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A cheat-sheet for physics formulas and trigonometric identities.
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PHYSIGS FORMULAS
SCIENTIFIC NOTATIONPrefixes and symbols to form decimal multiples and/or submultiples.
Power E Decimalof ten Notation Equivalent Prefix1012 E + 12 1 000 000 000 000 tera10e E + 09 1 000 000 000 giga106 E + 06 1 000 000 mega1 0 3 E + 0 3 1 0 0 0 k i l o1 0 2 E + 0 2 1 0 0 h e c t o10 E + 01 10 deka10 ' E - 01 0 .1 dec i1 0 2 E - 0 2 0 . 0 1 c e n t i1 0 3 E - 0 3 0 . 0 0 1 m i l l i10 6 E - 06 0.000 001 micro10 e E - 09 0.000 000 001 nano10'12 E - 12 0.000 000 000 001 pico10'1s E - 15 0.000 000 000 000 001 femto10'18 E - 18 0.000 000 000 000 000 001 atto
KINEMATIC FORMULASCoefficient of Friction: g =
#!r = coefficient of frictionF = force of friction N = force normal to surface
Velocity: ,", = I
r'" = average velocityd = distance
Acceferatio n: eav = 't
,'ta_ = dV€f€lge acceleration v; = initial velocityr' = final velocity r = elapsed time
Newton's 2nd Law of Motion: F = m.aF= force la= ITrdss a= accelerat ion
Law of Universal Gravitation: F = G ^'Y'tr
F = force of attraction ffifffi2 = prOduct of masses5; = gravitational constant d = distance between their centers
Centripetal Force: F= ryF = centriDetal forcern=n't€rsS ,=v:.!99ry
P e n d u l u m : T = 2 n - l Il s
1 = p e r i o d / = l e n g t h
Work: W = F.dt l '=1y9f l1 F=fOfce
Refationship between Mass and Energyi E = m.c2E = gnergY ru = ITISSS c = velocity of light
OPTICAL RELATIONSHIPSWaveFormula: ,= fLv = wdV€ speed /= frequency l, = w€lV€ length
Uniformly llluminated Surface: E=lmT
Phonicter'aj i 'gameg'aki l 'ohek'todek'ades'isen'limil ' imi'kronan'ope'kofem'toat'to
SymbolTGMkh
dadcmpnpta
A = uniformly i l luminated area
tmages in Mirrors and Lenses: & = +
E = i l luminationlm = luminous f lux
So = object sizeSi= image s ize
Do = object distanceD, = image distance
Focal Length of Mirrors and Lenses: 1 1 1T= q-E
(ldeaf Mechanical Advantage: IMA = do/d,d. = distance through which applied forc6 F actsd, = distance load moves against force W without frictionActual MechanicalAdvantage: AMA = WF
Mechanical Equivalent of Heat: W = J.Ql1'= work / = mechanical equivalent of heat Q = heal
ENERGY RELATIONSHIPSKinetic Energy: K - 1 12 m.v2K= kinetic energy ln= ITr€tsS v = velocity
Potentiaf Energy: V = m.9.htr'= potential energyg = acceleration of gravitynt = fll8SS h = vertical distance (height)
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,f = focal lengthDo = object distance D, = image distance
Sneff 's Law: n, sin 0, = nrsin 0,ni= refraclive index of ith material0, = €lrtgle between ray and normal to surface
ELECTRICITY AND MAGNETISMElectr icCurrent: I=+
1= cutreot 4 = quantit! of charge / = time
Coulomb's Law of Electrostatics: F=k Q,'Q'F = force between two charge
" T
2 = proportionality constantefez = Product of chargesd = distance sepdrating charges
Capacitance of a Capacitor: C = +C = capdcitance of a capacitorV = potential difference between plates4 = charge on eilher plate
Ohm's Law of Resistancei E = I.RE = €rTrf of source 1= CUIfe[t in the circuitR = resistance of the circuit
Jou le 'sLaw.Q-P.R. tQ = heat energy 1= cufleot R = resistance I = time
Faraday's Law of Electrolysisi 7n - 7olo1t?z = ITI€ISS z = electrochemical equivalent1=cu f f e f l t r = t ime
fnduced emf: Coil in a Magnetic Field: E = - N #E = induced emf N = Dumber of lurns
do3
= the change in flux linkage in a given interval of time
Induced emf: Gonductor in a Magnetic Field: E = fr.l.vE = induced emf B = flux density of the magnetic fieldI = length of conductorv = velocity of conductor across magneiic field
fnstantaneous Voltagei e = {* sin 0e = instantaneous voltageE*= maximum voltage0 = angle between the plane of the conducting loop and the
perpendicular to the magnetic flux (displacement angle)
Instantaneous Current: i = l.* sin 0I = instantaneous currentl.- = ITlaximum current0 = displacement angle
r = elapsed time
=qltI-
\
!I-
oI Ioo
r = radius of path
g = €lcceleration of gravity
d = distance
ffiffiwHLET fHE JOURIIEY BEGII!
