First slide

Angular momentum

Question

A particle of mass m is moving in a plane along a circular path of radius r. Its angular momentum about the axis of rotation is L. The centripetal force acting on the particle is

Easy

A

$\frac{L^{2}}{mr}$
B

$\frac{L^{2} m}{r}$
C

$\frac{L^{2}}{{mr}^{3}}$
D

$\frac{L^{2}}{{mr}^{2}}$

Solution

L = mvr $\Rightarrow v = \frac{L}{mr}$
$F_{c} = \frac{{mv}^{2}}{r} = \frac{m}{r} {(\frac{L}{mr})}^{2} = \frac{L^{2}}{{mr}^{3}}$

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