Physics - Rotation Question with Solution | TestHub

The angular momentum of a particle in a circular path is given by $L=mvr$.

From this, the velocity of the particle is $v=\frac{L}{mr}$.

The centripetal force acting on the particle is $F=\frac{m{v}^2}{r}$.

Substituting the value of $v$ in the expression for $F$, we get:

$F=\frac{m}{r}{\left(\frac{L}{mr}\right)}^2$

$F=\frac{m}{r}\left(\frac{L^2}{m^2{r}^2}\right)$

$F=\frac{L^2}{m{r}^3}$

Rearranging the terms, we obtain:

$\frac{L^2}{m}=F{r}^3$

Answer: $\frac{{\mathrm{L}}^2}{\mathrm{m}}={\mathrm{Fr}}^3$