of the top of the figure. The semi-minor axis, 'smi', can be found from the triangle shown in the next section.
From the top focus to the bottom
of the orbit is 2f + Rb. The bottom focal point contributes another distance
Rb to the overall sum, now 2f + 2Rb. The distance from the 2 foci to point
'S', 2h, needs to equal the just calculated length or 2h = 2f + 2Rb.
smi = sqrt(h²) - f²) # divided by 2, substituted 'smi', cancelled f and -f,...
= sqrt(Rb²) + 2f * Rb)
THIS DIDNT WORK! (WHEN TESTED). "ON HOLD" TIL TEST DONE.
click 'Explicit', pull down, choose 'implicit', then click 'add' fill in equation F(). eg: x² + y²/14.82 G() should be 6.75 // the right side of the eqn click OK ... click blue dot to edit equation. something at the bottom suggests you can save the image as an .svg file
The sum of the power you've expended to get something done (something moved, something lifted etc) gallon of gas=33433.9 watt-hours //SOON: these numbers don't all agree... gallon of gasoline contains the energy of 130 megaJoules, or 36.1 kwh Energy = Force x Distance // ref/link: FxDequalsE.html
amt of heat (to do something, like melt ice) XAM p43 see Hess's law. Wikip: "enthalpy is a meas of energy in a thermodynamic system. It's equal to the internal energy + (pressure * volume)". Internal energy is the energy needed to create the system. Units are Joules. Typical symbol 'H'. for total enthapy.
XAM p40-42, units are J/K !
SOON. excerpt fm wikip. Serway p110. equilibrium
solving chem output of a process using the quadratic equation. XAM p117-118
An object in free-fall is in actuality inertial, but as it approaches the planetary object the time scale stretches at an accelerated rate, giving the appearance that it is accelerating towards the planetary object when, in fact, the falling body really isn't accelerating at all.
Equivalence_principle, wikip
The V where an object's KE = gravitational PE. G universal Grav .667¤-10 M mass of Earth 6e24 kg r dist fm planet's center. 6.3781¤6 m (wikip) Earth's value is 11.186 km/s wikip
heat loss, radioactive decay, RC circuit decay are examples of exponential decay, 'e to the minus x' stuff. Often lower case 't' is time, upper case 'T' is temperature. heat loss example, text file
of a polynomial my Algebra 2 book, chapter 5 (?) quadratic discusses quadratic eqn, other poly topics The printed copy of gSci includes a page 'Completing the Square'.
One farad is defined as the capacitance across which, when charged with one coulomb, there is a potential difference of one volt. Equally, one farad can be described as the capacitance which stores a one-coulomb charge across a potential difference of one volt.
see capacitance for modifiers like micro, nano etc'F' = C/V, charge per volt (=J/V² = N•m/V²) (see wikip)
The online documentation, mostly wikip, describes a 'cup' as a part of an
in-vacuum detector system.
wikip
EMF = volts = -N dmFlux / dt where N is number of loops. neg sign due to Lenz, XAM p82 Faraday's Law
ref03: "F's law treats electric fields as product of moving magnets".
see Maxwells_equations, local
I wanna build this! (_metal_ ring needed(?) amplifies signal(?))
FBD, Real World Physics, BEST XAM p21,22 has some simple but interesting examples choose coordinate system, inertial. polar or rectangular. May need to reassess mid analysis. Issue. 2D? 3D? Define a sign convention for your diagrams. replace contact locations w/ Force and/or Moment vectors. If a magnitude isn't known, assign it a direction ?and a variable name? Account for constraints which restrict motion replace body forces (eg gravity) with F's thru CM simplify. eg: assume constant friction... draw FBDs for each body. When drawing the forces acting on pairs of bodies in contact with each other, apply Newton's Third Law. may need concept of a state machine to handle changes eg: model catapult to point object is launched. separate state for decel. FBD Serway p108,118. // probably influenced by traffic light problem draw only those force that act of the objects being isolated. Draw ALL forces, including field forces, such as Grav The forces are vectors, the (x,y) components will be in the simultaneous eqns. (be careful with signs...) The X equation should equal 0 The Y equation should equal the load Reduce the X equation to reveal the relation between the 2 tensions. substitute into the Y equation. pg 109 Serway's "Physics for Scientists and Engineers" Neglect friction (usually).. If the object is not being accelerated, then all the forces must sum to 0. see 'Atwood' as an example Physics book authored by Serway explained it well, have exercises.FBD, Atwood, tensions
a_{1} = 30; # left most angle wrt to horiz. 0-90 degrees a_{2} = 45; # right most angle. T_{3} = 90; # light's weight, Newtons) T_{3}.x = T_{2} * cos(a_{2}) + T_{1} * cos(a_{1}) # horiz force must = 0. T_{3}.y = T_{2} * sin(a_{2}) + T_{1} * sin(a_{1}) # to support light T_{2}overT_{1} = cos(a_{2}) / cos(a_{1}) # ratio of horiz pulls T_{2} = T_{3} / (sin(a_{2}) + T_{2}overT_{1} * sin(a_{1})) T_{1} = T_{2} * T_{1}overT_{2} CAUTION: ez to omit the T_{2}overT_{1} element in a test.
Variations ask 'at what angle does block start sliding'
wikip, Feynman_diagram simple wikip see also QED, local notes
centrifugal, corolis. Serway p145. wikip, Fictitious_force
wiki, Field
flywheel hoop stress = density * r2 * ω2 //cite? think this is given in I moment list. SOON 1st development. Theophilus Presbyter 1070-1125AD
see Newtons_laws Force = Mass x Acceleration; feynman defines as chg in momentum, vol 1 sect 15+, dMomentum / dT wikip, Force
Making the orbit of a nearby test particle precess (as in Mercury's orbit?).
Light, traveling in the direction of rotation of the object, will move
past the massive object faster than light moving against the rotation
frame dragging, wikip
stanford spacetime search frame-dragging
F (Newtons) = -Us * NormalForce_Newtons. F always works against motion so it's never larger than the motive force. It'll never, on its own, create a motion (opposing the force in question). CAREFUL; don't blindly take the force and subtract it.
The friction coef between 2 materials depends on the materials themselves, possibly modified by moisture. The speed of the objects also affects the coefficient. Normal treatment simplifies all this by declaring 2 'coefficients' of friction, Us (static, no motion) and Uk (kinetic, moving). These coefficients are mostly determined by the materials. Uk is always smaller than Us.
Truly Fn = m G cos(θ) + 'finger force' and the resultant Fn times the appropriate
coefficient of friction determines (completely) the
friction force shown as 'F'; that is:
F = Fn * Us // in the common, static case.
The down ramp acceleration uses Fd - F.
Serway p109 re names Us Uk etc. problems, sciCalcs wikip on Friction. See 'Dry friction'
1200000 / 3600 = 333 miles/sec. # == 536000 m/sec gamma = 1 / (sqrt(1 - (333/186000)²) ... = 1 / (0.99999839) = 1.0000016 => not a signif fraction of C => not "relativistic"
Derivation: PV = nRT starting place P = nRT/V P/RT = n/V ; after this, mult by mole wt, M, of the gas PM/RT = nM/V = density
The following 3 laws seem related. Each experimenter held one variable constant and commented on the connections between the other two. To recall which is which, note the T P V letters in the front of the following; they are the items held constant. Use the ideal gas law to figure out how the other 2 parameters varied.
T Boyle's Law: 1662. P1V1 = P2V2 XAM p46-p47; "ifT const , P,V inverses"Serway p542 above section P Charles Law,"Law of volumes": 1801. "ifP const , V,T proportional" XAM p47, Serway p542, (wk was 1780s). Charles Law, wikip V Gay-Lussac's Law,'Pressure Law': 1808. "ifV const , P,T proportional" XAM p47; Serway p542 Gay-Lussac Law, wikip Combined Gaw Law: Volume propor to T/P, often expressed as P1V1/T1 = P2V2/T2 XAM p47 Ideal Gas Law:PV = nRT XAM p47, 'R': see ideal gas constant. gas density:d = nM/V = PM/RT ( g/mol (?)) where M is molecular wt equation of state: Serway p542. p564 'state variables'. start at thermal equilibrium. thermodynamic variables: 'P' 'V' 'T' volume: for 1 mole any gas, 1 atm, 0C, the volume will be 22.414 'L' (liters). average KE of gas molecules: proportional to abs temperature XAM p45 Work,W = P deltaV , XAM p54, units L * atm = (Liters=0.001 m³) (atm=N/m²) = N•m = J examples integrate V.
Gauss's Law E "eFlux leaving a volume proportional to charge inside".
Maxwell, wikip
ref03: "electric field lines leave a charge and enter on neg end".
PT1_Q30 (no img): electric eFlux eqn: E A cos(θ)
Gauss's Law M "total mFlux thru closed surface is zero". implies no monopoles
'Pressure Law': Gas Laws
in / out 52/13 for early Bike Speed problem gearRatioOverall = rpmWheel(evDesiredMph,diaInches) / motorBestRpm
There are interesting lectures on youtube, by Leonard Susskin (?), a Stanford prof. (171014)
Used by Euclid and the other ancient Greeks. The Euclid book on the Kindle (2016) has the book in Greek and English, side by side. Book II "Propositions" (item 2?) shows the distributive law done in areas (it's clever). I believe the early stuff looks so bad b/c: - their number system was base-60 and not easy to read - they had no good way to represent fractions. - they really didn't have a clear way of expressing an expression. wikip, Geometric_algebra
math term for a series of numbers, each made by multiplying the predecessor by a 'common ratio'. (fgh calls the effect 'exponential').
A vector-valued version of derivative function.
The symbol is a 'nabla', an upside down triangle, widest at the top; it is often called 'del'.
see wikip
Newton's law of universal gravitation: m1 * m2 F = G * -------------- where G is 2/3 * 10¤-10 N r²
At center of earth ? YahooAnswers says best answer is Zero. EXCEPT the zero answer is ignoring the moon's effect. The barycenter is 1050 miles below the surface and, obviously, it moves.
earthole.html models a 'flight' through the earth, assuming no drag from air (and temperature etc). It ignores that the barycenter of the earth-moon system is 1050 miles below surface. And that barycenter is moving at an approx average of 12.8 degrees per day. Moreover the moon's orbit moves around so much that the actual path of the barycenter moves a lot.
Green's Theorem is mostly used to solve two-dimensional flow integrals, stating that the sum of fluid outflows at any point inside a volume is equal to the total outflow summed about an enclosing area. In plane geometry, and in particular, area surveying, Green's theorem can be used to determine the area and centroid of plane figures solely by integrating over the perimeter. (planimeter!)
Green's essay, 1828 in pub/doc/ George Green
(over my head. 171004) layman terms, quora "conservation of information," or "conservation of phase space volume." tries to describe (?) all the states (activities) within a certain config. tries to treat all such with the same approach. Connects to Langrangian. lagrange, quora They (lagrangian and hamiltonian) are mathematically equivalent, in the sense that the solution to the problem when formulated in one of Hamiltonian or Lagrangian mechanics is always the same as the solution when formulated in the other. Mathematically, the two formulations are dual to each other in the sense that each is the Legendre Transform of the other. This statement can often be lost on people in the context of classical physics as the Legendre Transform takes on a particularly trivial form for the kinds of problems that come up in classical mechanics, and so it often looks like you aren't really doing much of anything. ...
see SHM,'Simple Harmonic Motion'
(mostly music...) The harmonics of a note (or frequency appearing in an engineering situation) will be the integer multiples of the fundamental frequency. Don't confuse this with the power of 2 progression of octaves.
procs2study. fundamental freq* Serway p510 etc.
Energy (heat) req'd to raise a _sample_ 1 degree C Not about energy per unit mass (see specific heat) But the per mole aspect makes this pretty useful, given observations on XAM p43.
The word 'capacity' is interesting b/c it also measures how long it takes some material to transfer its energy enuf that it loses temp. Water's high capacity keeps the bay area warm in winter.
