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Ch 8 : Rotational Motion

Rotational Inertia
• Depends on the distribution of mass with respect to
the axis of rotation.
R
I = MR2
M
M
R
I = MR2
R
M
M
L
I = ½ MR2
1
2
I  ML
3
R
L
1
2
I  ML
12
1
2
I  MR
2
R
2
2
I  MR
5
Torque
A force times the perpendicular
distance to the point of rotation
(Lever Arm)
R
o = R F
R = Lever Arm
F
R
o
o = R F
F
R = Lever Arm
F
Center of Mass and Center of
Gravity
Center of Mass
Center of Gravity
The point on an object where all of
its mass can be considered to be
concentrated.
The point on an object where all of
its weight can be considered to act.
These are the same point for an object in a constant
gravitational field.
Center of
Mass
M
M
L/2
L/2
L
3M
Center of
Mass
1/4L
3/4L
L
M
The center of mass lies at the
geometric center for a symmetric,
uniform density object.
R
h
h
h
h/2
h/3
h/2
The center of mass can be outside
the mass of the body.
Center of mass
Stability
Stable Equilibrium
Less Stable
Equilibrium
Centripetal Force
v
Fc

2
v
Fc  mac  m
R
v  R
2
v
2
Fc  mac  m  mR
R
Simulated
Gravity
R

F  mR
F  mg
2
g  R
2
Angular Momentum =
Rotational Inertia x Angular velocity
L = I

v
R
I = MR2
M
L

t
Conservation of Angular Momentum
1
R
L = mR21
L
 0
t
2
R/2
L = m(R/2)22
L  0