Chapter 12: Rolling, Torque and Angular Momentum

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Chapter 12 Rolling, Torque and Angular Momentum
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Rolling
Smooth rolling motion
Reference frame
Rotation and Translation
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Kinetic Energy
Stationary observer Parallelaxis theorem
A rolling object has two types of kinetic energy
a rotational kinetic energy due to its rotation
about its center of mass and a translational
kinetic energy due to translation of its center
of mass.
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Forces
YoYo
A net force Fnet acting on a rolling wheel speeds
it up or slows it down and causes an
acceleration. The acceleration tends to make the
wheel slide. A static frictional force fs acts on
the wheel to oppose that tendency.
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Torque
Revisit Chapter III!
Definition of Torque
Vector (cross) product
(Righthand rule, order does matter!)
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Angular Momentum
Definition
kg m2/s
Angular counterpart of linear momentum!
System of particles
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Newtons 2nd Law
Single particle Linear form
Single particle Angular form
Proof
The (vector) sum of all torques acting on a
particle is equal to the time rate of change of
angular momentum of that particle!
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Conservation of Angular Momentum
Angular momentum of a solid body about a fixed
axis
If the net external torque ?net acting on a
system is zero, the angular momentum L of the
system remains constant, no matter what changes
take place within the system
Law of conservation of angular momentum
(Valid from microscopic to macroscopic scales!)