A 81.9-kg horizontal circular platform rotates freely with no friction about its

Question

A 81.9-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 9.83-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 21.1 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 1.55 m.

Explanation / Answer

conservation of angular momentum of 3 objects

I1W1i+I2W2i+I3W3i =I1W1f+I2W2f+I3W3f

initially the monkey and bananas are not spinning

W2i+W3i=0

I1W1i =I1W1f+I2W2f+I3W3f

in the end they rotate with same speed

W1f=W2f=W3f=Wf

I1W1i =(I1+I2+I3)Wf

Wf =(I1/I1+i2+I3)*W1i

I1=I -solid disk =m1r1^2/2 ;m1 =81.9 ;r1 =1.55; I1=98.38

I2 =I-pointmass =m2r2^2;m2=9.83;r2=4/5;I2=6.272

I3=I-point mass=m3r3^2;m3 =21.1;r3=4/5;I3=13.504

Wf =98.38*1.79/98.38+6.272+13.504 =21.566rad/sec

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