# How does mass affect angular momentum?

Aug 18, 2015

Angular momentum can be written as:

$L = I \omega$

where $I$ is moment of inertia and $\omega$ is rotational velocity.

If we suppose $I = k m {r}^{2}$, where $k$ is some coefficient corresponding to the particular shape of the solid and its axis of rotation, $r$ is the distance to the axis of rotation, and $m$ is the mass, then:

$L = k m {r}^{2} \omega$

With other variables held constant, as mass increases, angular momentum increases. Thus, mass is directly proportional to angular momentum.