Question

Obtain equation of angular velocity as a function of time for rotating bodies with constant angular acceleration from the first principles.

Answer 1

The angular acceleration is uniform, hence

$\frac{d\omega }{dt}=\alpha =$ constant ....................$\left(i\right)$

Integrating this equation,

$\omega =\alpha dt+c$

$=\alpha t+c$(as $\alpha$ is constant)

At $t=0,\omega ={\omega }_0$(give)

From $\left(i\right)$ we get at $t=0,\omega =c={\omega }_0$

Thus, $\omega =\alpha t+{\omega }_0$ as required.