Question

Starting from rest, a particle rotates in a circle of radius $R=2m$ with an angular acceleration $\alpha =\pi /4rad/s^2$.The magnitude of average velocity of the particle over the time it rotates quarter circle is

• A. $2\pi$
• B. $\frac{\pi }{2}$
• C. $3\pi$
• D. $4\pi$

Answer 1

The correct option is B $\frac{\pi }{2}$

Taking all parameters as :

Angular acceleration in $rad/s^2$.

Angular displacement as $rad$.

Angular Velocity as $rad/s$.

So $\alpha =\frac{\pi }{4}$.

$\theta =\frac{\pi }{2}$.

$w_i=0,w_f=?$.

$t=?$

Using equations of constant acceleration $w_f^2-w_i^2=2\alpha \theta$

$w_f=\frac{\pi }{2}$ and

$\theta =w_i.t+\frac{1}{2}\alpha .t^2$ ,

$t=2sec$,

$v=w.r$,

$v_f=\pi ,v_i=0$ so average velocity is $\frac{\pi }{2}$