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Question

Suppose in the previous problem, the child stays at rest on the platform and one of his friend throws a ball of mass m1 towards him with a velocity of v from a direction tangential to the platform and the child on the platform catches the ball. Find the angular velocity of the platform after he catches the ball.

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Solution

New moment of inertia of system about center of platform=I+mR2+m1R2=I+(m+m1)R2 (after ball is caught)
Again using conservation of angular momentum
m1.v.R=(I+(m+m1)R2)ω0
ω0=m1vRI+(m+m1)R2

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