How does mass affect angular velocity?

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How does mass affect angular velocity?

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Answer 1 · 2018-07-04T09:31:07

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

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How does mass affect angular velocity?

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