The angular momentum of particle describing uniform circular motion is L . It is kinetic energy is h

Question

The angular momentum of particle describing uniform circular motion is L . It is kinetic energy is halved and angular velocity doubled, its new angular momentum is\

Professor PC Thomas Classes · Answer

Angular momentum, $\mathrm{L}=\mathrm{I} \omega$ Rotational kinetic energy $\mathrm{K}=\frac{1}{2} \mathrm{I} \omega^{2}$\ $\frac{L}{K}=\frac{I \omega}{\frac{1}{2} I \omega^{2}}=\frac{2}{\omega} \Rightarrow L=\frac{2 K}{\omega}$\ $	herefore \frac{\mathrm{L}^{\prime}}{\mathrm{L}}=\frac{\mathrm{K}^{\prime}}{\mathrm{K}} 	imes \frac{\omega}{\omega^{\prime}}=\left(\frac{\mathrm{K}}{2 \mathrm{~K}}ight)\left(\frac{\omega}{2 \omega}ight)$\ $\mathrm{L}^{\prime}=\frac{\mathrm{L}}{4}$\