Question

Does angular momentum change with radius?

Answer 1

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

Explanation:

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

`\vec J=m(\vec r\times \vec v)`

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=mvr`

`J=m(r\omega)r`

`J=mr^2\omega`

`J\prop 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.