Physics - Rotation Question with Solution | TestHub

The angular momentum of a particle of mass $m$ moving in a circle of radius $r$ with velocity $v$ is given by $L=mvr$.

The kinetic energy of the particle is $K=\frac{1}{2}m{v}^2$.

Multiplying and dividing the expression for kinetic energy by $m{r}^2$, we get:

$K=\frac{m^2{v}^2{r}^2}{2m{r}^2}$

$K=\frac{(mvr{)}^2}{2m{r}^2}$

Substituting $L=mvr$, we obtain:

$K=\frac{L^2}{2m{r}^2}$

Answer: $\frac{{\mathrm{L}}^2}{2{\mathrm{mr}}^2}$