Question

Angular acceleration of a circular disc which is initially at rest, about a stationary axis is $\alpha =8\cos 2t$ (in ${\text{rad/s}}^2$). Which of the following graphs correctly represents the variation of angular velocity with respect to time ?

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Given $\alpha =8\cos 2t$
We know that $\alpha =\frac{d\omega }{dt}$
$\Rightarrow \frac{d\omega }{dt}=8\cos 2t$
$\Rightarrow d\omega =8\cos 2tdt$
Integrating on both sides,
${\int }_{{\omega }_0}^{\omega }d\omega ={\int }_0^{t}8\cos 2tdt$
$\omega -{\omega }_0=8\times \frac{1}{2}\sin 2t{|}_0^t$
$\Rightarrow \omega =4\sin 2t\text{rad/s}$
(because ${\omega }_0=0$)
Option A is correct.