A thin circular disc of mass M and radius R i | vedclass

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(C) The initial moment of inertia of the first disc about the central axis is $I_1 = \frac{1}{2} MR^2$.The initial angular momentum of the system is $

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$\frac{2}{3} \omega$

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(C) The initial moment of inertia of the first disc about the central axis is $I_1 = \frac{1}{2} MR^2$.The initial angular momentum of the system is $L_i = I_1 \omega = \frac{1}{2} MR^2 \omega$.When the second disc of mass $M/2$ and radius $R$ is placed co-axially,the new moment of inertia of the system becomes $I_2 = I_1 + I_{disc2} = \frac{1}{2} MR^2 + \frac{1}{2} (M/2) R^2 = \frac{1}{2} MR^2 + \frac{1}{4} MR^2 = \frac{3}{4} MR^2$.According to the law of conservation of angular momentum,$L_i = L_f$,which implies $I_1 \omega = I_2 \omega_2$.Substituting the values: $(\frac{1}{2} MR^2) \omega = (\frac{3}{4} MR^2) \omega_2$.Solving for the new angular velocity $\omega_2$: $\omega_2 = \frac{1/2}{3/4} \omega = \frac{2}{3} \omega$.

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