Question

A bug that has a mass mb = 1 g walks from the center to the edge of a disk that is freely turning at 38 rpm. The disk has a mass of md = 11 g. If the radius of the disk is R = 30 cm, what is the new rate of spinning in rpm?
Angular momentum (I*w) is conserved. However the moment of inertia (I) increases and the angular velocity (w) decreases.

The initial moment of inertia is
I1 = (1/2)md*R^2 = 4950 g*cm^2

The final moment of inertia is
I2 = (1/2)md*R^2 + mb*R^2
= 4950 + 900 = 5850 g*cm^2
new rpm/old rpm = 4950/5850

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