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Question

Suppose a kid is standing on the platform and the platform is brought to rest with the ball in the hand of the kid standing on the rim. The kid throws the ball horizontally to his friend in a direction tangential to the rim with a speed $$v$$ as seen by his friend. Find the angular velocity with which the platform will start rotating. Assume notations for platform's mass, kid's mass , radius of platform and the angular velocity.


Solution

Initial angular momentum = Final angular momentum
(the total extarnal torque $$=0$$)
Initial angular momentum $$=mvR$$ ($$m=$$ mass of the ball, $$v=$$ velocity of the ball, $$R=$$ radius of platform)
Therefore angular momentum $$=I \omega +MR^2 \omega$$
Therefore $$mVR=I \omega+MR^2 \omega$$
$$\Rightarrow \omega =\dfrac {mVR}{(I+MR^2)}$$

Physics

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