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. $4L$
• C. $2L$
• D. $L/2$

Answer 1

Answer: (A)

Angular momentum of a particle performing uniform circular motion
$L=I\omega$
Kinetic energy, $K=\frac{1}{2}{\omega }^2$
Therefore, $L=\frac{2K}{{\omega }^2}\omega =\frac{2K}{\omega }$
$\frac{L_1}{L_2}=\frac{K_1{\omega }_2}{K_2{\omega }_1}$
$\frac{L_1}{L_2}=2\times 2=4<br/>L_1=\frac{L}{4}$