_molar_ heat capacity is just the heat capacity for a mole of a substance. commonly used. eg: molar heat capacity = 28J/mol-K, XAM p42-43 These capacity values depend on phase. Solid H Cap isnt same as Molten H Cap
"energy transfer to cause a chg in Temperature" Serway p554
In ads, I see units of uH, not H. Haven't seen mH even when value is 1000 uH.
Henry gets around !
PT1_Q09 tests 'unit of self-inductance'. It's just the good ol' Henry.
law of constant heat summation. The total enthalpy change during the complete course of a chemical reaction is the same whether the reaction is made in one step or in several steps. PT1_Q74 wikip
1678. (F Newtons) = -(k N/m) * (x m)
F is called the 'restoring force'
notes on springs, constants
horsepower: 550lb lifted 1 ft in 1 sec = 550ft-lb/sec = 550 lb, ft/sec, 745.7 W "550 lbs 1ft/sec". a 'draft horse' pull is 800N. horsepower, wikip HP(force_lbs,v_mph) = force_lbs x v_mph / 375 //brant pg 152 top (brant==electric car book(?)) // "it takes 1 HP to move 37.5 lbs at 10mph" Brant p152 // i think this really says '1 HP pushes a 37.5 force at 10mph' (?) HP(torque_ft_lbs,rpm) = torque_ft_lbs x rpm / 5252
ok, ok, so it's not _constant_... "Hubble Parameter"
73.5 km/s/Mpc is the most recent value, published 180222. has changed 50 times(?).
Mpc is 'mega parsec' = 3.26 light years.
wikip
"each portion of a wave front acts as a source of new waves"
applies to atmos too. hydrostatic pressure, P = densityRho * g * h XAM p4
Hyperbola is y²/a² - x²/b² = 1 orbit when v greater than escape velocity hyperbolic functions: sinh etc wikip sinh(1) = 1.175; sinh(2) = 3.626 TODO: calculator sequence... cosh(1) = 1.543; cosh(2) = 3.762 tried to bend the hyperbola eqn into form seen in spacetime interval y2/a2 - x2/b2 = 1 ; or any constant ( a2 ) or sqrt( a2 - --- x2) ( b2 ) ( x2 ) or a * sqrt( 1 - --- ) ( b2 )
See animation, wikip. It shows relationship between circular values (sin,cos) and hyperbolic (sinh,cosh)
Note equation similarity to spacetime interval metric, Minkowski space.
ideal gas constant, 'R' = 8.314J/(K•mol) . ?? IS "molar gas constant" ??TODO ideal gas constant aka "Universal Gas Constant", "molar gas constant" XAM p47, Serway p543 0.082 L - atm # Liter 8.314 Pa - m³/mol-K Molar Gas Constant "as P approaches 0, PV/nT approaches R for all gases". Serway p543 If you google Ideal gas law. That will tell you that PV=nRT where P is pressure, V is volume, n is number of moles, R is the gas constant and T is the temperature. All units in the SI-system. You can rewrite it to PV=m/M*RT. Where m is mass and M is the mole mass. Calculate how much a given volume weighs at the ambient condition. Normal values for P is 1.013 KPa and R=8.314 J/(K*mol). Next, estimate how hot the air can be (this could be quite tricky) and then calculate the weight of that air. The difference in mass should tell you how much lift there is. wikipedia
impedance amplitude
F deltaT = (F=(m (a=dv/dt)) )*dT = d(m * v) Serway p232. impulse Since mV is momentum, m * deltaV must be the change in momentum. Impulse is a vector & is denoted by 'J' (but that isn't Joule!). // F = m a => 'N' = 'kg m/s2'; F * t => 'N s' = 'kg m/s' = 'm v' = momentum (but J = kg m2/s2 = energy) Impulse-Momentum Theorem (Serway p232) states that the impulse acting on any system changes the momentum of the entire system (depends on the scope of 'system'). impulse momentum theorem, wikip phys classroom. treats conservation of Mom too
L = (µ0 K N² Area) / len_m where: L inductance in henrys µ0 is the permeability of free space, 4 π ¤-7 henrys/meter K is the 'Nagaoka coef' which is about 1 when coil length >> diameter. N is the number of turns Area is cross section of coil in square meters L is theratio of the voltage to dI/dt , the rate of change of current, # hmm: NAB in electric power, local, SOON
No way (I know) to keep the mag field when detaching the inductor from current flow. Spark! (?chg thru R. drain thru R) "decays" (basically) instantly.
L has units of henrys (H). Inductors have values that typically range from 1 uH (¤-6 H) to 1 H. Many inductors have a magnetic core made of iron or ferrite inside the coil, which serves to increase the magnetic field and thus the inductance.
Inductance of the air core (above) can be magnified greatly with a ferrite core (permeable core). The core, however, can _saturate_ in which case the field partly 'escapes' and the effective L is reduced.
XL = ω L = AC angular freq L = 2π * freq * L XAM p93
energy stored is ½ L I², L is the inductance #of turns is in embedded in L, inductance (just above) Test equipment, commercial units: 2 each of { 1uH, 10uH, 100uH, 470uH }
resistance to momentum chg. reqs force. XAM p1
things so small that there is no way to measure them. The insight with exploiting infinitesimals was that entities could still retain certain specific properties, such as angle or slope, even though these entities were quantitatively small. Archimedes used what eventually came to be known as the method of indivisibles in his work "The Method of Mechanical Theorems" to find areas of regions and volumes of solids. Johannes Kepler, area calc of a circle, representing it as an infinite-sided polygon. 1670 by either Nicolaus Mercator or Gottfried Wilhelm Leibniz. wikip
units="ft² degF hours / BTU" Serway p574 DOW claims XPS styrofoam has an R value of "five per inch". The SI equiv might be: (?) //Note dimensional analysis problem w/ F -> C ft² degF hour m² degC(degF) 3600s BTU R = --------------------- = ------- * ---------------- * ----- * -------- BTU 3.3ft² 1 hour 1055J There are 2 ways of defining R, SI and 'whatever', (one is 5.68 times the other) see wikip, R-value
fill in common integrals. need for test SOON. IndefInt(1/r)(dr)=ln(r) XAM p208 single-page-integral-table, also printed wikip, antiderivative
example ref'd in Feynman, bk 2, pg 19-5
spin or vibes yes, heat no. Serway p554, SEE XAM p147 motions wrt vol's ctr
Feynman, Book 2, has a chapter "Electricity in the Atmosphere". 10 pA / sq meter, pos charges falling towards negative earth. a video talked of a 120' wire driving a "corona motor"wikip
determinant of jacobian matrix jacobian matrix: partial derivatives
there's an image in pub/doc. used by small electrometer prjt. think the printed note on that is in the box "library". 2n3819(?) mouser shows many. other than getting N channel, dunno what the other attributes are...
1 N over 1 m gives 1 J. # Time not involved. ref: Serway p166. joule: N•m = Kg m²/s² = Kg v² = Pa - meters³ = Watt-sec = cal/4.186; Joule's Law: P = VI, volts * amps, XAM p87 (=I² R = V²/R) "(ability to do) work" (wiki) 'work done. = newton-meter' = 1 watt-second // Joule(f,dist) // uses 1 force_lb = 4.448 N bingo! 1 N = .2248 lbs of force Joules(force_lbs, miles) = = (force_lbs * 4.448) x (miles x 1609 m/mile) = (N) x ( meters ) // force times distance. == force_lbs x miles x (1609/4.448=7157) Joules(nCalories) = 4.185 x nCalories // phys cals. not kCal (nutrition) Joules * 0.2389 = nCalories // 1 / 4.185 = 0.2389
The following 3 (local) images should show parts of the proof of Kepler's second law. From relativitycalculator.com
Law 2 derives from the conservation of Angular Momentum. An interesting, related calculation, from XAM p35, compares speeds at perasis against the speed of apoasis: ω_{a} r_{a}² = ω_{b} r_{b}² (// and ω == v/r) (v_{a}/r_{a}) r_{a}² = (v_{b}/r_{b}) r²implication: if ANY 2 planets have the same constant binding their period and orbit area, then all the planets around that star share the same constant, meaning it's a property of the star's mass !v_{a} r_{a} = v_{b} r_{b} # wow! valuable, useful v_{a}/v_{b} = r_{b}/r_{a} or, also valuable, v_{b} = v_{a}*r_{a} / r_{b} Law 3, rearranged algebraically, makes an interesting statement about _all_ the planets (and comets etc) orbiting one star (or moons around a planet): (t1/t2)² = (a1/a2)³ t1²/t2² = a1³/a2² expand t1²/a1³ = t2²/a2³ rearranged
The bottom equation is rearranged to solve for M, the mass holding the planets in
their particular orbits. By measuring 'r' and 'T' for an exoplanet, the mass of the star can
be calculated. See sciCalcs.html#ps_orbits
An elastic collision conserves both KE and momentum. (ref: wiki momentum) In cases where an stationary object is about to fall, you can often calc KE directly from(KE = ½ mv²) = (mgh = PE)
Kinetic_energy, wikip Serway P174. '1/2' fm integration? W = integral of F dx KE rotational= ½ I ω2 See collision entry above.
Kirchoff's 1st Law. currents at any node must sum to 0.
XAM p88,91
Kirchoff's Circuit Laws, wikip
sum of voltages around a loop = 0
Kirchoff's 2nd Law: XAM p88,91
Kirchoff's Circuit Laws, wikip
names Varuna, Ixion, Quaoar, UP313 bigger than pluto
'Kilo-Watt Hour' is electrical
cost of electric energy. $0.085 per kwh (quote from tech writer on web. US average. 2006/7?) $0.10 Ed Ring used this value in 2005. might have been a purposefully high approximation. $0.12 / kwh: current cost of electricity in Calif (?) 1 gallon of gasoline contains the energy of 130 megaJoules, or 36.1 kwh.
Lagrangian, wikip Hamilton, wikip
"The French Newton", 1749-1827 wiki. on the person Laplacian differential operator Laplace transform, like fourier transform. Laplace's_equation, 'potential theory', second-order partial differential equation
Light Ampliflied Stimulated Emission of Radiation predicted by Einstein. photons clone themselves. see "Stimulated and spontaneous emission" section of Photon, wikip
("hidden heat") energy needed (or released) per J/mass plus sign if E released. latent heat of fusion, synonym 'enthalpy' L.ice(T) =(2834.1 - 0.29T - 0.004T2) J/g Taylor_series latent heat of vaporization. "condensation'. L.water(T)=2500.8 - 2.36T + 0.0016T2 - 0.00006T3) J/g (wikip) pls see specific heat, local python examples/hotAirBalloon1.py had to model the latent heat of vaporization (steam energy) (as of 180416, examples/hotAirBalloon2.py doesnt wk) Serway p560. and wikip
P=k A abs(dT/dx), P power A area cross section, dx is thickness, dt/dx is gradient. matl W/(meter . C) SOON check units k thermal conductivity for matl: ON THE TEST? REFs! glass 0.8 rubber 0.2 water 0.6 wood 0.08 air 0.0234 pls see Conduction, Thermal
"induced voltage resists magnetically induced current", 'back EMF'
"the direction of current induced in a conductor by a changing magnetic field
due to induction is such that it creates a magnetic field that opposes
the change that produced it."
PT1_Q34. careful: diagram shows Phi symbol and a Phi(i) (induced(?). phi often mean flux.
There isn't a big algraic expression for his law; the minus
sign just shows up in Faraday's Law of Induction.
c²=a² + b² - 2ab cos(oppositeAngle),
any triangle, c is side 'c' in diagram. see XAM p76
from wikip which has a derivation.
len(a)/sin(A)=len(b)/sin(B) = len(c)/sin(C) = diam of circumCircle from wikip which has a derivation.
can be stated w/ reciprocals (except for circumscribed circle). XAM p76
A "tuned circuit" with minimal R generally used in radio receivers. The tiny R keeps it from consuming power. Of course there is alway some R (resistance) so another way of examining the circuit is called LCR.
