vs = v0s + as�t

s = 12as�t2 + v0s�t+ s0 vs =

ds

dt

as =dvsdt

v2s = v20s + 2as�s

KINEMATICS

vt = !r ! =d✓

dt↵ =

d!

dtat = ↵r

CIRCULAR MOTION

s = ✓r⌃~F = m~a

DYNAMICS

ROTATION OF A RIGID BODY⌧ = rF sin� = rF? = r?F ` = I!

Ihoop

= MR2

CONSERVATION LAWS

Ik = Icom

+Md2

Ilog or disk

= 1

2

MR2

Ibaton

= 1

12

ML2

Wext

= �K +�U +�Eth

Us(x) =1

2kx

2

Ipoint

=NX

i

mir2

i

#»J =

Z t2

t1

#»F (t)dt = Favg�t

#»` i =

#»` f

#»` = #»r ⇥ #»p = m( #»r ⇥ #»v )#»⌧ net = I #»↵

#»F spring = �k

#»x

#»p = m #»v

#»FA onB = � #»

FB onA

#»J = � #»p

ar = acentrip =v2

r= r!2

#»p i =#»p fKtrans =

1

2mv2

fs µsn fk = µkn

Krot

=1

2I!2

Isphere =25MR2 Ipipe =

12MR2

1 +R22

SIMPLE HARMONIC MOTIONT =

1

f! = 2⇡fx(t) = A cos(!t+ �0)

v(t) = �!A sin(!t+ �0

) = �vmax

sin(!t+ �0

)

!spring =

rk

m!pendulum =

rg

L!phys-p =

rMgl

I

x(t) = Ae

�bt2m

cos(!t+ �0)

⌧ =m

b

TRAVELING WAVESD(x, t) = A sin(kx� !t+ �0)

� = (10dB) log10

⇣II0

⌘

f± =f0

1⌥ vs/vf± = (1± v

o

/v)f0�0 = �0

s1± vs/c

1⌥ vs/cDnet =

Pi Di

D(x, t) = A(x) cos!t = 2a sin kx cos!t

fbeat = f2 � f1

!damp =q!20 � b2

4m2

E = 1

2

mv

2 + 1

2

kx

2 = 1

2

kA

2 = 1

2

m(vmax

)2

��destr. = 2⇡�r� +��0 =

�m+ 1

2

�2⇡

��const.

= 2⇡�r� +��

0

= m · 2⇡v = �T = �f k = 2⇡

�

n = cv

�m = 2Lm

I = Pa

vstring =pTs/µ

I1/I2 = r22/r21

1

1

p245�

45�p3

1260�

30�

a

b

pa2 + b2

✓

g = 9.8066ms2

c = 2.99782⇥ 108 ms tan ✓ ⇡ sin ✓ ⇡ ✓ (small ✓)

nair = 1.003 nwater = 1.33 nglass = 1.5

I0 = 10�12 Wm2

tan ✓ = ba

vsound

= 343m

s

PHYSICS 132 MIDTERM 2

EQUATION SHEET

OPTICSn =

c

v� =

�0

n✓i = ✓r n1 sin ✓1 = n2 sin ✓2

sin ✓crit =n2

n1f =

R

21

s+

1

s0=

1

fm =

h0

h= �s0

s

n1

s+

n2

s0=

n2 � n1

R

d sin ✓m = m� a sin ✓p = p�

d sin ✓m =�m+ 1

2

��

1/f = (n� 1)⇣

1R1

� 1R2

⌘