Question

Starting from rest a wheel rotates with uniform angular acceleration $2\pi rad/s^2$ . After $4s$, if the angular acceleration ceases to act , its angular displacement in the next $4s$ is:

• A. $8\pi rad$
• B. $16\pi rad$
• C. $24\pi rad$
• D. $32\pi rad$

Answer 1

The correct option is D $32\pi rad$

Angular speed at the end of first $4$ sec

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

$=0+2\pi \times 4$

$=8\pi rad/sec$

As after $4$ seconds, the angular acceleration ceases to act , hence wheel will keep rotating with $8\pi rad/sec$ afterwards.

Hence angular displacement in the enxt $4$ second is

$=\omega t$

$=8\pi \times 4$

$=32\pi rad$