As frequency increases inductive reactance increases and capacitive reactance decreases. passes only the resonant frequency.
removes the resonant freq from a signal.
less than a full theorem. Like a procedure offered to speed work/understanding/proving
rimstarorg video how to make. w/ lg pop bottle. wikip
def freq2joules(hz) : # yes. hz. 'freq' doesn't wk (here) in radians (ω) h = 6.63¤-34 # Planck's constant joules = h * hz return joules def lambda2joules(lambda_m) : h = 6.63¤-34 # Planck's constant c = 3¤8 # speed of light joules = h * c / lambda_m return joules lambda2joules(656¤-9) # H α (Hydrogen Alpha) spectral line
Refractive_index and Snell's law of refraction, n1 sin(θ_{1}) = n2 sin(θ_{2}), n == index of refraction = speedOfLight / speedInMaterial = c / v PT1_Q07 "refractive index a func of both speed and wavelength. index = C / speed_other_medium internal_reflection see critical angle, local Brewster's Angle == polarization angle. Dispersion, separation into colors
Cherenkov_radiation Cherenkov radiation results when a charged particle, most commonly an electron, travels through a dielectric (electrically polarizable) medium with a speed greater than that at which light propagates in the same medium. Moreover, the velocity that must be exceeded is the phase velocity of light rather than the group velocity of light. SOON: img diagram.
An average bolt of (negative) lightning carries a current of 30,000 amperes (30 kA), and transfers 15 coulombs of charge and 5¤8 joules. Speed 1¤8 m/s. Can emit gamma rays.
Lightning creates light in the form of black body radiation from the very hot plasma created by the electron flow.
1000 cm³ and 10¤-3 meters³ == volume of 1000 cu cm or,1 liter = 1/1000 m³ . For water1 liter = 1 kg (at 4 degrees C). 1 liter = 61.02 cu in. so 28.3 liters = 1 cu ft. 1 liter = 0.035 cu ft. wikip
locus,loci lg class of porisms (!)
TODO
130127: 'gamma' derivation in book "Why E=MC²", loc 575
"force on charged particle in E and/or M fields" With E & M fields:history of the Lorentz Force Law, RHR exampleF = q(E + V x B) Just a B field:F = q v B sin θ # XAM p79 mid and btm and XAM p85. if no V, or sin(θ)==0, this reduces to justF = qE B field measured in Teslas Maxwell's equations 1861. summary of related equations relativity calculator
Least Squared Error. See link to leastSquares.html vv_regression. define residuals... TODO
2. Note also how the P magnet's field lines emanate close to the upper right corner of the magnet while the electromagnet, E, has field lines emanating from its mid section.
How to make a '3D compass', measure the local vector, then calculate field: northwestern.edu article. a WOW. excerpt:"The radial component is given by (eqn below). It varies with the cube of the distance from the Earth (instead of the square)
Br = 2µ0 m cos θ / (4 pir³ ) The article also says indirectly that the field is distorted near walls or even furniture! Also found a $50 european article on how to measure dip with a cell phone.
Good section on history, people: Serway vol2, chap 29 alt names for B //wikip, 'Magnetic_field'. In a vacuum, B = µ0 H mag flux density (wikip) == 'mflux' (fgh term) mag flux intensity magnetic field B is measured in Teslas (symbol: T) and Newtons/(meter • ampere) (symbol: N/(m·A)). B is most commonly defined in terms of the Lorentz Force it exerts on a moving 'test charge'. The electric current, I amps, is scaled by µ0, the 'magnetic constant', 4π ¤-7 T m/A Scaling by 'u' means the action occurs inside a materials with this constant. Diagram conventions: a circle w/ dot in middle is the field vector coming out of page. When the field goes into the page, the symbol is a circle w/ an X in middle. (the tail feathers of the arrow). See example diagram, below drawing a magnet. draw S to N (= - to +) (left to right(?)) field lines only conceptual. findingB for common wirings: :
About a wire | B = µ0 I / 2π R | # 2π r == circumference XAM p80 |
Loops | B = µ0 I / 2 R | # |
Solenoid | B = µ0 I N / len; | # If N/len, the 'turns density', gets very small ('len' very # large), there's very little external field. XAM p80+ |
The relation between H and B:
Many sources say "
And... for B = u H, note that u can be freq dependent.
The units don't seem to work:
B (Teslas=(Newtons /(Amp meter)) = Newtons/meter per Amp
µ0 Newtons/Amp * H Amps/meter = Newtons/meter
whew! I'm so happy that the image at left says "simplified"...
torque (tau) = F\ d sin(angle) // angle wrt field, per wire
= (B\ I h) w/2 // add 'N' loops. combine w,h into Area
= (N I A) B sin(angle) // NIA defines 'magnetic moment' TODO where 1/2?
sin(angle) => No torque when hoop seen edge on.
RHR (Right Hand Rule). Thumb in direction of current; fingers curl in direction of field.
For the magnitude of a field. use | |
|B\| = (µ0 * I) / (2 π r) = µ0 I / circum T=Teslas
What force 'F' is applied to wire 2 from wire 1 (Newtons).
'L', a vector aligned with the current, is the Length of the wire affected
by the other wire.
F12 is the Force made by wire 1 affecting wire 2. It pulls wire 2 towards 1.
For the other case, F21, imagine stepping behind the wire pairs. The equation
is basically the same (assuming currents are equal).
SI unit: Amp m², same unit as 'magnetization' First source was ref19 (wikip, "magnetic field") The following is mostly from motor winding: magnetic moment = N I A // NIA is #of turns, current, area The related expression "(N I A) B sin(θ)" calculates a force using the magnetic moment. see dipole TODO: dipole related to 'moment' ? Believe 'dipole' is more conceptual; magnetic moment is a calc (vector)
"Although this odd attraction was stated initially as an empirical law of nature and the formal calculation was explained as the direction of magnetic fields, as some other answers correctly explain, the root of this apparent oddity was explained by Albert Einstein with special relativity.
When two parallel wires have moving electric charges, let's say negative charges, then they see the non-moving positive charges of the opposite wire more closely spaced since objects in relative motion experience length contraction. This causes opposite electric charges to appear more densely spaced, thus more electrostatic attractive than the two moving charges which are at rest relative to each other. Einstein calculated the forces between these wires and proved that they are identical to the forces one would calculate using magnetic formulas. In essence, "magnetic" forces are just electrostatic forces observed in motion."
The + side of an electromagnet points towards earth's north m pole.
gravity 3/8 that of earth mean density 3.9 g/cm vs 5.5 for earth
XAM p85 btm meas's charge to mass ratio, m/q
intensity of polarized light passed thru analyzer depends on the angle TODO between axis of analyzer and polarizer PT3_Q30
make a very smooth magnetic field. wikip
POE Nov '16 prjt/presentation was to calc this # POE 'Principles of Engineering', MDHS class IMA Ideal AMA Actual 'effort force' lever pulley ramp for praxis q 1C6e want MA for each simple machine ? TODO. screw wedge wheel
Mechanical_advantage, wikip
mechanical efficiency = 100 * AMA/IMA IMA Ideal AMA Actual 'effort force' (IMA) of ramp is Ht/rampLength # not tangent !
Mechanical_efficiency, wikip
energy used to describe masses. Physicists will often refer to the energy of a particle in MeV, its momentum in MeV, and its mass in MeV. They should say MeV, MeV/c, and MeV/c2, Physicists should say MeV (energy), MeV/c (momentum), and MeV/c2 (mass). quarknet eV entry local
1 millionth of a meter
mass = {0.7 to 2.0} 2e(30+12=42) kg ~= 2e42 kg MWay mass as much as "0.7 to 2 trillion solar masses". //trillion = 10e12 solar mass = 2e30 kg radius, at sun's position = 26400 ly = 2.64e4 ly = 2.5e20 meters ly = 9.5 trillion km = 9.5e12 km = 9.5e15 m spin rate, at sun. 8.3e-16 radians/sec period = 240e6 years * 3.15e7 sec/yr = 7.5e15 sec/rotation = 1.2e15 sec/radian diameter between 1.5e5 and 200e5 ly frame dragging
aka Young's Modulus, aka Elastic Modulus Elastic_modulus, wikip Bending_stiffness, wikip youTube compares 2 sheets. bending saw a note somewhere that steel has a Young's Modulus of 30¤6 psi Youtube on Mod of E spring algebra, good. series, parallel metal (stretching) is just like a spring. "mexicolibre" ?! Force/Area (units of pressure) = Young's Modulus x deltaL / L where deltaL is the increased length of rod (spring,whatever) and L is the original length of the rod.deltaL/L is "strain" easier to stretch a rod w/ low value of Y Y's * ¤10 N/m² deltaL = F/A x l/Y or F l = ----- A Y
Y Break Rho Vs steel 20 5.2 al 7.0 0.78 nylon 0.36 3.2
8.314 J/(K • mol)
#of kg for 1 mole of a substance. often (wrongly) called 'molecular weight'
moles per unit volume, m^{-3}
expressed by the Avogadro constant, which has a value of 6.02214e23, the number of atoms in 12 grams of carbon-12 The mole is one of the base units of the SI, and has the unit symbol 'mol'.
Mole, wikip I somewhat expected that 1 Amp would be a mole / sec. Nope 1 Coulomb/sec and 1 Coulomb has 96485 moles of electrons (or protons) in it. A mole of gas, at STP, requires 22.414 liters of volume. ~6 gallons
ideal gas.M = dRT/P , d=density in g or Kg, T kelvin, P atm or Pa
nth moment, U_{n} = distance^{n} Quantity // like a point. (otherwise this expands into an integral with the above exponent) 'n' is the moment number (as in 'first moment', 'second moment' etc)"Moment_(mathematics), wikip said "a moment is a specific quantitative measure, used in both mechanics and statistics, of
Moment_(physics), wikip said "a moment is an expression involving the product of a distance and a physical quantity. In its most simple and basic form, a moment is the product of the distance to some point, raised to some power, multiplied by some physical quantity such as the force, charge, etc. at that point...
the closest eye can focus: 25cm. XAM p61
eyes focus in front of the retina
celestial body orbiting the Sun with a Apoapis-Periapsis which includes any part of the earth's orbit (Aphelion-Perihelion). Examples Bennu space vehicle to visit 1808xx Eve Bennu-bound vehicle getting gravitational boost for trip to Bennu 2018BD passed earth jan 18. mentioned in space.com 2001AJ129 alt range min ~same as geosync satellites.
teach/doc/physicsSubtest2_*.txt"_1i. Evaluate the statics and dynamics of Newtonian fluids." Newtonian fluids: air, water. no fluid perfectly this non-Newtonian fluids: _ 1i_1 statics looks like a 'normal' fluid _ li_2 dynamics sudden applied force causes fluid to stiffen. see wikip
1 N = 1 Kg * 1 m/s²9.81 N = 1 Kg * 9.81 9.81 N = .2248 lbs * 9.81 # implies 1 force_lb = 4.448 N Newton, wikip
simplest mathematical models of fluids that account for viscosity. most general models use tensors viscous stresses arising from flow are proportional to the rate of deformation over time. wikip youtube, complex discussion newtonian: Water, air, alcohol, glycerol, and thin motor oil sand w/ just the right (wrong) amt of water (quicksand) non-newtonian fluids: what could commonly be called "weird fluids" It looks like a low viscosity until you do something to it and it suddenly stiffens up. There are examples, videos, of people riding bikes over a trough of such a fluid. Many salt solutions and molten polymers ketchup, custard, toothpaste, starch suspensions, maizena, paint, blood, and shampoo youtube, cornstarch and water
'newton-meter',E=Fd energy. recall that the line integral of force over a path gives total energy For straight line motion, E = F * d
also known as 'bell curve', 'bell-shaped curve'
also known as the 'normal distribution'
wikip article is huge. 31 printed pages
In the std normal, the denominator (sqrt(2 pi)) makes the area under the curve == 1.
binding energy == equiv mass lost as nucleons combine. PE goes neg is the E needed to break apart a nucleus max's about Fe or nickel = [Z * mass(H) + N mass(Neu) - massOfIsotope] * 931.5 Mev/mass_unit carbon12 '12C' used as basis for some constants. mass set at 12.0000001 electric charge, proton or electron, is 1.6¤-19 Coulombs mass unit: Mev/C² neutrons in nucleus dilute the electric 'Coulomb repulsion' nuclear density =~ 2.3¤17 kg/m3 nuclear radius, r, = r0 A^{1/3} where r0 = 1.2 'fm' = 1.2¤-15 m radioactive decay: Natoms(t) = Norig * e^(lambda tsecs) where lambda = ln2/(halflife time in secs) Strong Force.range 2fm = 2¤-15 m (have seen this limit written as 2¤-14 m) symbols: Z #protons, N #neutrons, A amu, Z+N 'fm', 'fermi', = 1¤-15m 'u' Serway p1295 (== amu = atomic mass units)
V=IR. 1827. XAM p86 wikip German Edu System called it a "web of naked fancies"
Millikan. determined charge on the electron. TODO: add more. like how did he charged the oil drops ! wikip
'optical resolution' quantifies the ability of an imaging system to resolve detail. Rayleigh criterion, the theory, often doesn't match reality, pro and con. For telescopes, the atmosphere, eye health, light pollution will all introduce effects.
