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Rotational Mechanics — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsRotational Mechanics2 Marks
Question
Suppose the platform of the previous problem 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.
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Answer

Initial angular momentum = Final angular momentum (The total external torque = 0) Initial angular momentum = mvR (m = Mass of the ball, v = Velocity of the ball, R = Radius of platform) Therefore angular momentum $=\text{l}\omega+\text{MR}^2\omega$ Therefore $\text{mVR}=\text{l}\omega+\text{MR}^2\omega$$\Rightarrow\omega=\frac{\text{mVR}}{(1+\text{MR}^2)}$

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