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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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 ).

Stars form as large clouds of gas and dust collapse.

Image courtesy of NASA/ESA/STScI/J. Hester and P. Scowen

Images courtesy of NASA/JPL-CalTech/N. Evans and Spitzer Space Telescope
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