A horizontal platform in the shape of a circular disk rotates in a horizontal ab

Question

A horizontal platform in the shape of a circular disk rotates in a horizontal about a frictionless vertical axis, as seen in the figure. The platform has a mass of M = 100 kg and a radius of R = 2.0 m (I = 1/2 MR^2). A student whose mass is 60 kg walks slowly from the rim of the disk towards its center. If the angular speed of the system is 2.0 rad/s when the student is at the rim, what is the angular speed when she reaches a point r = 0.5 m from its center? Find the kinetic energy of the system before and after the student the student moves.

Explanation / Answer

Initial Moment of Inertia = 1/2MR2 + mR2 = 200+240 = 440

Final Moment of Inertia = 1/2MR2 + mr2 = 200+15 = 215

I1 w1 = I2 w2

w2 = 440*2/215 = 4.1 rad/s.

B)

KE (before) = 1/2 I1 w12 = 220*4 = 880 J

KE (after) = 1/2 I2 w22 = 1800 J.

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