Question

A body starts rotating from rest and completes 10 revolutions in 4 sec. Find its angular acceleration

• A. $2.5\pi \text{rad/}{\text{s}}^{\text{2}}$
• B. $5\pi \text{rad/}{\text{s}}^{\text{2}}$
• C. $7.5\pi \text{rad/}{\text{s}}^{\text{2}}$
• D. $10\pi \text{rad/}{\text{s}}^{\text{2}}$

Answer 1

The correct option is A $2.5\pi \text{rad/}{\text{s}}^{\text{2}}$

Given,

N0. of revolution, $n=10$, $1rev=2\pi$

${\omega }_0=0rad/sec$

$\theta =20\pi$ rad

$t=4sec$

2nd equation of motion in rotational motion,

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

$20\pi =0\times 4+\frac{1}{2}\alpha (4{)}^2$

$\alpha =2.5\pi rad/s^2$

The correct option is A.