Physics - Rotation Question with Solution | TestHub

Kinetic energy of a rotating body is given by $K=\frac{1}{2}I{\omega }^2$

Angular momentum is $L=I\omega$

Thus, $K=\frac{1}{2}L\omega \Rightarrow L=\frac{2K}{\omega }$

Since $\omega =2\pi f$, we can write $L=\frac{2K}{2\pi f}=\frac{K}{\pi f}$

Given that the new frequency is $f^{\prime }=2f$ and the new kinetic energy is $K^{\prime }=\frac{K}{2}$

The new angular momentum is $L^{\prime }=\frac{K^{\prime }}{\pi f^{\prime }}=\frac{\frac{K}{2}}{\pi (2f)}=\frac{1}{4}\frac{K}{\pi f}=\frac{L}{4}$

Answer: $\frac{\mathrm{L}}{4}$