Question

How does mass affect angular velocity?

Answer 1

For a freely rotating rigid body

`omega\prop1/m`

Explanation:

For a freely rotating rigid body having mass `m`, radius of gyration `k` & an angular velocity `omega`, net torque `T_{\text{net}}` on the body must be zero

`T_{\text{net}}=0`

`I(\frac{d\omega}{dt})=0`

`\frac{d(I\omega)}{dt}=0`

`I\omega=\text{const}`

`mk^2\omega=\text{const}`

`\omega=\frac{\text{const}}{mk^2}`

`omega\prop1/m`

thus when the mass `m` of a freely rotating rigid body increases its angular velocity `\omega` decreases & vice-versa