A horizontal platform in the shape of a circular disk rotates on a frictionless bearing about a vertical axle through the center of the disk. The platform has a radius of 3.22 m and a rotational inertia of 275 kg·m2 about the axis of rotation. A 62.3 kg student walks slowly from the rim of the platform toward the center. If the angular speed of the system is 1.33 rad/s when the student starts at the rim, what is the angular speed when she is 0.861 m from the center?

The angular speed is .

Explanation:

The law of conservation of angular momentum says that for an isolated system

Now, when the student is at the rim of the platform the moment of inertia of the system is

,

and the angular speed is

.

When the student is from the center,the moment of inertia of the system becomes

Thus, from conservation of angular momentum

which is the angular speed when the student is 0.861 meters from the center.

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