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Constant Acceleration
v = v
0
+ at
x –x
0
= v
0
t + (1/2)at
2
v
2
= v
0
2
+ 2a(x – x
0
)
x – x
0
= (1/2)(v
0
+ v)t
x – x
0
= vt – (1/2)at
2
Range
= (v
0
2
/g) sin(2
Ѳ
o
)
Cross Product
C = absin ,
= angle between two
Ѳ Ѳ
vectors
a =
(a
√
x
2
+ a
y
2
)
tan
= (a
Ѳ
y
/a
x
)
Uniform Circular Motion
a = v
2
/r (centripetal acceleration)
T = 2 r/v (period)
π
T = 2 /
π ω
F = m(v
2
/R)
Relative Motion
v
PA
= v
PB
+ v
BA
Tension
T – mg = ma
T = Mmg/(M+m)
a = mg/(M+m)
Friction
f
k
= u
k
F
N
f
s,max
= u
s
F
N
When pushing at angle, N = mg +
Fsin
Ѳ
When pulling at angle,
N = mg 
Fsin
Ѳ
u
s
= tan
Ѳ
Drag
D = (1/2)CpAv
2
C = drag coefficient, p = air density,
A = effective crosssectional area
V
t
=
(2F
√
g
/CpA)
K = (1/2)mv
2
Work
W = Fd cos
Ѳ
W = F
.
d
W
g
= mdg cos
Ѳ
W =
(
τ Ѳ
f
–
Ѳ
i
)
W = K
f
 K
i
Springs
F
x
= kx
W
s
= ½ kx
i
2
– ½ kx
f
2
Power
= F
.
v (instant)
P
avg
= W/ t
Δ
P =
τω
P = F · v (instantaneous power)
K
2
+ U
2
= K
1
+ U
1
E
mec
= K + U
Center of mass
= x
com
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This note was uploaded on 04/07/2008 for the course PHYS 211 taught by Professor Staff during the Spring '08 term at Pennsylvania State University, University Park.
 Spring '08
 staff
 mechanics, Acceleration

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