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

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

System of Particles and Rotational Motion

Solution:

Angular momentum, $L=I \omega$....(i)
Kinetic energy, $K=\frac{1}{2} I \omega^2=\frac{1}{2} L \omega$ (Using (i))
$\therefore L=\frac{2 K}{\omega}$
When $\omega$ is halved and $K$ is doubled, the new angular momentum becomes
$L^{\prime}=\frac{2(2 K)}{(\omega / 2)}=\frac{4(2 K)}{\omega}=4 L$ (Using (ii))