Question

A solid body starts from rest. Angular acceleration of the body spinning about a stationary axis is given by $\alpha =2\cos \theta$ (in $rad/s^2$) where $\theta$ is the angle of rotation from initial position. Then which of the following graphs correctly represents the variation of angular velocity with respect to $\theta$?

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Angular acceleration, $\alpha =2\cos \theta$
$\Rightarrow \alpha =\omega \frac{d\omega }{d\theta }=2\cos \theta$
Integrating on both sides,
${\int }_0^{\omega }\omega d\omega =2{\int }_0^{\theta }\cos \theta d\theta$
$\Rightarrow {\left[\frac{{\omega }^2}{2}\right]}_0^{\omega }={\left[2\sin \theta \right]}_0^{\theta }$
$\Rightarrow w=2\sqrt{\sin \theta }rad/s$
$\sin \theta$ is positive between 0 & $\pi$. So option A is correct.