A particle performs rotational motion with an angular momentum ' $L$ '. if frequency of rotation is doubled and its kinetic energy becomes one fourth, the angular momentum becomes.

Question

Aicharya · Accepted Answer

Kinetic energy $\mathrm{k}=\frac{1}{2} \mathrm{I} \omega^2$ $\begin{aligned} & 	herefore \frac{\mathrm{K}_2}{\mathrm{~K}_1}=\frac{\mathrm{I}_2 \omega_2^2}{\mathrm{I}_1 \omega_1^2} \ & 	herefore \frac{1}{4}=\frac{\mathrm{I}_2}{\mathrm{I}_1} \cdot 4 \ & 	herefore \frac{\mathrm{I}_2}{\mathrm{I}_1}=\frac{1}{16} \ & \frac{\mathrm{L}_2}{\mathrm{~L}_1}=\frac{\mathrm{I}_2 \omega_2}{\mathrm{I}_1 \omega_1}=\frac{1}{16} 	imes 2=\frac{1}{8} \ & 	herefore \mathrm{L}_2=\frac{\mathrm{L}_1}{8} \end{aligned}$ *

A particle performs rotational motion with an angular momentum ' $L$ '. if frequency of rotation is doubled…

Solution