Question

The wheel of a motor, accelerated uniformly from rest, rotates through 2.5 radian during the first second. Find the angle rotated during the next second.

• A. 10 rad
• B. 7.5 rad
• C. 5 rad
• D. 12.5 rad

Answer 1

The correct option is B

7.5 rad

As the angular acceleration is constant, we have

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

Thus, 2.5 rad = $\frac{1}{2}$ $\alpha$ $(1s{)}^2$

$\alpha$ = 5 $rad/s^2$

or $\alpha$ = 5 $rad/s^2$

The angle rotated during the first two seconds is

= $\frac{1}{2}\times \left(5\frac{rad}{s^2}\right)(2s{)}^2$ = 10 rad.

Thus, the angle rotated during the $2^{nd}$ second is 10 rad - 2.5 rad = 7.5 rad.