Question

A stationary wheel starts rotating about its own axis at uniform angular acceleration $8rad/s^2$ . The time taken by it to complete $77$ rotations is:

• A. $5.5s$
• B. $7s$
• C. $11s$
• D. $14s$

Answer 1

Answer: (C)

$11s$

From the equations of circular motion, we get:

$\theta ={\omega }_{0}t+\frac{1}{2}\alpha t^2$

From the given conditions,

$\theta =77\times 2\pi rad$, $\alpha =8rad/s^2$ and ${\omega }_0=0$ as the wheels starts rotating from rest
So, we get:

$77\times 2\pi =\frac{1}{2}\times 8\times t^2$
or, $t=11s$