# Conservation of Angular Momentum

• 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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• watch her spin at about 2:50 into the video
• watch her prepare for a triple jump, and then jump and spin, at about 2:15 into the video

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