A 91.9-kg horizontal circular platform rotates freely with no friction about its

Question

A 91.9-kg horizontal circular platform rotates freely with no friction about its center at an initial angular velocity of 1.79 rad/s. A monkey drops a 8.25-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 22.1 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 1.67 m. ANSWER IN RAD/SEC

Explanation / Answer

Here ,

let the angular velocity of the platform with load is wf

mass , m = 91.9 kg

Using the conservation of angular momentum

Ii * wi = If * wf

(0.5 * 91.9 * 1.67^2 ) * 1.79 = (0.5 * 91.9 * 1.67^2 + 8.25 * (4/5 * 1.67)^2 + 22.1 * 1.67^2) * wf

Solving for wf

wf = 1.122 rad/s

the angular velocity is 1.122 rad/s

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