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General Formula Sheet for PHY 53
Kinematics
Constant acceleration:
r
=
r
0
+
v
0
t
+
1
2
a
t
2
,
v
=
v
0
+
a
t
,
v
2
=
v
0
2
+
2
a
!
(
r
"
r
0
)
Circular motion:
a
r
=
v
2
/
R
=
R
!
2
,
v
=
R
Dynamics
Gravitational force:
F
g
=
m
g
Elastic force (Hooke’s Law):
F
=
!
kx
Friction:
f
k
=
μ
k
N
,
f
s
!
s
N
Effective gravity:
g
eff
=
g
!
a
Potential Energy
Gravity near earth’s surface:
U
=
mgy
Elastic force:
U
=
1
2
kx
2
Rotational motion and rigid bodies
Circular motion in vectors:
v
=
! "
r
Radial acceleration:
a
r
=
!
"
2
r
Tangential acceleration:
a
t
=
! "
r
Rotational kinetic energy:
K
rot
=
1
2
I
2
Symmetric bodies:
!
=
I
"
,
L
=
I
!
Rolling:
v
CM
=
R
,
a
CM
=
R
Oscillations (SHM)
Displacement:
x
(
t
)
=
A
cos(
t
+
)
Force:
F
=
!
m
2
x
Potential energy:
U
=
1
2
m
2
x
2
Total energy:
E
=
1
2
m
2
A
2
Mass on ideal spring:
=
k
/
m
Gravity and satellite motion
Spherically symmetric object of mass
M
with point mass
m
outside at
distance
r
from center:
F
=
GMm
r
2
,
U
=
!
GMm
r
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View Full DocumentEnergy of mass
M
with satellite of
mass
m
in orbit of semimajor axis
a
:
E
=
!
GMm
2
a
Wave motion
Harmonic wave:
y
(
x
,
t
)
=
A
cos(
kx
!
"
t
+
#
)
Notation:
k
=
2
!
/
,
=
2
f
,
v
=
f
=
/
k
Loudness:
=
10log
10
(
I
/
I
0
)
Interference, waves of equal
amplitude and intensity
I
0
:
I
=
2
I
0
(1
+
cos
)
Phase difference only due to path
difference
!
x
:
=
k
"
x
Doppler effect (source chasing
receiver, receiver fleeing source):
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This note was uploaded on 10/19/2011 for the course PHYSICS 53L taught by Professor Mueller during the Spring '07 term at Duke.
 Spring '07
 Mueller
 Physics, Acceleration, Circular Motion, Energy, Kinetic Energy

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