Question 14 Marks
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.
Answer
View full question & answer→A kid of mass $M$ stands at the edge of a platform of radius $R$ which has a moment of inertia $I.$
A ball of $m$ thrown to him and horizontal velocity of the ball $v$ when he catches it.
Therefore if we take the total bodies as a system Therefore $\text{mvR} = {I + (M + m)R^2}ω ($The moment of inertia of the kid and ball about the axis $= (M + m)R^2)$
$\Rightarrow\omega=\frac{\text{mvR}}{1+(\text{M}+\text{m})\text{R}^2}$
A ball of $m$ thrown to him and horizontal velocity of the ball $v$ when he catches it.
Therefore if we take the total bodies as a system Therefore $\text{mvR} = {I + (M + m)R^2}ω ($The moment of inertia of the kid and ball about the axis $= (M + m)R^2)$
$\Rightarrow\omega=\frac{\text{mvR}}{1+(\text{M}+\text{m})\text{R}^2}$
