Question

A disc rotating about its axis, from rest it acquires a angular speed $100rev/s$ in $4$ second. The angle rotated by it during these four seconds (in radian) is

• A. $100\pi$
• B. $200\pi$
• C. $300\pi$
• D. $400\pi$

Answer 1

The correct option is D $400\pi$

Initial angular speed, ${\omega }_o=0$ $rad/s$

Final angular speed, $\omega =100$ $rps$

$⟹\omega =100\times 2\pi$ $rad/s$

$⟹\omega =200\pi$ $rad/s$

Time, $t=4$ $s$

From kinematics:

$\omega ={\omega }_o+\alpha t$

$⟹200\pi =4\alpha$

$⟹\alpha =\frac{200\pi }{4}$ $rad/s^2$

where, $\alpha$ is angular acceleration.

Also,

$\theta ={\omega }_{o}t+\frac{1}{2}\alpha t^2$

$⟹\theta =0+\frac{1}{2}\times \frac{200\pi }{4}\times 16$

$⟹\theta =400\pi$