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

Question

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 (A) (L/4) (B) 2 L (C) 4 L (D) (L/2)

Tardigrade Admin · Accepted Answer

Angular momentum, L=I ω....(i) Kinetic energy, K=(1/2) I ω2=(1/2) L ω (Using (i)) ∴ L=(2 K/ω) When ω is halved and K is doubled, the new angular momentum becomes L prime=(2(2 K)/(ω / 2))=(4(2 K)/ω)=4 L (Using (ii))

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

$\frac{L}{4}$

$2 L$

$4 L$

$\frac{L}{2}$

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

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

4L​

2L

4L

2L​