= height
d
= distance
I
= rotational inertia
E
= electric field
(
2
2
0
2
a x
x
u
u
=
+

e
=
emf
J
= impulse
0
=
Ú
E
A
i
�
Q
d
H9280
K
= kinetic energy
F
= force
net
m
Â
=
=
F
F
a
k
= spring constant
I
= current
dV
E
dr
= 
d
dt
=
p
F
�
= length
J
= current density
L
= angular momentum
L
= inductance
m
= mass
�
= length
0
1
4
i
i
i
q
V
r
p
=
Â
H9280
dt
D
=
=
Ú
J
F
p
N
= normal force
n
= number of loops of wire
per unit length
P
= power
m
=
p
v
N
= number of charge carriers
per unit volume
p
= momentum
1
2
0
1
4
E
q q
U
qV
r
p
=
=
H9280
r
= radius or distance
fric
F
N
m
£
P
= power
r
=
position vector
Q
= charge
Q
C
V
=
T
= period
=
Ú
F
r
i
W
d
q
= point charge
t
= time
R
= resistance
U
= potential energy
2
1
2
K
m
u
=
0
A
C
d
k
=
H9280
r
= distance
u
= velocity or speed
t
= time
W
= work done on a system
U
= potential or stored energy
dW
P
dt
=
p
i
i
C
C
=
Â
x
= position
V
= electric potentia
l
m
= coefficient of friction
u
= velocity or speed
q
= angle
1
1
s
i
i
C
C
=
Â
=
F v
i
P
r
= resistivity
t
= torque
g
U
mg
D
=
h
f
m
= magnetic flux
w
= angular speed
dQ
I
dt
=
k
= dielectric constant
a
= angular acceleration
2
2
c
a
r
r
u
w
=
=
f
= phase angle
2
1
1
2
2
c
U
QV
CV
=
=
0
m
=
Ú
B
i
�
d
I
H5129
s
k
= 
F
x
=
¥
r
F
t
net
I
Â
=
=
t
t
a
2
2
I
r dm
mr
=
= Â
Ú
cm
m
m
= Â
Â
r
r
r
u
w
=
I
=
¥
=
L
r
p
w
2
1
2
K
I
w
=
0
t
w
w
a
=
+
2
0
0
1
2
t
t
q
q
w
a
=
+
+
2
1
2
s
U
k
=
x
)
R
A
r
=
�
I d
d
r
0
3
4
m
p
¥
=
r
B
H5129
max
cos(
x
x
t
w
f
=
+
r
=
E
J
I d
=
¥
Ú
F
B
H5129
d
I
Ne
u
=
A
2
1
T
f
p
w
=
=
0
s
B
nI
m
=
V
IR
=
f
=
Ú
B
A
i
m
d
f
e
=
=
Ú
E
i
�
m
d
d
dt
H5129
dI
L
dt
e
= 
2
1
2
L
U
L
=
2
s
m
T
k
p
=
i
i
s
R
R
=
Â
2
p
T
g
p
=
�
1
2
2
ˆ
G
Gm m
r
= 
F
r
1
1
i
i
p
R
R
=
Â
P
IV
=
I
M
q
=
¥
F
v
B
1
2
G
Gm m
U
r
= 
© 2012 The College Board. Visit the College Board on the Web: .
ADVANCED PLACEMENT PHYSICS C EQUATIONS DEVELOPED FOR 2012
GEOMETRY AND TRIGONOMETRY
CALCULUS
Rectangle
A
= area
C
= circumference
A
bh
=
V
= volume
Triangle
S
= surface area
1
2
A
bh
=
b
= base
h
= height
A
= length
Circle
w
= width
2
A
r
p
=
r
= radius
2
C
r
p
=
Rectangular Solid
V
w
h
r
=
A
Cylinder
2
V
r
p
=
A
2
2
2
S
r
p
p
=
+
A
Sphere
3
4
3
V
r
p
=
2
4
S
r
p
=
Right Triangle
2
2
a
b
c
+
=
2
sin
a
c
q
=
cos
b
c
q
=
tan
a
b
q
=
c
a
b
90
°
q
d f
d f du
dx
du dx
=
(
)
1
n
n
d
x
nx
dx

=
(
)
x
x
d
e
e
dx
=
(
)
1
ln
=
d
x
dx
x
(
)
sin
cos
d
x
x
dx
=
(
)
cos
sin
d
x
x
dx
= 
1
1
,
1
1
n
n
x dx
x
n
n
+
=
π
+
Ú

x
x
e dx
e
=
Ú
ln
dx
x
x
=
Ú
cos
sin
xdx
x
=
Ú
sin
cos
xdx
x
= 
Ú
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 Physics, AP, Harlan Hanson