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
⌘