Rayleigh's theory is based on the 'airy disk', the diffraction pattern made by cylindrical optics.
Wikipedia notes that this
The slow f-number and long focal length used for this photo amplified the effect(?). A normal telescope doesn't show this.
550e-9m λ (green), 2000mm/25 = 0.08m aperture gives:
1.22 * 550e-9m/0.08m = 8.39e-6 radians. Converting to degrees:
radians * 57.3 = 4.8e-4 degrees. Converting to arc-sec:
degrees * 3600 = 1.73 arc-sec
lens resolution, wikip airy disk, wikip a telescope site
It's a 'real image' if you can put film or sensor there and actually
intercept light - otherwise it's virtual.
If, in a mirrored setup, the 'image' is behind the mirror, it's virtual.
'f' will be negative for the example at the left.
Note that the image itself only appears at the 'f' distance WHEN the object is at infinity (to the left). When the object is close to the lens, the image moves to the right of the point 'f'.
The green, yellow, and grey lines are the ray tracings. '1' starts horizontal. '2' heads to the Focal point then bounces to the head of the Real Image. '3' (not always used) goes
Note that, though the image is virtual, it's erect.
elliptical usually. angular momentum conserved. XAM p35 can go 'hyperbolic' if speed > escape velocity A parabolic orbit has eccentricity 1 and its energy is exactly enuf to bring the object to a stop at infinity. vis viva Orbit, wikip Parabolic_trajectory, wikip Elliptic_orbit, wikip Orbital_state_vectors, wikip
harmonic, SHM, .damped, .driven Serway p436 simple harmonic motion
how to use, SFE lecture.
power,exhaust,compression,firing The Otto Cycle is a 4 cycle version of Carnot Cycle, Serway P623, XAM p52.
paraboloid
3.26 light years, 30¤12 km = 19¤12 mi. distance at which 1 AU subtends an angle of 1 arc-sec. wikip
1623-1662 wikip
1648. P = rho g h # h = fluid column depth XAM p4 "The pressure in a confined incompressible fluid is the same throughout the fluid (at that same height)". deltaP (hydrostatic pressure, Pa, Kg/m3) = (density 'rho') g (9.8m/s²) (heightAboveSensor meters) Pascal's works are frequently shown with fluid systems having 2 round openings - but of different diameters. multiplication of forces. hydraulic brakes etc. Since the pressures at the different pistons are the same, but the areas of the 2 are different, the forces on the two pistons can differ from one another (and often 'will').
physics classroom, KE <=> PE energy transformation. not a video. pendulum, wikip, general. some math
Relationship to Simple Harmonic Motion, XAM_Q13, p171 F = - (mg/L) s, compare to Hooke's Law (F = - k x) "A simple pendulum may be modeled using the same expression as Hooke's Law for displacement 's', but with a spring constant equal to (mg/L)".TODO. substitute. try it XAM p23-24, p171; Serway p433-435 periodTsec = 2π sqrt(L/g) period T = 2π sqrt(I/mgd), I = moment of Inertia.m g D?, TODO physical_pendulum, type of. torsional low angle span, similar to harmonic osc Acceleration, wikip shows tangential and centripetal accel
The ability of a material to 'accept' more magnetic field (than what it has). That is, when a material reaches magnetic saturation, its permiability is now close to 1.
from table. last ref below:
material | perm, µ H/meter | rel perm u/u0 | notes |
---|---|---|---|
mu-metal | 6.3¤-2 | 20k-50k | used to shield magnetic fields. hmm. |
iron | 6.3¤-3 | 5000 | pure but not the extreme alloys |
ferrite,Nickle-Zinc | 8¤-4 | 16-640 | one of several 'ferrites' |
carbon steel | 1.26¤-4 | 100 | a typical bolt (?) |
neodymium | 1.32¤-6 | 1.05 | |
water | ~ µ0 | 0.999 | where µ0 is vacuum perm. |
superconductors | 0 | 0 | weird. the previous floor was 1 |
e0, epsilon 0 = 8.854187¤-12 F/m (Farads/meter) The relative permittivity of a material under given conditions reflects the extent to which it concentrates electrostatic lines of flux (eFlux). In technical terms, it is the ratio of the amount of electrical energy stored in a material by an applied voltage, relative to that stored in a vacuum (see: vacuum permittivity). Likewise, it is also the ratio of the capacitance of a capacitor using that material as a dielectric, compared to a similar capacitor that has a vacuum as its dielectric.
units same as ? (? m-3 kg-1 s4 A² (electrical) permittivity of free space. TODO: clean up this area. 171213 is now DEFINED == 1 / (µ0 C²) which nicely guarantees that C² will equal 1/(e0 µ0). µ0 must be easier to measure accurately... e0 appears in Coulomb's Law and Maxwell's calculation of the Speed of Light wikip
(from p18 of ref21): "The permittivity of a material determines its response to an applied electric field - in nonconducting materials (called 'insulators' or 'dielectrics'), charges do not move freely, but permittivity in Gauss's law for electric fields is the permittivity of free space (or "vacuum permittivity"), which is why it carries the subscript 0.
(also ref21): most precise units are C/Vm (Coulomb / VoltMeter). Most fundamental units C² s² / (kg m3). C/Vm == Farads/meter
(also ref21): Inside a dielectric, the amplitude of the total E field is generally less than that of the applied field.
Dielectric_permittivity, wikip _relative_ Permittivity_of_free_space, wikip _absolute_. free space. speed_of_light entry
material 'state': solid, liquid, gas, plasma.
"Phase-velocity represents the vel with which the disturbance is transferred from one particle to another w/o the actual motion of the particles". Velocity V, omega angular vel, and k is propagation constant. V = w/k PT4_Q59
Specific chlorophyll molecules absorb red-light photons at a wavelength of 700 nm,
corresponding to a photon energy ~3¤-19 J.
A minimum of 48 photons is needed for the synthesis of a single glucose molecule
from CO2 and water (chemical potential difference 5¤-17 J) with a maximum
conversion efficiency of 35%.
wikip, Photon_energy
Solar power 1 kw / sq meter incident energy. pointing at sun. having sun unobscured... 20% efficient (?)
error in 15th place for disk held vertically, at earth's surface(?) 3.1415 926 535 8979 3238 4626 43 3832 ... ideal 1234 567 890 1234 5678 9012 34 5678 M C C = carbon, portion of 1m circle carbon atom radius' somewhere around 100pm (averaging VanDerWahls and D orbital) 100pm is 1¤-13m Considering distortions of what is conceptually a circle (or ellipse)... Distortion at Mercury's distance fm Sun causes 43 arcsec/100yrs. 87.969 day orbit. 415.2 orbits/century. *360 = degrees/C = 149472 deg/Cent * 3600 arcsec/deg = 5.38¤8 arcseconds of orbit/century. has 43 arcsec error or 8¤-8 ~= 1¤-7 C/D defines Pi. D gets larger so π smaller.
The "quantum of action", units physical 'action'. E = h * (nu=frequency), 2/3¤-33 J sec,
hBar, the 'reduced Planck Constant', is h/2π and appears in examples of the uncertainty principle The angular momentum value L must be a multiple of hBar; it's not just a constraint on atoms.
There are 2 similar renditions of his equation, one using the frequency of the photons, the other using the wavelengths. I am more comfortable with wavelength. Wikip shows both equations.
"gaseous mixture of highly charged ions". 4th state of matter. Chemically very active (corrosive).
usually created by heating a gas or by subjecting gas to a strong electromagnetic field. Highly corrosive. Eg: fire, lightning, gas in a florescent or neon lamp. The Sun. Welding arc (?)
St Elmo's fire (plasma), wikip saltlamp $60 'loud'. ordered it anyhow. 18082x
wikip plasma ball 'tricks' v good.
Simeon Poisson. 1781-1840 contributions, wikip, electric fields too. Some vector equations work in Minkowski space.
most of the attention to polynomials focusses on quadratic
PE = mgh (mass grav height) units Joules lift 100N 1m = 100J // N•m U_joules = massKg x gravConstant_m/s² x heightMeters = (183+32)lbs/2.2 x 9.81 m/s2 x 1000'/(32.2/9.81 ft/meter) = 215/2.2 x 9.81 m/s2 x 304.8 m = 97 Kg x 9.81 m/s2 x 304.8 m = 290000 J 1 nutritional Calorie is 1 kCal 290000 J / (4185 J/kCal) = 69 kCals kWh = 860.4 kCals so lifting bike & body up 1000' takes 69/860 = 0.08 kWh "walking burns 1/8 kwh per mile", 0.125 kWhPotential_energy, wikip
calc average power { energy,work (joules) from (kg,metersLifted) // assumes grav 9.8N * kg * meters = joules // to lift something 9.8N * ((190+35)lbs / 2.2 lbs/kg) * (1000ft / 3.275 ft/m) 9.8N x 102 kg * 307 = 307 kJ // to lift me+bike 1000' // wt is probably low; time could be short energy (kCal) from (power(watts)) f_kCal(204 watts) = ( 204 J/s) / (4185 J/kCal) = kCal/s ; kCal/s * 1500sec = 73 kCal f_kCal(1000 watts) = (1000 J/s) / (4185 J/kCal) = 0.23 kCal/s ## # calc time (secs) to boil a given quantity of water # A calorie of input causes 1g water to rise 1C; 1J increases 4.185 C # # water_g grams of water, 1000g / liter. same as # of mL # start_C starting temp of water # power_w input power, watts def secsTilBoil(water_g,start_C,power_w) : TODO: add extra heat for phase change tDiff_C = 100 - start_C calNeeded = water_g * tDiff_C # of calories needed. jNeeded = calNeeded * 4.185; # 4.185 J / Cal tNeeded = jNeeded / power_w # 1 watt-second = 1 J return tNeeded def powerFmHeat_w(water_g, tempStart_c, boilTime_s) : return (water_g * (100 - tempStart_c) * 4.185 J/cal) / boilTime_s the effort a motor system exerts to cause motion. This is also the instantaneous rate of energy being consumed. When summed over some time interval, this becomes your energy figure.
If the Earth's pole wanders, then the orbital location where equinox occurs will similarly wander. Yes, recall that the direction the pole is tilted in its 2x23.5 degree circle determines where the equinox is.
wikipwhy Earth's orbit axis slowly rotates. causes: nBody's pulling in mercury's case, 'Sun's oblateness' (central bulge); mercury's total is 574.10 secs±0.65 per century Gen relativity. Another way of looking at it is that the circumference of a circular orbit near the Sun is slightly less than 2π r because of the positive curvature of space-time. – Pete Jacksongeneral_relativity, wikip
PT1_Q52: (in printed sheaf). Deriving 'max height': time2apex = Vy / acc ht = ½ acc time2apex² ht = ½ Vy²/acc # and where 'acc' == G ht = Vy² /(2*9.8 = 19.6) ht = Vy² * 0.051 # ........as in P51... # and they made Vy == muzzleSpeed * sin(θ)
PT1_Q54: Target at 400m, height 100m. Cannon pointed 37 degrees above horizon and hits the target. Find muzzle speed, v0
mass 1.67¤-27 kg electron
eg magnetic field 'B'. in a mirrored image, vector doesnt also reflect, must reverse sense too. wikip, the "Fake News" of the math set ?
