Question

A thin uniform circular disc of mass $M$ and radius $R$ is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity $\omega$. Another disc of the same dimensions but of mass $M/4$ is placed gently on the first disc coaxially. The angular velocity of the system now is $2\omega /\sqrt{5}$.

Answer 1

$Applyingconservationofangularmomentum:\frac{1}{2}M{R}^2\omega =(\frac{1}{2}M{R}^2+\frac{1}{2}\frac{M}{4}{R}^2){\omega }^{\prime }\Rightarrow {\omega }^{\prime }=\frac{4}{5}\omega$