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Conservation of angular momentum of a Large Turntable

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A large turntable rotates about a fixed vertical axis, making one revolution in a time of T. The moment of inertia of the turntable about this axis is I. A child with a mass of m, initially standing at the center of the turntable, runs out along a radius.

What is the angular speed of the turntable when the child is a distance of R from the center? (Assume that you can treat the child as a particle.)

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Solution Summary

We use conservation of momentum law to obtain the final angular velocity.

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We can use Newton's first law transformed to rotating systems:

Without external toques, angular momentum is always conserved.
(compare to "without external forces, an object will have constant velocity")

The angular momentum of the system is the sum of the angular momentums of the turntable and the child.

For an object with ...

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