Does angular momentum change with radius?

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Answer 1 · 2018-07-27T18:10:04

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

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.