A 99.5 kg horizontal circular platform rotates freely with no frictions about it

Question

A 99.5 kg horizontal circular platform rotates freely with no frictions about its center at an initial angular velocity of 1.77 rad/s.  A monkey drops a 9.73kg 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 continues to rotate with it.  Then the monkey, whit a mass of 21.3kg, drops vertically to the edge of the platform, grasping it and continues to rotate with platform.  Find the angular velocity of the platform with its load.  Model the platform as a disk

Explanation / Answer

moment of inertia of disk about an axis passing through center is I=M*R^2/2=


from law of conservation of angular momentum...\

I1*W1=I2*W2...

I1=(1/2)(M*R^2)=(1/2)(99.5*R^2)....

W1=1.77 rad/s...

I2=I1+[M_monkey*R^2+m_banana*(4R/5)^2]=49.75 R^2+21.3*R^2+6.23*R^2=77.28 *R^2

W2=I1*W1/I2=1.139 rad/sec

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