A horizontal platform in the shape of a circular disk rotates on a frictionless

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 127.0 kg, a radius of 4.30 m, and a rotational inertia of 2.35×103kgm2 about the axis of rotation. A student of mass 60.0 kg walks slowly from the rim of the platform toward the center.
If the angular speed of the system is 1.06 rad/s when the student starts at the rim, what is the angular speed when she is 0.780 m from the center?

Explanation / Answer

here,

rotational inertia of plateform , I = 2350 kg.m^2

radius , r = 4.3 m

r' = 0.78 m

initial angular speed , w0 = 1.06 rad/s

let the final angular speed be w

using conservation of angular momentum

I * w + m * r^2 * w0 = ( I + m * r'^2) * w

( 2350 + 60 * 4.3^2) * 1.06 = ( 2350 + 60 * 0.78^2) * w

solving for w

w = 1.54 rad/s

the final angular speed is 1.54 rad/s

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