Question

A particle performing uniform circular motion has angular momentum $L$. If its angular frequency is doubled and its kinetic energy halved, then the new angular momentum is :

• A. $L/4$
• B. $2L$
• C. $4L$
• D. $L/2$

Answer 1

The correct option is A $L/4$

Angular momentum of a particle performing uniform circular motion

$L=I\omega$

Kinetic energy, $K=\frac{1}{2}I{\omega }^2$

Therefore, $L=\frac{2K}{{\omega }^2}\omega =\frac{2K}{\omega }$

$\frac{L_1}{L_2}=\frac{K_1{\omega }_2}{K_2{\omega }_1}$$\frac{L_1}{L_2}=2\times 2=4$

$L_2=\frac{L}{4}$.