A thin uniform circular dise of mass ' M ' and radius ' R ' is rotating with angular velocity ' ω ' in a horizontal plane about an axis passing through its centre and per

Question

A thin uniform circular dise of mass ' M ' and radius ' R ' is rotating with angular velocity ' ω ' in a horizontal plane about an axis passing through its centre and perpendicular to its plane. Another disc of same radius but of mass ( 3 M ​ ) is placed gently on the first disc co-axially. The new angular velocity will be

TestHub · Accepted Answer

Initial moment of inertia of the first disc is $I_{1} = \frac{1}{2} M R^{2}$ .

Initial angular momentum of the system is $L_{i} = I_{1} ω = \frac{1}{2} M R^{2} ω$ .

When the second disc of mass $\frac{M}{3}$ and radius $R$ is placed gently on the first disc, no external torque acts on the system. Thus, angular momentum is conserved.

Moment of inertia of the second disc is $I_{2} = \frac{1}{2} (\frac{M}{3}) R^{2} = \frac{1}{6} M R^{2}$ .

Final moment of inertia of the system is $I_{f} = I_{1} + I_{2} = \frac{1}{2} M R^{2} + \frac{1}{6} M R^{2} = \frac{2}{3} M R^{2}$ .

By conservation of angular momentum, $L_{i} = L_{f} \Rightarrow I_{1} ω = I_{f} ω^{'}$ .

$\frac{1}{2} M R^{2} ω = \frac{2}{3} M R^{2} ω^{'}$

$ω^{'} = \frac{3}{4} ω$

Answer: $\frac{3}{4} ω$

Physics - Rotation Question with Solution | TestHub

Options:

Doubts & Discussion