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 3.70 m and a rotational inertia of 274 kg·m2 about the axis of rotation. A 67.8 kg student walks slowly from the rim of the platform toward the center. If the angular speed of the system is 2.62 rad/s when the student starts at the rim, what is the angular speed when she is 0.456 m from the center?

10.93 rad/s

Explanation:

If we treat the student as a point mass, her moment of inertia at the rim is

So the system moment of inertia when she's at the rim is:

Similarly, we can calculate the system moment of inertia when she's at 0.456 m from the center

We can apply the law of angular momentum conservation to calculate the post angular speed when she's 0.456m from the center:

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explanation: