A cylinder of mass M and radius R is rotating | vedclass

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Question

(A) According to the principle of conservation of angular momentum,the total angular momentum before the impact is equal to the total angular momentum

Vedclass · Accepted Answer

$\frac{I\omega + mvR}{I + mR^2}$

Vedclass · Answer

(A) According to the principle of conservation of angular momentum,the total angular momentum before the impact is equal to the total angular momentum after the impact.Initial angular momentum of the cylinder = $I\omega$Initial angular momentum of the particle about the axis of the cylinder = $mvR$Total initial angular momentum $L_1 = I\omega + mvR$After the particle sticks to the rim,the new moment of inertia of the system becomes $I' = I + mR^2$.Let the new angular velocity be $\omega'$.Total final angular momentum $L_2 = (I + mR^2)\omega'$Equating $L_1 = L_2$:$I\omega + mvR = (I + mR^2)\omega'$$\omega' = \frac{I\omega + mvR}{I + mR^2}$

$A$ cylinder of mass $M$ and radius $R$ is rotating about its axis with angular velocity $\omega$. $A$ particle of mass $m$ moving with velocity $v$ hits the cylinder and sticks to its rim. Calculate the angular velocity of the cylinder after the impact.

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