Question

If $L$ and $m$ denote the angular momentum and mass of particle, respectively and $p$ its linear momentum, which of the following can represent the kinetic energy of the particle moving in a circle of radius $R$?

• A. $\frac{L^2}{2m}$
• B. $\frac{P^2}{m}$
• C. $\frac{L^2}{2m{R}^2}$
• D. $\frac{1}{2}m{P}^2$

Answer 1

The correct option is C $\frac{L^2}{2m{R}^2}$

evaluating each option:
A : $\frac{l^2}{2m}=\frac{{\left(mvr\right)}^2}{2m}=\frac{m{v}^2{r}^2}{2}$

B : $\frac{p^2}{m}=\frac{{\left(mv\right)}^2}{m}=m{v}^2$

C : $\frac{l^2}{2m{r}^2}=\frac{{\left(mvr\right)}^2}{2m{r}^2}=\frac{m{v}^2}{2}$

D : $\frac{1}{2}m{p}^2=\frac{1}{2}{m}^3{v}^2$

Option (C) only gives KE.