If L, m denote the angular momentum and mass of the particle a:rd p is linear momentum, which of the following can represent the kinetic energy of the particle moving in a circle of radius .R ?

 In terms of linear momentum, the K.E. is given by $\text{ K.E. }=\frac{{\mathrm{p}}^2}{2\mathrm{m}}$

Now we consider the K.E in terms of angular momentum L

 $\begin{array}{r}\mathrm{L}=\mathrm{mvR}\text{ or }\mathrm{V}=\mathrm{L}/\left(\mathrm{mR}\right)\\ \text{ K.E. }=\frac{1}{2}{\mathrm{mv}}^2\end{array}$

$$\begin{gathered} \text{ Substituting the value of }\mathrm{v}\text{ from eq. (1) in eq. (2), we get } \\ \text{ K.E. }=\frac{1}{2}\mathrm{m}(\mathrm{L}/\mathrm{mR}{)}^2=\frac{{\mathrm{L}}^2}{2{\mathrm{mR}}^2} \end{gathered}$$