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A particle of mass ' $\mathrm{m}$ ' is rotating along a circular path of radius ' $r$ ' having angular momentum ' $L$ '. The centripetal force acting on the particle is given by
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$\frac{\mathrm{L}^2}{\mathrm{mr}^3}$
$\begin{array}{ll} & \text { Centripetal force }=m \omega^2 r \\ \therefore \quad & \omega=\frac{L}{I}=\frac{L}{m r^2} \quad \ldots(\because L=I \omega) \\ \therefore \quad & F=m\left(\frac{L}{m r^2}\right)^2 \quad r=\frac{m^2 r}{m^2 r^4}=\frac{L^2}{m r^3}\end{array}$
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