Question

Angular velocity of a particle is $\omega =\frac{{\theta }^2}{2}$, where $\theta$ is angular position of particle. Tangential acceleration of particle when it has covered $1$ revolution in a circle of radius $2\text{m}$ is

• A. $4{\pi }^3$
• B. $8{\pi }^3$
• C. $2{\pi }^3$
• D. $16{\pi }^3$

Answer 1

The correct option is B $8{\pi }^3$

Given $\omega =\frac{{\theta }^2}{2}$
Relation between tangential and angular acceleration is
$a_t=r\alpha =r\omega \frac{d\omega }{d\theta }$
$a_t=\left(2\right)\left(\frac{{\theta }^2}{2}\right)\left(\theta \right)(\because r=2)$
$a_t={\theta }^3$
for one revolution, $\theta =2\pi$
$a_t=8{\pi }^3.$