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

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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