- If a rigid body rotates around a fixed axis, its angular momentum is oriented along the rotation axis
- It often helps to arrange the coordinate axes so that a body rotates in the xy-plane, so that angular momentum is entirely along the z-axis.
- When a rigid body rotates around a fixed axis, its angular
momentum around that axis can be expressed as
angular momentum = (moment of inertia) * (angular velocity)

- When a rigid body rotates around a fixed axis, the derivative
with respect to time of its angular momentum around
that axis can be expressed as
dL/dt = (moment of inertia) * (angular accleration) = sum of external torques

- If the sum of external torques on a body around some axis is zero, then its angular momentum around that axis is constant.
- If such a body changes its moment of inertia, its angular velocity must change to keep angular momentum constant.

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Given m = 500 kg, r = 10 m, torque = 600 N-m ccw, can you figure out at time T = 10 seconds a) the linear speed of a point on the equator? b) the rotational kinetic energy of the sphere? c) the angular momentum of the sphere around its center?

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In this performance by Yu-na Kim at the 2013 Worlds (or you can see a local copy ),

- watch her spin at about 2:50 into the video
- watch her prepare for a triple jump, and then jump and spin, at about 0:50 into the video

Dorothy Hamill spins in the 1985 World Pros artistic program. (or look at local version ).

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