A horizontal platform in the shape of a uniform disk (I = 1/2mr^2 for an axis at

Question

A horizontal platform in the shape of a uniform disk (I = 1/2mr^2 for an axis at its center) is rotating without friction about a vertical axis at its center. The platform has a mass 8.00 kg and radius 0.400 m. The platform is initially rotating at an angular velocity of 0.300 rev/s. Then a small bag of sand with mass 6.00 kg is dropped from a small height onto the platform at its rim. The bag of sand can be treated as a point mass. What is the final angular velocity of the platform after the bag of sand has been dropped onto it?

Explanation / Answer

initial angular momentum L1 = I1*W1 = (0.5*8*0.4*0.4*0.3) = 0.192

final angular momentum L2 = (I1 + m*R^2) *W

L2 = 1.6 * w

L2 = l1

w = 0.12 rev/s

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