# Does angular momentum change with radius?

Yes, angular momentum of a rotating body changes with radius.

#### Explanation:

The angular momentum $\setminus \vec{J}$ of a point mass $m$ rotating with a linear velocity $\setminus \vec{v}$ at a radius $\setminus \vec{r}$ about an axis is given as

$\setminus \vec{J} = m \left(\setminus \vec{r} \setminus \times \setminus \vec{v}\right)$

In scalar form, the angular momentum $J$ of a point mass $m$ rotating with an angular velocity $\omega$ at a radius $r$ about an axis is given as

$J = m v r$

$J = m \left(r \setminus \omega\right) r$

$J = m {r}^{2} \setminus \omega$

$J \setminus \propto {r}^{2}$

The above equation shows that the angular momentum of a rotating body varies with the square of radius $r$.

In case of an extended body $r$ is the distance of center of mass from the axis of rotation.