Test sets. PT's are ExamEdge.com's Praxis Test #1 (of the 5 I purchased in dec or jan). 1st tried 180109 SS was a short list of questions put out by the agency that makes the test (?) See prjt re testing, testPhys
In particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved.
wiki, Quantum_electrodynamics wiki, Field paperback copy in office 171014
170206 important degree 2 stuff in 'ballistics', for roboticsFirst/. see notebook, py much simpler stuff in solarOven/ (excel...) equation-solver ariz edu derivation of quadratic equation. implies -b/2a is x val for apex and other part is x distance fm apex to each root. Completing the square part of factoring (Khan) For example, solve x˛+6x=-2 by manipulating it into (x+3)˛=7 and then taking the square root. x + 3 = sqrt(7); x = sqrt(7) - 3 //sqrt 7 is 2.6457 quadratic eqn solver says roots are -5.645 and -0.354 sciCalc [(sqrt(7)=2.6457) - 3 ] = -0.354 but -2.64 squared is also 7 [ -2.64 - 3 = -5.64 ] wiki 'quadratic eqn' had this: 2x² + 4x -4 = 0. Ans: x = -1 + sqrt(3), -1 - sqrt(3)// in Note: //from vex. FIRST, robotics efforts. projectile trajectory calculation. The quadratic formula can be dissected into 2 parts -b/2a and (+- sqrt(b² - 4ac))/2a The -b/2a locates the apex and the 2nd part defines the distance from the apex to each of the roots. 2.6457 is -b/2a of the equiv polynomial +-sqrt(7) are the distances from the apex to each of root
Serway p1159, vol 2. What is PE of a stretched spring and mass. ½ k x² (?)
A number system that extends the complex numbers. Used by Maxwell in his original papers on electrodynamics. Tossed by Heaviside in favor of the more conventional vector calculus.
I J = K but J I = -K ! (some similarly to cross products (which is real-valued))
Addition is associative and commutative; multiplication is associative but not commutative.
I have books on Q's but this 'Definition' section of the wikip article was better. See 'versor' below, a unit-length quaternion.
There are books on how to use Q's for rotations in computer graphics. Python's 'numpy-quaternion' package is a special download, a WHL file which unpacked with Zip.
Mr Hamilton, wikip
Also Hamilton's last book is on Pinot. 1866. published by his elder son.
It interested Feynman.
There's a binder, "Octanions", in the garage or office. 161107 (still around.
2" blue binder 171010)
radio tuner, variable caps max out at 360pF. DIY radio design "modified boyscout radio"; principle mod is "antenna coupler" youtube author 'squarewave2" "Boyscout Crystal Radio Upgrade" youtube: "popular crystal radio deisng that's a waste of time - and why" it was bogged down w/ antenna's properties. this was resolved w/ an "antenna coupler" antenna coupler: on a toilet paper tube. 90 turns of #22 wire, 1/8" space, 25 turns #24 the 25T section connects to antenna. The antenna coupler was mounted 1" off the board. Antenna 50' or (better) 100' as high as possible Can buy a variable capacitance tuner at Antique Electronics == tubesAndMore.com Book at Amazon "Radios that work, for free". K E Edwards
Wheeling a stone in a sling of radius 'r' gives an inertial value of mass * r² For an irregular object, not a simple stone, the force can be found by F = m * k² where 'k' acts like the 'r' in the sling example above. 'k', RofG is principally about calc'g rotational inertia and the result of RofG considerations is a multiplicative item, k².Values define where the average mass would be located as a portion of the full radius.
F = m r² # for wheeling a sling, rock 'm' kg and r the full ____
At left is the real meaning of 'k', the Radius of Gyration. Note that it uses the root(2/5) while some use correction factor, the square, 2/5.
For the sphere example, 'I' can be found with either formula but the 2/5, by itself is not 'k'. Many online aids use the true 'k'.
shape | true Coef | Radius of Gyration, k |
correction k² | resultant I m * k² | notes |
---|---|---|---|---|---|
sphere, ball | sqrt(2/5) | sqrt(2/5) * R | 2/5 R² | M * 2/5 R² | XAM p15,p35 Serway p278 |
cigar | sqrt(1/3) | sqrt(1/3) * L | ⅓ L² | M * 1/3 L² | rotation fm 1 extreme end. (parallel axis derived, Serway p281) |
cylinder | sqrt(½) | sqrt(½) * R | ½ R² | M * ½ R | or disk of const thickness |
hoop | 1 | R | 1 R² | M * R² | just like a mass at distance R. duh. |
rod/baton | sqrt(1/12) | sqrt(1/12) * L | 1/12 L² | M * 1/12 L² | L==length |
rectangle | sqrt(1/12) | sqrt(1/12) * ? | (a²+b²)/12 | M*(a²+b²)/12 | a,b are length, width |
180207 US railgun aiming to accelerate a 23 pound metal projectile to 4,500 miles an hour, and the Navy’s goal is an effective range of more than 100 miles. To achieve this feat, the railgun requires 25 megawatts of power per shot, enough to power 19,000 homes (for how many milliseconds?). (source: Popular Science)
primary rainbow. from 'axis', blue wavelengths bends more than red so the blue-ish colors show up on the inner part of the rainbow's arc. (Blue 40deg, red 42) secondary rainbow( not shown). has the opposite ordering of colors. Blues are on the outside of the arc. Because there are 2 reflections inside each water droplet. (blue 53,red 50) Reds 'face' each other.
1 time constant, RC, takes the value to 63% of max.2.2RC to 90%; 5 RC to 1%. see impedance and ref31, pg 24, top
seconds to rise (or fall) 63% 'tau' = (R.ohms) * (Capacitance.Farads) charging: V(t) = V0(1 - e^(-tSecs/tau)) //SOON: python(?) discharging: V(t) = V0( e^(-tSecs/tau)) ------------------ When the R & C are to function as a (passive) low pass filter RC = 1 / (2π cutoffFrequency_Hz) => cutoffFrequency_Hz = 1/(2π RC) At frequencies > 100khz, it's advised to use RLC, not just RC. The L (inductor) in RLC is paired w/ the C to make a tuned ckt, the R dampens the response. For more on RLC, see wikip.
refractive index = "C / speed in other medium". // not func(freq) prism PT1_Q93 vv_rainbow
XAM_Q43, XAM_Q46 SOON w/ diagrams standard resistor values 11 12 13 15 16 18 20 22 24 27 30 33 36 39 43 47 51 56 62 68 75 82 91 11 12 15 18 20 22 27 30 33 39 47 51 62 68 82 fgh's preferred values
eg 3:2. planetary orbit, atomic orbital, or sound
1928. logarithmic. replaced by moment magnitude scale. energy per base (10) goes up 30 per division. zero pt 1micron at __... ; amplitude and ? wave types. kt event about mag 13 or 14.
There is a 'left-hand rule' seen in wikip Faraday. The left-hand rule finds the direction of the electromotive force (EMF) directly from Faraday’s law
wikip on magnetic field calls it 'the right hand GRIP rule'. diff ? Curl rh fingers around wire ST thumb points in I's dir, B follows curled fingers.
The same article shows the ? 'right hand palm rule' :-) palm up... Thumb points w/ I, palm up points w/ Force, straight fingers point w/ B field
For the field around a wire carrying current, align thumb with current dir. fingers wrap in dir to integrate, 'B' field. Serway p845
Similar process for identifying the angular momentum vector of a spinning object. Wrap right hand fingers in the direction of rotation, thumb aligns w/ the vector.
A summary of 2 RHRs was found here
ω is the most common unit for spin rate. While it IS radians/sec its units are really 'per second' or sec^{-1}.
Some problems are expressed in full, 360 degree rotations. The spin rate is 'frequency', 'f', and (always) ω = 2π * f. Its units too are really 'per second' or sec^{-1}.
'α' is rotational acceleration, d&ω;/dt, units 'radians/s². ============ TODO !? s^{-2} ?
To see large copy summarizing rotational and linear, click here. The following image is a subset.
Rotational KE = ½ I ω².
Tangent velocity at disk rim = r * ω
Tangent acceleration at disk rim = r * α
Centripetal Acc, Fc = m v²/r, (r meters)
work torque * angleInRadians = Work, Joules (== N-m) // like Work = F D
example: Earth's rotational KE: 2¤29 Joules, rot KE ============ TODO !? k² ? day: 23.93 hrs, or 86148 secs, or 7.29¤-5 radians/s rotational momentum I = 8¤37 kg m² => 2¤29 Joules, rot KE // ref: Serway (?)
rpmWheel(mph,diaInches) = (mph * 5280 / 60) / (2π * diaInches / 12) mph * 5280 * 12 mph * 168 = ----------------------- = ------------ 2π * diaInches * 60 diaInches
Zermelo's axioms went well beyond Gottlob Frege's axioms of extensionality and
unlimited set abstraction, and evolved into the now-canonical
Zermelo–Fraenkel set theory (ZFC).
Zermelo's solution to the paradox ... turned out to be first-order logic
while Russell altered the logical language itself.
wikip
Since the 17th century, consisting in systematic observation measurement experiment and hypothesis.formulation, hypothesis.testing hypothesis.modificationScientific_method, wikip
"Physics for Scientists and Engineers", volume 1, 7th edition, 2008
Raymond Serway puts out a new physics text every year (?), seemingly changing the 2nd author as often. Even tho the editions are different, much of the text, photos and diagrams are the same.
characterized by (eg) y = A sin(kx - ω t) #waveEquation! oscillation freq f = sqrt(k/mass) / 2π 'Solve periodic motion problems': XAM p23 wikip Phys By Example, end 'math notes' (red tab). (un)damped harmonic oscillator motion. in Angel Flight binder (think this has moved...) TODO_180128 Serway, vol 1, pg 418 notes "force always directed to equilibrium point (x axis in sine wave example). F = -k x restoring force, sure similar to spring eqn. accel = d2x/dt2 = - kx/m (substitute ω² for k/m SO accel = - ω² * x
XAM_Q17, pg 175: "What is the max displacement from equilibrium of a 1 kg mass that is attached to a spring with constant k = 100 kg/s² if the mass has a velocity of 3 m/s crossing the equilibrium point? "
KE (½ m v²) at fastest point must equal the spring potential energy (½ k A²) where 'A' is the amplitude of the wave (largest pull-back). KE = ½ 1kg (3m/s)² = 0.5kg * 9 m²/s² = 4.5 kg m²/s² PE = ½ k A² = ½ (100 kg/s²) (A meters)² = 50 A kg m² / s²
KE = ½ 1kg (3m/s)2 KE = 0.5kg * 9 m2/s2 KE = 4.5 kg m2/s2 PE = ½ k A2 PE = ½ (100 kg/s2) (A meters)2 PE = 50 A kg m2 / s2
4.5 kg m2/s2 = 50 (A m2) kg /s2 # (set KE = PE) A2 = 4.5 / 50 = 0.09 # find A squared A = 0.3 m
Simple Harmonic Motion is also covered in AP Physics bk pg 313: y(t) = A sin(ω T + initialAngle). comes from d²y/dt² = -ω² y #differential eqn in acceleration F = ma // on floor (in x) -kx = m d²x/dt² -kx/m = d²x/dt²
unit conversions (not all SI). back cover of Serway Force 1N = 0.224 lbs // about 2/9 Force 1 lb = 4.448 N // recip .2248 lbs of force Veloc 1 mi/hr = 1.47 ft/s = .447 m/s = 1.61 km/h Veloc 1 m/s = 100cm/s = 3.281 ft/s Veloc 1 mi/min = 60 mi/h = 88 f/s accel 1 m/s2 = 3.28 ft/s2 = 100 cm/s2 accel 1 ft/s2 = 0.3048 m/s2 = 30.48 cm/s2 presr 1 bar = ¤5 N/m2 = 14.5 lb/in2 presr 1 atm = 760 mm Hg = 76.0 cm Hg presr 1 atm = 14.7 lb/in2 = 1.013w5 N/m2 presr 1 P = 1 N/m2 = 1.45 ¤-4 lb/in2 time 1 yr = 365.24 days = 3.16¤7 sec time 1 day = 24h = 1.44¤3 min = 8.64e4 sec energy 1 J = 0.738 ft lb = N m energy 1 cal = 4.186 J energy 1 BTU = 252 cal = 1.054¤3 J energy 1 eV = 1.602¤-19 J energy 1 kwh = 3.60¤6 J power 1 hp = 550 ft-lbs/s = 0.746 kW power 1 W = 1 J/s = 0.738 ft - lbs/sec power 1 BTU/h = 0.293 W
against stars; vs synodic. SOON
a derived unit of ionizing radiation dose in the International System of Units (SI). It is a measure of the health effect of low levels of radiation on the human body. Quantities that are measured in sieverts are intended to represent the stochastic health risk, which for radiation dose assessment is defined as the probability of cancer induction and genetic damage.