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TRIGONOMETRIC IDENTITIES
adjacent
s e c 0 =hypotenuse
adjacent
^ hvpotenusecSCo= - - - : - =
opposite
PYTHAGOREAN I DENTITIES:
s i n 2 0 + c o s 2 0 = 1t a n 2 0 + 1 = s e c 2 0c o t 2 0 + 1 = c s c 2 0
SUM OR DIFFERENCE OF TWO ANGLES:
sin (0+Q) = sirl 0 cos Q + cos 0 sin qsin (e-Q) = sin 0 cos Q - cos 0 sin Qcos (0+Q) = Gos 0 cos Q - sin 0 sin Qcos (0-Q) = cos 0 cos S + sin 0 sin q
t a n 0 + t a n d
REDUCTION FORMULA:
sin (-0) = -sin 0cos (-e) = cos 0tan (-0) = -tan 0cot (-e) = -cot 0sec (-e) = sec 0csc (-0) = -csc 0
PRODUCT:
sin 0 sin 0 = '/r[cos (0 - O) - cos (e + Q)]cos e cos Q =1/r[cos (e - 0) + cos (e + 0)]sin 0 cos 0 = '/ ' [sin (e + 0) + sin (e - Q)]cos e sin Q = 1/z[sin (0 + 0) - sin (e - $)]
THE LAW OF SINES
sin A sin B sin C
THE LAW OF COSINES
a 2 = t f + C - 2 b c c o s A
f f = e 2 + C - 2 a c c o s B
C = a 2 + f f - 2 a b c o s C
GREEK ALPHABET
opposite
oopositeo i l t U =
nyporenuse
^ adiacentwlJo v -
nyporenuse
tan o = oPpositeadjacent
adiacentC O I U =
opposlre
1= csce
1= seae
= t =
a D c
1COS€
1
sin 0
sin 0cos e
cos 0= s rne
tan (0+Q) =
tan (e-Q) =
LetterABfAEZH@IKAMN
oIIP
TYoXYO
Namealphabetagammadeltaepsilonzetaetathetaiotakappalambdamunuxiomicronpirhosigmatauupsi lonphichipsiomega
1 - t a n 0 t a n q
t tne - tan0
cl
B6erqetKl.trv
oE
pot1J
axvo
1 + t a n 0 t a n d
DOUBLE ANGLE:
s i n 2 0 = 2 s i n 0 c o s 0c o s 2 0 = 2 c o s 2 0 - 1 = 1 - 2 s i n 2 0
2 t a n 0r?n zH = 1-: tenz e
HALF ANGLE:
s i n 2 0 = 1 l z ( 1 - c o s 2 0 )cos2 0 =1lz(1 + cos 20)
e 1 - c o s 0 s i n 0t a n - = - = -
2 s i n 0 1 + c o s 0