Question

A disc of moment of inertia $I$, is rotating freely with angular velocity $\omega_{1}$ when a second, non rotating disc with moment of inertia $I_{2}$ is dropped on it gently the two then rotate as a unit. Then the total angular speed is.

• A. $\frac{I_{1} \omega_{1}}{I_{2}}$
• B. $\frac{{I}_{2} \omega_{1}}{I_{2}+I_{2}}$
• C. $\frac{I_{1} \omega_{1}}{I_{1}+I_{2}}$
• D. $\frac{\left(I_{1}+I_{2}\right)}{I_{2}} \omega_{1}$

Answer 1

Answer: (C)

According to the conservation of angular momenturm
$I \omega=$ constant
When second disc is dropped on it and forms a unit
$I_{1} \omega_{1}=\left(I_{1}+I_{2}\right) \omega_{2}$
(angular momentum always constant)
$\frac{I_{1} \omega_{1}}{I_{1}+I_{2}}=\omega_{2}$