Traditionally used for radiation intensities lower than those that make acute and direct damage to a body.
31 emissions/s per gram of natural potassium. BED==Banana Equivalent Dose = 2.3uSv. 31 emissions/sec/g = 31 Bq/g human flesh. BED. 70kg human, 2.5 potassium g/kg(human flesh), * 31 Bq/g of K = 5400 emissions/s BED, wikip gone(?) are: REM (Radiation Equiv Man), RADs Sievert, wikip
A BBCCCCCDD A is only for readability. not signif B only used to locate the decimal pt. not signif C signif D signif. indicates the precision of the measurement image showing rules
Clocks that are running at different rates lead to the effect of simultaneity being relative. What causes two objects to be simultaneous? " Whether two things are simultaneous depends on the _reference frame_ wiki: In physics, the relativity of simultaneity is the concept that distant simultaneity – whether two spatially separated events occur at the same time – is not absolute, but depends on the observer's reference frame. ARE THESE ASSUMED TO BE INERTIAL? (non accelerating) // seems sowikip
This shows how addition of lengths can represent multiplication (or division). Basic multiplication is supported by the A-B (single decade) and C-D (double decade) scales. more on AB,CD
A,B 2 decade log scales. used for finding squares and roots C,D single-decade log scales K 3 decade logs. used for finding cubes and roots CF,DF "folded" versions of C-D, start from Pi. 1. avoid possibility of going off scale w/ a number near 10 2. multiplying by π is simplified CI,DI; CIF,DIF "inverted scales", run fm right to left. simplifies 1/x steps S used for finding sines, cosines on C or D scales. T find tangents and cotangents on C, CI (or D, DI) scales ST sines and tangents of small angles and degree-radian conversion L linear scale. used w/ C,D for finding base-10 logs and powers of 10. LLn a set of -log-log scales. find logs, exponentials of numbers Ln a linear scale, used w/ C,D for finding base e logs and e^{x} squares B,C cubes D,K TODO. list need then approp scales to use.
unit of mass (not weight). "Imperial" unit, about 14.6 kg or 32.1 lbs.
n_{1} * sin(θ_{1}) = n_{2} * sin(θ_{2}) θ_{2} = arcsin(n_{1} * sin(θ_{1}) / n_{2}) eg: incident raw, in air, 30deg off vertical, hits horiz water surface (n_{2} == 1.33). At what angle is the ray traveling in water? θ_{2} = arcsin(1.0 * sin(30) / (4/3)) = arcsin( 0.5 * 3/4 ) = arcsin(0.375) = 21.5 degrees see critical angle, local about total internal reflection.
CME. Coronal Mass Ejection; prominence; video on phone 'Pixel' Carrington Solar event 1859
refs prjt solarOven "Science Lab", pg 82, using an umbrella
field 'B' = (µ0 I nTurnsPerMeter), XAM p81 THE FIELD IS REALLY INSIDE THE COIL; DOESN'T GEN MUCH OUTSIDE ! The magnetic field inside an infinitely long solenoid is homogeneous and its strength neither depends on the distance from the axis, nor on the solenoid's cross-sectional area. wikip Rt Hand Rule (grip), wiki
sound levels. dB, 130dB max for humans (?), Serway p482 resonant freq
sound wave propagation. PT2_Q60 says "according to Laplace, the prop of sound waves thru a gaseous medium is an adiabatic process, not (Newton's) isothermal process."
(better 'specific energy transfer') Serway p556 Specific heat,'c' = heat (Joules) per unit mass (Kg) to raise temp 1 degree C. (Specific heat sometimes called 'specific heat capacity') c = Q / (mass * delta T) OR, equivalently, Q (J) = m (Kg) c deltaT air's value is 1.00J / (1 Kg * 1 degree) // degree C or K iun.edu At most temps, to raise 1 gram water's temp 1deg C, it takes 1 calorie = 4.186J water takes 4186J to raise 1kg water 1C; copper takes 387J to raise 1kg water 1C; 1/10.8 that needed for water! see sciCalcs tags _zhe.gold, zhe.phase See latent heat for a heating other examples which goes thru a phase change.
R is the Rydberg constant, (1.09737¤7 m^{-1}).
The electromagnetic field is described by Maxwell's equations, which predict that the speed c with which electromagnetic waves (such as light) propagate through the vacuum is related to the electric constant, e0 and the magnetic constant, µ0 by the equation C² = 1/(e0 µ0)
quantized angular momentum, atomic level
WikipXAM p31 has the following list of spring properties: KE = ½ k A² sin²(ω t + phi) PT = ½ k A² cos²(ω t + phi) TE = ½ k A² // total energy
Newton entry in gsci Young's modulus, local
fast method for doing sqrt's in your head. pretty accurate. youtube. tecmath "fast square roots". example 1: sqrt(87) 81 nearest square below 87. 9 write this down. draw lines to its right to make a fraction 6 = 87-81. write this in the numerator of the fraction area. 18 = double the 9; make this the denominator of the fraction // The above step is from (x+c)² = x² + 2 x * c + c² 9 1/3 is the technique's answer; calculator says 9.32737... example 2: sqrt(138) 121 nearest below. 11² = 121 < 138 11 write this down. make fraction area (just a line at this point) 17 = 138-121 ; make this the numerator 22 = double the 11; make this the denominator 17/22 isn't an easy fraction; 16/22 = 8/11. 1/11 = 0.090909 so 8/11 would be .7272 18/22 = 9/11, same apch, = 0.8181 calculator says 11.74
img of matrix including the Higgs boson
waves of same freq, opposite directions. Serway p505, XAM p66, procs stationary points are called 'nodes'. points of max motion 'antinodes'. y = (2 A sin(kx) cos(ω t) // 'wave function'. left part is envelope, rt part fills w/ signal See trig identity needed
tabby's star. weird light curve. amateurs v active. TED talk.
P = sigma A e T^{4} ; SAET4, == Power, S-Tconst, Area, emissivity0-to-1, T thermo Temp "Total (blackbody) radiant heat E is proportional to 4th power of T_kelvin" Stefan-Boltzmann Constant, 'sigma', = 5.67¤-8 W/(m² * T^{4})5-6-7-8 mnemonic 'e' is 'emissivity' in 0=>1 (mirror 0, black 1) range, (emissivity is a fudge factor which allows this equation to cover not-so-black bodies. emissivity is 1 for a true black body and less than one if the object doesn't follow true BB). Also 'e' has some wavelength dependencies in real life. history: rayleigh-jeans law tried to define BB curve but went infinite as wavelen approached uV. uV catastrophe. planck sciCalcs,problems Planck's Law, local S B constant Black-body_rad
4 π steradian covers a sphere
K=appliedForce / deflection; independent of hardness (tempered, rolled etc) p applied force K = --- w deflection Wikip
frictional force – also called drag force – exerted on spherical objects with very small Reynolds numbers in a viscous fluid. Stokes's law is derived by solving the Stokes flow limit for small Reynolds numbers of the Navier–Stokes equations. (Much different than aero drag for large objects like airplanes) From wikip Seen in a wikip discussion on the Millikan oil drop experiment.
dimensionless, a ratio of stretch over original length Wikip, Elastic_modulus Wikip, Pascal SI N/m² = 1 Kg/m s²
Force per unit area, measured in pascals, ref12, item 27 PT2_Q75. good
solar corona. 10^{6}K Hbomb, 10^{8}K Serway p536
liquid sodium acetate in hand warmers. super cooling.Serway p562.
10^{44} joules, Quora aug 28,2017. At 4.e ly, would deliver how far? must have been a beam? 5¤9 J/m² at earth. from stars w/ masses 8 to 20 times the sun's mass. T2_Q34
Serway p501. re interference too
refers to a physical condition where a set of predictable outcomes are possible but not yet resolved (or chosen). When a particular change occurs, and some of the previous possible outcomes are no longer possible, "order" has increased but symmetry is said to be "broken". Examples: pencil standing on its point - has possible motions. Once fallen, fewer options.
wrt earth's positions. mercury 116 days, 780 mars
KE+PE+internalE, from 'Transfer mechanisms' = heating,electricity,... Serway P197
Tension is a force, units N (Newtons). mass * acceleration etc. 'T' often represents tension in an FBD (Free Body Diagram). Serway p110,p117. See Atwood machine and the FBD traffic light problem.
air resistance geese in V formation. b/c tip vortex creates small updraft.wikip
1 Weber of mag flux per square meter == B mag fld strength.
1 T equiv units are: N/(A m) (Newton per (Amp meter)) and because Coulomb/sec is an Ampere, 1 T also has units of N/(C m/s) Serway vol2, pg 812
1 N from 1 C at 1 m/s thru 1 T field (B,v perpendicular)
From an argument on Quora
hand closer - more (capacitative) charge - current osc at lower freq farther - higher freq. But prettyWoman's video showed pitch higher when hand near vert antenna. And someone said the freq's were reversed in the electronics. See entry in electrometer prjt The instrument's controlling section usually consists of two metal antennas that sense the relative position of the thereminist's hands and control oscillators for frequency with one hand, and amplitude (volume) with the other. The electric signals from the theremin are amplified and sent to a loudspeaker. See wikip Operating principles,
The four laws of thermodynamics are: thermo Law 0: total E const. if sysA equilib sysB AND sysB equilib sysC then sysA equilib sysC thermo Law 1: Energy i/o chgs system's E per conservation rules. thermo Law 2: sum of entropies increases; perpetual machines impossible thermo Law 3: Entropy approaches constant as T => 0. S at 0K is about 0. more detail, from wikip: Zeroth law of thermodynamics: If two systems are in thermal equilibrium with a third system, they are in thermal equilibrium with each other. This law helps define the notion of temperature. First law of thermodynamics: When energy passes, as work, as heat, or with matter, into or out from a system, the system's internal energy changes in accord with the law of conservation of energy. Equivalently, perpetual motion machines of the first kind (machines that produce work with no energy input) are impossible. Second law of thermodynamics: In a natural thermodynamic process, the sum of the entropies of the interacting thermodynamic systems increases. Equivalently, perpetual motion machines of the second kind (machines that spontaneously convert thermal energy into mechanical work) are impossible. Third law of thermodynamics: The entropy of a system approaches a constant value as the temperature approaches absolute zero. With the exception of non-crystalline solids (glasses) the entropy of a system at absolute zero is typically close to zero, and is equal to the natural logarithm of the product of the quantum ground states. from ref18, chap 16, "Thermodynamics and Chemical Equilibrium" law 1: energy neither created nor destroyed. Or "total E is constant" and deltaE = q + w // q is heat input, w is work done on system. law 2: entropy of Universe increases during spontaneous reaction. (deltaEntropy=deltaS) .ge. q/T // q E and H are properties of the system. G is Gibbs free energy reactions for which deltaS > Q/T can be spontaneous, otherwise not. "all spontaneous processes in nature increase entropy of universe" law 3: provides means of calc'g E. Zero E is crystal at 0K (from Serway (?)) alcohol expands (fastest of common choices(?)) w/ T // max 85C 0 deg water and ice are at equal T's. => no E flow. "ice point of water" can use pressure chg to reveal T (?presuming volume constant(?)) lines extropolate to absolute zero at -273.16 C thermal expansion of joints. p537 ways to handle that. atoms osc amplitude is 10¤-11 meters. freq 10^13 Hz, spacing 10^-10m coef of linear exansion α = (deltaL / Li) / deltaT calcite expands on 1 axis, shrinks on other. CaCO3
TODO. enhance with notes on plastic 'equations' doc adiabatic const heat isobaric const pressure isochoric const volume isothermal const temperature (not nec heat) wikip isothermal vs adiabatic fm Isothermal_process, wikip for PT3_Q60
An isothermal process is a change of a system, in which the temperature remains constant: ΔT = 0. This typically occurs when a system is in contact with an outside thermal reservoir (heat bath), and the change will occur slowly enough to allow the system to continually adjust to the temperature of the reservoir through heat exchange. In contrast, an adiabatic process is where a system exchanges no heat with its surroundings (Q = 0). In other words, in an isothermal process, the value ΔT = 0 and therefore ΔU = 0 (only for an ideal gas) but Q Δ 0, while in an adiabatic process, ΔT 0 but Q = 0. praxis: 0% In isothermal process, no change in internal energy takes place. TODO check. after Delta installed...
model at terminals as open circuit.
