JEE Main · PhysicsMedium

$A disc of radius $R$ and mass $M$ is rotating with angular velocity $\omega$. A second identical disc is dropped coaxially onto the first. What is the final angular velocity?$

Show correct answer & step-by-step solution

Correct answer: B — $\frac{\omega}{2}$

Solution

By conservation of angular momentum,

I_{1} ω_{1} = I_{2} ω_{2}

. Here

I_{1} = \frac{1}{2} M R^{2}

and

I_{2} = \frac{1}{2} M R^{2} + \frac{1}{2} M R^{2} = M R^{2}

. Thus,

(\frac{1}{2} M R^{2}) ω = (M R^{2}) ω_{f}

, giving

ω_{f} = \frac{ω}{2}