A 83.5-kg horizontal circular platform rotates freely with no friction about its

Question

A 83.5-kg horizontal circular platform rotates freely with no friction about its center at an initial angular velocity of 1.75 rad/s. A monkey drops a 8.97-kg bunch of bananas vertically onto the platform. They hit the platform at 4/5 of its radius from the center, adhere to it there, and continue to rotate with it. Then the monkey, with a mass of 21.3 kg, drops vertically to the edge of the platform, grasps it, and continues to rotate with the platform. Find the angular velocity of the platform with its load. Model the platform as a disk of radius 1.63 m.

Explanation / Answer

given,

mass of platform = 83.5 kg

initial velocity = 1.75 rad/sec

initial moment of inertia = 0.5 * 83.5 * 1.63^2

final moment of inertia = 0.5 * 83.5 * 1.63^2 + 8.97 * 1.63 * 4 / 5 + 21.3 * 1.63^2

by conservation of momentum

initial momentum = final momentum

0.5 * 83.5 * 1.63^2 * 1.75 = (0.5 * 83.5 * 1.63^2 + 8.97 * 1.63 * 4 / 5 + 21.3 * 1.63^2) * v

v = (0.5 * 83.5 * 1.63^2 * 1.75) / (0.5 * 83.5 * 1.63^2 + 8.97 * 1.63 * 4 / 5 + 21.3 * 1.63^2)

angular velocity of platform v = 1.083 rad/sec

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