What is the total moment of inertia of the system about the center of the disk w

Question

What is the total moment of inertia of the system about the center of the disk when the person stands on the rim of the disk?

A person with mass mp = 78 kg stands on a spinning platform disk with a radius of R = 1.8 m and mass m sigma = 187 kg. The desk is initially spinning at omega = 2.1 rad/s. The person then walks 2/3 of the way toward the center of the disk (ending 0.6 m from the center) What is the total moment of inertia of the system about the center of the disk when the person stands on the rim of the disk?

Explanation / Answer

The total moment of inertia is I of a disk plus the person at the person

I = mr2

I for a disk is .5mr2 = (.5)(187)(1.8)2 = 302.94 kgm2

I of the person at the rim is (78)(1.8)2 = 252.72 kgm2

Total I = 302.94 + 252.72 = 555.66 kgm2

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