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Physics 211
Formula Sheet
Fall 2009
Kinematics
v
=
v
0
+
a
t
r
=
r
0
+
v
0
t + at
2
/2
v
2
= v
0
2
+ 2a(xx
0
)
g = 9.81 m/s
2
= 32.2 ft/s
2
Uniform Circular Motion
a = v
2
/r =
ω
2
r
v =
ω
r
ω
= 2
π
/T = 2
π
f
Dynamics
F
net
= m
a
= d
p
/dt
F
A,B
= 
F
B,A
F = mg
(near earth's surface)
F
12
=
Gm
1
m
2
/r
2
(in general)
(where G = 6.67x10
11
Nm
2
/kg
2
)
F
spring
=
kx
Friction
f
=
μ
k
N (kinetic)
f
≤
μ
S
N (static)
Work & Kinetic energy
W =
∫
F
⋅
ds
W =
F
⋅
S
= FS
cos
θ
(constant force)
W
grav
= mg
Δ
y
W
spring
=  k(x
2
2
 x
1
2
)/2
K = mv
2
/2 = p
2
/2m
W
NET
=
Δ
K
Potential Energy
U
grav
= mgy
(near earth surface)
U
grav
= GMm/r
(in general)
U
spring
= kx
2
/2
Δ
E =
Δ
K +
Δ
U = W
nc
Power
P = dW/dt
P =
F
⋅
v
(for constant force)
System of Particles
R
CM
=
Σ
m
i
r
i
/
Σ
m
i
V
CM
=
Σ
m
i
v
i
/
Σ
m
i
A
CM
=
Σ
m
i
a
i
/
Σ
m
i
P
=
Σ
m
i
v
i
Σ
F
EXT
= M
A
CM
= d
P
/dt
Impulse
I
=
∫
F
dt
Δ
P
=
F
av
Δ
t
Collisions:
If
Σ
F
EXT
= 0 in some direction, then
P
before
=
P
after
in this direction:
Σ
m
i
v
i
(before) =
Σ
m
i
v
i
(after)
In addition, if the collision is elastic:
* E
before
= E
after
* Rate of approach = Rate of
recession
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 Fall '09
 TonyLiss
 mechanics, Circular Motion

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