PYQ NEET- Rotational Motion L-7

Question: A round disc of moment of inertia $I_2$ about its axis perpendicular to its plane and passing through its centre is placed over another disc of moment of inertia $I_1$ rotating with an angular velocity $\omega$ about the same axis. The final angular velocity of the combination of discs is#

A) $\frac{I_2 \omega}{I_1+I_2}$

B) $\omega$

C) $\frac{I_1 \omega}{I_1+I_2}$

D) $\frac{\left(I_1+I_2\right) \omega}{I_1}$

Answer: $\frac{I_1 \omega}{I_1+I_2}$#

Solution:#

Concept Apply conservation of angular momentum

The angular momentum of a disc of moment of inertia I, and rotating about its axis with angular velocity $\omega$ is $$ L_1=I_1 \omega $$

When a round disc of moment of inertia $I_2$ is placed on first disc, then angular momentum of the combination is $$ L_2=\left(I_1+I_2\right) \omega^{\prime} $$

In the absence of any external torque, angular momentum remains conserved i.e., $$ \begin{aligned} L_1 & =L_2 \ I_1 \omega & =\left(I_1+I_2\right) \omega^{\prime} \ \omega^{\prime} & =\frac{I_1 \omega}{I_1+I_2} \end{aligned} $$