Question

The motor of an engine is in rotation about its axis with an angular velocity of 100 rev/min. It comes to rest in 15s after being switched off, assuming constant angular deceleration. What is the number of revolutions made by motor before coming to rest?

• A. $12.5$
• B. $40$
• C. $78.25$
• D. $15.6$

Answer 1

Answer: (A)

According to equation of motion (angular),
$0=\omega_{0}-\alpha t$
$\Rightarrow \alpha=\frac{\omega_{0}}{t}$
$=\frac{(100 \times 2 \pi) / 60}{15}=0.69 rad / s ^{2}$
Now, angle rotated before motor coming to rest will be
$\theta=\frac{\omega_{0}^{2}}{2 \alpha} $
$\Rightarrow =\frac{\left(\frac{100 \times 2 \pi}{60}\right)}{2 \times 0.7}=78.25 rad$
$\therefore $ Number of revolutions $=\frac{\theta}{2 \pi}=12.5$