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A kid of mass M stands at the edge of a platform of radius R which can be freely rotated about its axis. The moment of inertia of the platform is I. The system is at rest when a friend throws a ball of mass m and the kid catches it. If the velocity of the ball is v horizontally along the tangent to the edge of the platform when it was caught by the kid, find the angular speed of the platform after the event.


Solution

A kid of mass M stands at the edge of the platform of a radius R which has a moment of inertia I. A ball thrown to him and with horizontal velocity of the ball -v when we catches it.

Therefore, if we take the total bodies as a system,

mvR={1+(M+m)R2}ω

The moment of inertia of kid and ball about the axis

= (M+m)R2

             ω=mvR1+(M+m)R2

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