Sum

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 \[\nu\] 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.

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#### Solution

On considering two bodies as a system, we get

Moment of inertia of kid and ball about the axis

\[= \left( M + m \right) R^2\]

Applying the law of conservation of angular momentum, we have

\[m\nu R = \left\{ I + \left( M + m \right) R^2 \right\} \omega\]

\[\Rightarrow \omega = \frac{m\nu R}{I + \left( M + m \right) R^2}\]

Concept: Moment of Inertia

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