Physics - Rotation Question with Solution | TestHub

The angular momentum of a body in purely rotational motion is given by $L=I\omega$.

The rotational kinetic energy is given by $K=\frac{1}{2}I{\omega }^2$.

The ratio of angular momentum to kinetic energy is:

$\frac{L}{K}=\frac{I\omega }{\frac{1}{2}I{\omega }^2}=\frac{2}{\omega }$

Given that this ratio is $\frac{\pi }{22}$, we have:

$\frac{2}{\omega }=\frac{\pi }{22}$

$\omega =\frac{44}{\pi }$

Substituting $\pi =\frac{22}{7}$:

$\omega =\frac{44}{\frac{22}{7}}=44\times \frac{7}{22}=14\text{ rad/s}$

Answer: $14\mathrm{rad}/\mathrm{s}$