A Sapling Learning A 93.3-kg horizontal circular platform rotates freely with no

Question

A Sapling Learning A 93.3-kg horizontal circular platform rotates freely with no friction about its center at an initial angular drops a 8.57-kg bunch of bananas vertically onto the platform. They hit the platform at 415 of its radius from the center, adhere to it there, and continue to rotate with it. Then the monkey, with a mass of 20.9 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 1.87 m. Number rad/ s

Explanation / Answer

platform: I_p = 1/2mr^2 = 1/2 * 93.3kg * R^2 = 46.65kg*R^2

bananas: I_b = mr^2 = 8.57kg * (4R/5)^2 = 5.4848kg*R^2

monkey: I_m = mr^2 = 20.9kg * R^2

Conserve angular momentum:

I_p * 1.79rad/s = (I_p + I_b + I_m) *

46.65kg * R^2 * 1.81rad/s = (46.65 + 5.4848 + 20.9)kg * R^2 *

notice that R^2 cancels

= 1.81rad/s * (46.65 / 73.03) = 1.156 rad/s

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