A 97.3-kg horizontal circular platform rotates freely with no friction about its

Question

A 97.3-kg horizontal circular platform rotates freely with no friction about its center at an initial angular velocity of 1.53 rad/s. A monkey drops a 9.49-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 1.99 m.

Please help answer and explain this problem. Thank you.

Explanation / Answer

CONSERVATION OF ANGULAR MOMENTUM

I1W1=I2W2

I1=PLATFORM MOMENT OF INERTIA=1/2 MR^2=1/2*97.3*1.99^2=192.66 Kg m^2

I2=MOMENT OF INERTIA OF( PLATFORM+FIRST MONKEY +SECOND MONKEY)

I2=192.66+9.49*4/5*1.99^2+22.1*1.99^2=310.24 Kg m^2

w2=I1W1/I2=0.95 rad/sec

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