Question

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 mass of 114.0 kg, a radius of 3.80 m, and a rotational inertia of 1.65×10³kgm² about the axis of rotation. A student of mass 57.0 kg walks slowly from the rim of the platform toward the center.
If the angular speed of the system is 1.89 rad/s when the student starts at the rim, what is the angular speed when she is 0.710 m from the center?

Answer 1

Using law of conservation of energy,

Ii = If

(0.5 MR^2 + mR^2) wi = (0.5 MR^2 + mr^2)wf

wf = [(0.5 x 114 x 3.8^2 + 57 x 3.8^2)/(0.5 x 114 x 3.8^2 + 57 x 0.71^2)] x 1.89

wf = 3.65 rad/sec

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