Originally it applied only to DC resistive circuits. And each such could be modeled as a voltage source (battery like) and a single resistor. It also works, however, with AC circuits containing both resistive and reactive impedances. Doesn't always get the power consumption right.
All About Circuits adds: Thevenin’s Theorem states that it is possible to simplify any linear circuit, no matter how complex, to an equivalent circuit with just a single voltage source and series resistance connected to a load. The qualification of “linear” is identical to that found in the Superposition Theorem, where all the underlying equations must be linear (no exponents or roots). If we’re dealing with passive components (such as resistors, and later, inductors and capacitors), this is true. However, there are some components (especially certain gas-discharge and semiconductor components) which are nonlinear: that is, their opposition to current changes with voltage and/or current. As such, we would call circuits containing these types of components, nonlinear circuits.
wikip shows how mentioned in "Phys By Example" page 274
dL/dt, units N•m; Ang Mom T = r χ F torqueAtWheel = torqueMotor / overallGearRatio * overall Drivetrain efficiency
"Mathematically, torque is defined as the cross product of the lever-arm distance vector and the force vector, which tends to produce rotation."
The magnitude of torque depends on three quantities: the force applied, the length of the lever arm connecting the axis to the point of force application, and the angle between the force vector and the lever arm. In symbols:
T = r χ F = ||r|| ||F|| sin(θ)
fgh: note that mechanical tracks or other constraints may prevent the force applied to be ideal (perpendicular to the radial line from the center of rotation) - hence the sine etc.
Torque, wikipThe torr (symbol: Torr) is a unit of pressure based on an absolute scale, now defined as exactly 1/760 of a standard atmosphere. Thus one torr is exactly 101325/760 pascals (~133.3 Pa).
Historically, one torr was intended to be the same as one "millimetre of mercury". However, subsequent redefinitions of the two units made them slightly different (by less than 0.000015%). The torr is not part of the International System of Units (SI), but it is often combined with the metric prefix milli to name one millitorr (mTorr) or 0.001 Torr.
The unit was named after Evangelista Torricelli, an Italian physicist and mathematician who discovered the principle of the barometer in 1644 Wikip
Vs/Vp = Ns/Np where Vs is the secondary voltage, Vp is the primary voltage, Ns is the number of secondary windings and Np is the number of primary windings. Divide the number of secondary windings by the number of primary windings, and multiply the source voltage by this ratio. This will give you the output voltage. For example, a voltage source that sends 240 volts through a transformer with 500 primary windings and 100 secondary windings would have an output voltage of 240 * (100/500) = 48 volts.
XAM p82
Trebuchets get their energy from gravity. They (often?) have a sling but that's not the defining characteristic; it's the gravity.
Catapults get energy from tension (usually torsion) and the arm hits a stop near the top of its arc to release the projectile.
"triboelectric " series in the order of most electron attractive to electron repulsive: (top entries get very negative) sulphur (hmm sulphuric acid good in batteries... Loves more electrons) brass items at the top of this list become more negative. copper ebonite paraffin silk vs glass lead cat fur vs glass. wool glass ? saran wrap is somewhere on this side of the sequence (rubber) shoes on carpet; styrofoam balloon (neg) vs hair (pos) on head wool, paper or cotton cloth and 4' PVC pipe; AM radio noise; rod attracts empty can I rubbed a half meter piece of schedule 40 pvc w/ old T shirt and it picked up paper scraps. Most of the papers only stayed w/ the PVC for a few seconds. Then dropped. VDG uses such materials to transport charge into the big sphere at the top. PVC charging a cap: sparkbangbuzz.com In one VDG, a rubber belt driven by plastic pulley moves charge up to VDG's dome (w/ combs). tinsel ? saran wrap removes electrons; cat fur adds; styrofoam PLATES will 'launch' one by one off VDG. rub w/ wash cloth ! vocab TODO. "Wimhurst machine" ? 'electrophorus' school-for-champions rubbing silk on amber wikip, Inductance balloon against hair, wall... wikip PT1_Q59
sine(a+b)=sin(a)cos(b)+cos(a)sin(b), memorize SOON Seen in Serway ~p508(?) under Standing Waves and whatever other identities aren't covered on the plastic review sheets.
physical conditions in which all 3 phases of a material are present: solid, liquid, and gas. The 'conditions' are temperature and pressure.
Water's triple point is 0.01C, 4.58mm mercury. Used to define 0 Kelvin as this - 273.16 ref01, Serway p536
Twin_paradox, wikip my project
Its name: Historically called 'mu naught', written 'µ0'. The µ0 is staying around but standards boards have been pushing the name "magnetic constant". Units: wikip shows several equivalent sets of units for it: T m/A : Tesla meters/Amp. most popular (?) H / m : "henrys" (Inductance) / meter N / A² : Newtons per (Amps squared) 1.256¤-6 (= 4π ¤-7) T m/A (or Newtons/Amp) # magneticConstant Seems this is the reluctance of the vacuum to take on a magnetic field - that the success in building a field is like compressing a spring. The B fld is PE. Could be backwards; 'reluctance' doesn't quite feel right. Maxwell's cross terms suggest the e and m fields play off each other. // wikip 'Magnetic Field' article implies that the constant linking H and B fields // is none other than µ0 ! torque = m χ B = µ0 m χ H, in vacuum. The 4π typically present. But µ0 can be written 1.2566370614¤-6 Newtons/Amp². This is a 'defined value' and not the result of an experiment. wikip article Magnetic Fields discusses H fields (b/c perm magnets so avail(?)). When describing B field, article uses µ0 as above . When describing H field, they use µ0 as 4π ¤-7 (v*s)/(A•m)torque 'tau' = m→ x B→ = µ0 m→ x H→ // "same, up to a multiplicative constant, µ0"
terms being discarded: according to wikip (strong trend towards "magnetic constant") mu naught magnetic permittivity of vacuum permittivity of free space vacuum permittivity permiability of vacuum Utility. Where used. mid 1800's it was used to calculate the Speed of Light Ampere's Law wikip, µ0 = 1.256¤-6
name | nm | eVolts | notes |
---|---|---|---|
UVA | 315-400 | 3.10-3.94 | long wave, 'black light', not absorbed by ozone layer |
UVB | 280-315 | 3.94-4.43 | mostly absorbed by ozone layer |
UVC | 100-280 | 4.43-12.4 | germicidal, completely absorbed by ozone layer and air. |
heisenberg. 1927. product of the uncertainties of complementary variables, such as position and momentum, must be greater than or equal to hBar/2. hBar is planck's_constant/2π, 'h', divided by 2π.
eg: delta X * delta P >= h/2π SOON units of the multiplication should be J-sec ? examples of conjugate pairs: mass, velocity position and momentum And, far from least important, most/all wave calcs experience precision problems == uncertainty. You tighten down the delta wavelength and have little/no signal... wikip
The wikip article, linked below, gives a brief description of the history of these definitions. The evolution began in the 1700's and kg's last tweak rolls out in May, 2019.
Several of these derived units, like Tesla, are composed of several fundamental units. EACH unit, eg N/C * m/s, is a strong hint about how the Tesla (in this case) relates to other concepts and what a user in that area expects from a Tesla (numerator often N, Newtons, FORCE). (N/C)*(m/s) = This conversion factor will output N•m (the numerator) when given C/s (denom). This makes it worthwhile to know the various units, not just one.
1T = (N/C)*(m/s) // Newton per CoulombOfCharge x meters/sec 1 Wb/m2 = // webers per square meter 1 N/ A • m // Newtons per Amp•meter possibly a worthy subject for lectures. wiki SI base units wiki SI derived
-- endings -ane alkane, methane -ate -CH3 methyl group JUST PLAYING. DUNNO if SIGNIF. -cytes -ene alkene DNA pairs: adenine - thymine; guanine - cytocine -graphy topography -ine guanine (DNA pieces). fluorine, chlorine, -line ethylene -lipid phosphlipid -loid for chromasome pairing. haploid -nine implies 'amino acid'(?) eg: serine, alanine -patric Allopatric -phase anaphase -philic -phobic -some allosome, autosome, chromosome -somic -sis mitosis -sphere photosphere, mesosphere, -yl methyl
74.3 plus or minus 2.1 kilometers (46.2 plus or minus 1.3 miles) per second per megaparsec (a megaparsec is roughly 3 million light-years). Spitzer Space Telescope. 74 km/s per 3.086¤19 km.
used in "FM radio kit" to tune freqs. see the assembly pg that came with the kit TODO
youTube van de graaf w/ coke can. SciJoy, 5:02 Safety issues rubber belt driven by plastic pulley is example of 'triboelectric' material, metal combs at either end. sphere is a capacitor. 200kv - 300kv rough values of sphere, 10 pF, and body 1000 ohms, the discharge will be nanoseconds, < msec 'van de graffs work best in low humidity'. body resistance == left to right hand at least 575 ohms 'discharge wand'. some insist 'necessary!'. sold online. metal ball at one end. grounds the big dome. can store 0.5 J ; 'discharge of 1 J hurts everyone severly'. advise 20cm or less sphere diameter and voltage < 250kv (so E < 0.35 J) keep computers, memory sticks, disks, ?phones? away. no if heart condition, pace maker, has embedded medical device of any kind. volunteers only. some may not like the small shock. after person charges themselves, they are charged. do not grab metal anything (like a pipe) touch desk top (?) til charge dissipates. large mixing bowls. 350kv, good. 'triboelectric transfer', b/w img Googled 'charging styrofoam balls' 'DIY particle accelerators' ('cyclotron'NotGdResults). Could cockcroft-walton supply charge things? VDG/wand, bowl/ball, 5 "things you should never do...", 36min interesting use of 'discharge wand': she holds it against sphere while near sphere. Crash Course Phys #32, Indian woman. re Oersted 1820 vacuum pump, expensive, long wine bottle, drilled hole w/ special bit. steel 'anode wire' "sputtered" all over inside of bottle; author suggests aluminum next time. Subscribed DIY Electron Accelerator - Cathode Ray Tube. "GooFerking Science" TODO shows variac to 'oil burner ignition transformer' 'homemade crt', zinc sulphide screen, vac pump, hi V 'electrophoresis power supply'. 'homemade crt' gooferking version. erlenmyer vac tube. x-rays possible w/ CRT. coated bottom of flask w/ 'beta reactive phosphor' phosphor can be scraped out of old phosphorescent tubes. TODO $300 325 kV van de graff, sci-supply.com
a quaternion of length 1. even r² = -1, Wikip, Versor
In astrodynamics, the vis-viva equation, also referred to as orbital-energy-invariance law, is one of the equations that model the motion of orbiting bodies. It is the direct result of the principle of conservation of mechanical energy which applies when the only force acting on an object is its own weight.
Vis viva (Latin for "living force") is a term from the history of mechanics, and it survives in this sole context. It represents the principle that the difference between the aggregate work of the accelerating forces of a system and that of the retarding forces is equal to one half the vis viva accumulated or lost in the system while the work is being done.
For any Keplerian orbit (elliptic, parabolic, hyperbolic, or radial), the vis-viva equation:
# of 'digits', eg: '3 ½ digits' etc. 'impedance, circuit loading'
W = J/sec = volts * amps ; W = N•m/sec a small amount of power. A bathroom light, before LEDs used to take 7 watts. It was barely warm to the touch. The human brain, I've heard, takes 60watts at minimum (? after coffee ?) watt = Joules/sec = volts * amps = Newtons * meters/sec // pg 3 of 4, physics of auto energy consumption, Koon watts(force_lbs,v_mph) = force_lbs x v_mph x 746watts/HP / 375 = force_lbs x v_mph x 2 watt-hour = 3600 Joules power, W = V I and V = I R so I = V/R, so W = (V/R * R) * I = I² R
electrical energy. A 'Watt Hour' is 1 watt for 1 hour, 1/N watts for N hours. Usually written "WH" or "Watt-Hr" in referenced material. watt-hour = 3600 Joules // derived fm above. works in ev.c too watt-hours(force_lbs, miles) = Joules(force_lbs,miles)/3600 = force_lbs x miles x 7157/3600 = force_lbs x miles x 1.98
types: testPages/imgs/PT2_Q87_waveTypeFmEqn.png offers 4 named wave types: y = A sin(wt + kx) progressive longitudinal -kx for progressive progressive transverse if 'x' goes w/ +/-k then perpen to y => transverse retrogressive longitudinal +kx for retro retrogressive transverse my drawing, gsci vv_waveEqn3D, is Y = A sin(x - ct), retro transverse (?) vv_waveEqn y = A cos(kx - wt) vv_waves #is where the result of this study should go. It links Wave Speed. some matl in vv_waves, top longitudinal (osc in direction of motion) v = sqrt(elasticity / density) transverse (oscillations perpendicular to motion). eg guitar string. v = sqrt(tension / linearDensity)
A key notion regarding waves is that the matter of the supporting medium is not being moved permanently. It's displaced temporarily then returns to its original position. (physicists have never had surf break on them!)
Light waves are composed of both types of waves. The longitudinal part always obeys the speed of light but the transverse portion reacts to the index of refraction. (sorry. don't really understand this! fgh 171104). Feynman? QED book? soon
standing waves (XAM p66) typ result from interference of 2 waves of same freq traveling in opposite directions. There are 'nodes' where no movement. max motion at anti-nodes. dbbl slit Young, local interference Serway p501. maxima dbbl slit interference given by "n lambda/ d = x / D = sin θ", n == integers wave types if rope constrained == transverse, PT1_Q23 wavelengths permitted in certain tube lengths PT1_Q79 XAM p58, ref11, "Physics", plasticized summary. other types of waves: traveling, standing, quantum mech, harmonic
y = A cos(kx - ω t) will build trial problems in sciCalcs see Retrogressive...
If a time-current 2D image were displayed on a screen, the waves would appear to march towards the right.
P wave 'Primary'. longitudinal. 7-8 km/s Serway p451 S wave 'Secondary' or 'Surface'. transverse 4 - 5 km/s XAM p59 defines subtype (Love wave, Rayleigh waves (both Surface waves) ).
A flux change of 1 Wb/s induces 1 V in a single loop of wire. The _changing_ flux field _defines_ the Weber: SI unit of magnetic flux. The directions of the field matter (vs those of the wire). 'A' = B A cos θ, where 'B' is field strength mag flux DENSITY of 1 Wb/m² = 1 T (Tesla) (the vv_tesla entry shows T = J/(A m) = Wb/m² implying Wb = J/A)
This was even confusing for standards people. Related discussions started in 1861, got reviewed in 1902, got more focus in 1927, and took a task force 11 years to make solid recommendations. Related standards questions were resolved in 1950. Weber_(unit), wikip
Faraday's LawWeight is a FORCE , not a mass. So wt = Mass * GravAccel(9.81) Mass is 'kg' or 'slugs', Wt is Newtons, 'N', or lbs wt,N = (m,kg) (A=9.8m/s2) som,kg = (wt,N) / G wt,N = wt,lbs * 2.2046 (N=kg 9.81)/lb * g. Note: a pound (mass) is 2.2 kg; to get force (N) fm mass, mult by Grav mass, local
'
Invented by Samuel Hunter Christie 1833. Improved by Wheatstone 1843. Wheatstone's initial uses included soils analysis.
Wikip article VERY INTERESTING ! thought-provoking.
Consider using w/ salt water rheostat, ref22, pg 21.
watt hours per mile. written several ways: WH/Mile etc.
This is "energy / mile" and is useful for determining theoretical range of an electric vehicle. A curious aspect of this is that it is E/distance whereas our gas-powered world talks of mpg which is distance/E.
'Watt-Hour per Mile'. The energy needed to move a car one mile. Typical values at 50 mph would be: (figures predate Tesla car, Li batts)
// derived fm horsepower(F,Dist). works in ev.c too whpm(force_lbs) = watt-hours(force_lbs, 1 miles) = Joules(force_lbs,miles)/3600 = force_lbs x miles x 7157/3600 = force_lbs x 1.98
40mJ Energy (liter of gasoline) / 500N = 80km XAM_Q10, XAM p143. CAREFUL! 10kg item pushed by 5N for 5m is 25J. mass doesn't count! V = W/Q XAM p34,p77 Work on 2 charges: W = F r = k (Q1 Q2/ r²) r = k (Q1 Q2 / r) and b/c V=W/Q, divide abv by Q2: V = k Q1/r, k is Coulomb's constant (9¤9 N m²/C²)
context: photoelectric effect (which includes, but isn't limited to, solar panels).
The energy needed to dislodge an electron from a specific metal. Reading on the topic suggests further that the needed energy is also dependent on the local conditions; that is, the electric field being made by the surrounding conditions and materials.
In solid-state physics, the work function (sometimes spelled 'workfunction')
is the minimum thermodynamic work (i.e. energy) needed to remove an electron
from a solid to a point in the vacuum immediately outside the solid surface.
Here "immediately" means that the final electron position is 'far' from the
surface on the atomic scale, but still too close to the solid to be influenced
by ambient electric fields in the vacuum. The work function is not a characteristic
of a bulk material, but rather a property of the surface of the material
(depending on crystal face and contamination).
wikip
when only sys chg is speed, net work = chg in KE. Serway pg175
ref# | title | subject | locations | notes |
---|---|---|---|---|
ref01 | Serway | physics | paper,ofc | volume 1,2008. A principle reference |
ref02 | CSET Physics 123,127 | physics | paper,office | my notes call this 'XAM'. good text,test |
ref03 | CSET Physics Exam Secrets | physics | kindle only, tablet | 'study guide'. no opinion yet |
ref04 | AP Physics C Exam | physics | paper,office | huge. good, HARD sample tests. |
ref05 | feynman | physics | paper,ofc;kindles | volume 1, online copies, all 3 volumes |
ref06 | feynman | physics | paper,ofc;kindles | volume 2 |
ref07 | feynman | physics | paper,ofc;kindles | volume 3 |
ref08 | Weyl,"Space Time Matter" | physics | paper,office | Dover, 4th edition, 1922; covers tensors. |
ref09 | College Physics 744 Solved Problems | physics | Kindle, on phone and tablet | "Schaum's Outlines", 11th ed. The ultimate review(?). |
ref10 | PhysicsByExample.pdf Physics By Example |
physics | $pub/doc, and Angel Flight binder | whew! hard. good.
Only printed a few questions from each chapter |
ref11 | "Physics" | physics | plasticized summary, Fry's | |
ref12 | "Physics Equations" | physics | plasticized summary, Fry's | |
ref13 | Calculus Rev Shts1 | math | plasticized review shts | |
ref14 | Calculus Rev Shts2 | math | ||
ref15 | QED paperback | physics | office bookshelf | local notes |
ref16 | Magnetics prjt | physics | p/magnetics/ | link to define_ prjt file |
ref17 | "Electricity and M" | physics | Kindle | unused (?) 171014 |
ref18 | College Chemistry | chemistry | Kindle, tablet | Schaum's outline. |
ref19 | "Magnetic Field" | physics | good on tablet | wikip,Magnetic_field |
ref20 | glossary of Physics | physics | online | huge, new to me 170914 |
ref21 | A student's guide to Maxwell's Equations | physics | Pinot C:pub/doc/ office, binder | 250 pages. great reviews. free
book-read-learn project |
ref22 | Build It Yourself Science Laboratory | chemistry | office bookshelf. yellow paperback |
Really good! hands on |
ref23 | Illus. Guide to Home Chemistry Experiments | chemistry | office bookshelf | "All Lab, No Lecture" |
ref24 | The Story of Spin | atomics | paper, ofc | difficult reading but well written |
ref25 | (California) Algebra 2 | math | ofc bookshelf | wonderful book. 2008 |
ref26 | Euclid's Elements | math | Kindle | pre-fractions, pre-algebra! see his proof of distributive law, ch 2! |
ref27 | kjmagnetics.com | physics | online | v good. taught me H and M mag fields Has a calculator |
ref28 | Real World Physics | physics | online | awesome collection of readable articles, FDBs,catapult,trebuchet,...180326 |
ref29 | "Why E = M C²" | physics | kindle | a great book. history, how's and why's |
ref30 | Higgs...Symmetry.. | physics | kindle. which device? | need to reread it... |
ref31 | Art of Electronics | duh | office book. + lab book. | OMG. but dated...1989, 2nd Ed |
see Feynman, volume 2, 26-7 (on tensors) kindle book on Higgs...Symmetry. Mr Hamilton, wikip. also his last book is on Pinot George Green's paper is available, file ($doc) or print in office.Taken from prjt 'magnetics':
use | symbol | text | notes |
---|---|---|---|
multiplication | * | * | multiplication in all computer languages. |
10exp | ¤ | curren | '10 to the power', 'raquo' was considered |
r accel | α | alpha | rotational acceleration |
relativity | β | beta | portion of the speed of light, v/C |
cross product | χ | chi | alternative? 'times'='×' |
dot product | º | ordm | a º b ; not used as of 180310 |
curl | © | copy | curl operator |
degrees | ° | deg | degree sign, temperature |
delta | Δ | Delta | delta, math, differential |
- | η | eta | |
spin rate | ω | omega | |
Ohms | Ω | Omega | |
relativity | γ | gamma | relativistic compression |
wavelength | λ | lambda | |
frequency | ν | nu | |
mag flux | φ | phi | ?? both cases represent |
mag flux | Φ | Phi | the magnetic flux ?? |
angle | θ | theta | |
u0 | µ | micro | magnetic constant. |
units | • | bull 'bullet' | for units multip, esp in denom.
options 'sdot' mult dot or 'middot' |
--- | ' | apos | single '. to get around html string convention |
--- | δ | delta | could use instead of 'd', derivatives |
--- | ÷ | divide | |
--- | ½ | frac12 | ½ |
--- | ¼ | frac14 | 1/4 |
--- | ¾ | frac34 | 3/4 |
--- | · | middle dot | |
--- | π | pi | |
--- | ± | plusmn | plus-minus |
--- | » | raquo | ? could be used for '10 to the power __' |
--- | ⋅ | sdot | |
--- | ² | sup2 | |
--- | ³ | sup3 | |
--- | ↑ | uarr | ? replace '10 to the..' |