First slide

Angular momentum

Question

A particle is making uniform circular motion with angular momentum L. If its kinetic energy is made half and angular frequency be doubled, its new angular momentum m will be

Moderate

A

L/4
B

L/2
C

2 L
D

4 L

Solution

We know that
$L = mvr and E = (1 / 2) {mv}^{2}$
Now $L = (2 E / v) r$
or $L = \frac{2 E}{rÏ} Ã r = (\frac{2 E}{Ï}) (âµ V = rÏ)$
When E is halved and $Ï$ is doubled, then
$L^{â²} = \frac{2 E}{2 Ã 2 Ï} = \frac{E}{2 Ï} = \frac{L}{4}$

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