Question

A 86.9-kg horizontal circular platform rotates freely with no friction about its center at an initial angular velocity of 1.65 rad/s. A monkey drops a 8.57-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 20.5 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 1.71 m.

Answer 1

here,

mass of platform, m = 86.9 kg
angular velocity, w1 = 1.65 rad/s
radius of platform, r = 1.71 m

moment of inertia of platform, I1 = 0.5*mr^2
moment of inertia of platform, I1 = 0.5*86.9*1.71^2
moment of inertia of platform, I1 = 127.052 kg.m^2

mass of bananas, mb = 8.57 kg
distance of bananas, d1 = 4/5 * 1.71 = 1.368 m

mass of monkey, mm = 20.5 kg
distance of monkey, d2 = r = 1.71 m

moment of inertia after monkey and banana's
I2 = 127.052 + 8.57*1.368^2 + 20.5*1.71^2
I2 = 203.034 kg.m^2

From conservation of angular momentum :
before = after

I1 * w1 = I2 * w2

Final angular velocity, w2 = (I1 * w1)/I2

Final angular velocity, w2 = (127.052 * 1.65)/203.034

Final angular velocity, w2 = 1.033 rad/s