A system of particles on which there is no net force undergoes
unconstrained rotation about the
center of mass
:
The gravitational torque on a body can be found by treating the body as
a particle with all the mass
M
concentrated at the center of mass.
x
cm
5
1
M
3
x
dm
y
cm
5
1
M
3
y
dm
SUMMARY
The goal of Chapter 12 has been to understand the physics of rotating objects.
General Principles
Rotational Dynamics
Every point on a
rigid body
rotating about a fixed axis has the same
angular velocity
and angular acceleration
Newton’s second law
for rotational motion is
Use rotational kinematics to find angles and angular velocities.
a5
t
net
I
a
.
v
Conservation Laws
Energy
is conserved for an isolated system.
•
Pure rotation
•
Rolling
Angular momentum
is conserved if
•
Particle
•
Rigid body rotating about axis of symmetry
L
r
5
I
v
r
L
r
5
r
r
3
p
r
t
r
net
5
0
r
.
E
5
K
rot
1
K
cm
1
U
g
5
1
2
I
v
2
1
1
2
Mv
cm
2
1
Mgy
cm
E
5
K
rot
1
U
g
5
1
2
I
v
2
1
Mgy
cm
Important Concepts
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 Spring '08
 Dick
 Physics, Acceleration, Angular Momentum, Moment Of Inertia, Rigid Body, Rotation, Rotational Dynamics

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