Physics 12—Equation Sheet

Motion

v =∆d

∆t(1)

vf = vi + at (2)

d =(vf + vi)t

2(3)

d = vit + 1

2at2 (4)

v2

f = v2

i + 2ad (5)

Forces

Fnet = ma (6)

Ff = µFN (7)

Fg = mg (8)

g = −9.80m/s2 (9)

F = kx (10)

Energy

KE = 1

2mv2 (11)

PE = mgh (12)

KE1 + PE1 = KE2 + PE2 (13)

EE =1

2kx2 (14)

Work

W = Fd cos θ (15)

Wnet = ∆KE + ∆PE (16)

P =W

t(17)

Momentum

∆p = m∆v (18)

J = F∆t = m∆v (19)

Machines

MA =FR

Fe

(20)

IMA =de

dR

(21)

eff =MA

IMA× 100% (22)

eff =Wo

Wi

× 100% (23)

Wo = FR dR (24)

Wi = Fe de (25)

Waves

v = λf (26)

v =λ

T(27)

f =1

T(28)

f ′ = f

(

v + vo

v − vs

)

(29)

v = 331 + 0.6T (30)

Light

n =c

v(31)

ni sin θi = nr sin θr (32)

c = 3.00 × 108 m/s (33)

Mirrors/Lenses

1

f=

1

di

+1

do

(34)

m =hi

ho

= −di

do

(35)

di =fdo

do − f(36)

do =fdi

di − f(37)

f =dido

di + do

(38)

KeplerPeriod of Period of constant

Mass Radius of rotation Mean radius revolution of R3/T 2

Object (kg) object (m) on axis (s) of orbit (m) orbit (s) (m3/s2)

sun 1.98 × 1030 6.95 × 108 2.14 × 106 — — 3.35 × 1018

Mercury 3.28 × 1023 2.57 × 106 5.05 × 106 5.79 × 1010 7.60 × 106 3.35 × 1018

Venus 4.83 × 1024 6.31 × 106 2.1 × 107 1.08 × 1011 1.94 × 107 3.35 × 1018

Earth 5.98 × 1024 6.38 × 106 8.61 × 104 1.49 × 1011 3.16 × 107 3.35 × 1018

Mars 6.37 × 1023 3.43 × 106 8.85 × 104 2.28 × 1011 5.94 × 107 3.35 × 1018

Jupiter 1.90 × 1027 7.18 × 107 3.54 × 104 7.78 × 1011 3.74 × 108 3.35 × 1018

Saturn 5.67 × 1026 6.03 × 107 3.60 × 104 1.43 × 1012 9.30 × 108 3.35 × 1018

Uranus 8.80 × 1025 2.67 × 107 3.88 × 104 2.87 × 1012 2.66 × 109 3.34 × 1018

Neptune 1.03 × 1026 2.48 × 107 5.69 × 106 4.50 × 1012 5.20 × 109 3.37 × 1018

Pluto 6 × 1023 3 × 107 5.51 × 105 5.9 × 1012 7.82 × 109 3.36 × 1018

moon 7.34 × 1022 1.74 × 106 2.36 × 106 3.8 × 108 2.36 × 106 —

Torque

τ = F⊥leverarm (39)

Centripetal

vc =2Πr

T(40)

ac =vc

2

r(41)

Fc =mv2

r(42)

Fc =4Π2mr

T 2= 4Π2mrf2 (43)

tan θ =v2

rg(44)

Gravitational

Fg =Gm1m2

d2(45)

g =Gm1

d2(46)

k =r3

T 2(47)

v =

√

Gm

r(48)

T = 2Π

√

R3

Gm(49)

Electricity and Magnetism

Fe = kq1q2

r2(50)

ε = kq1

r2(51)

ε =Fe

q(52)

I =q

t(53)

V =∆E

q(54)

V = lvB (55)

V = IR (56)

P = IV = I2R (57)

Fm = B⊥Il sin θ (58)

Fm = Bqv sin θ (59)

Np

Ns

=Vp

Vs

=Is

Ip

(60)

Simple Harmonic Motion

T = 2Π

√

1

g(61)

T = 2Π

√

m

k(62)

Fs = −kx (63)

EE = 1

2kx2 (64)

Quantum and Nuclear

En =−13.6

n2eV (65)

λ =h

mv(66)

p =h

λ=

hf

c(67)

c = fλ (68)

Ephoton = hf =hc

λ(69)

Ephoton = pc (70)

Ephoton = |Ef − Ei| (71)

E = mc2 (72)

Ek = hf − hf0 (73)

Ek = QV0 (74)

N = N0

(

1

2

)∆t

T1/2

(75)

Constants

G = 6.67 × 10−11 Nm2/kg2

k = 9.0 × 109 Nm2/C2

e = 1.6 × 10−19 C

me = 9.11 × 10−31 kg = 0.000549 u

mp = 1.672 × 10−27 kg = 1.007276 u

mn = 1.675 × 10−27 kg = 1.008665 u

1 u = 1.6605 × 10−27 kg

h = 6.63 × 10−34 J/Hz or Js

c = 3.00 × 108 m/s

1 eV = 1.6 × 10−19 J