Physics - Rotation Question with Solution | TestHub

The kinetic energy of a rotating body is given by $K=\frac{1}{2}L\omega$.

Since angular velocity is $\omega =2\pi f$, we can write:

$L=\frac{2K}{\omega }=\frac{2K}{2\pi f}=\frac{K}{\pi f}$

Given that the new frequency is $f^{\prime }=3f$ and the new kinetic energy is $K^{\prime }=\frac{K}{3}$.

The new angular momentum is:

$L^{\prime }=\frac{K^{\prime }}{\pi f^{\prime }}$

Substituting the given values, we get:

$L^{\prime }=\frac{K/3}{\pi (3f)}=\frac{1}{9}\left(\frac{K}{\pi f}\right)$

$L^{\prime }=\frac{1}{9}L$

Answer: $\frac{1}{9}\mathrm{L}$