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),
$0={\omega }_0-\alpha t$
$\Rightarrow \alpha =\frac{{\omega }_0}{t}$
$=\frac{(100\times 2\pi )/60}{15}=0.69rad/s^2$
Now, angle rotated before motor coming to rest will be
$\theta =\frac{{\omega }_0^2}{2\alpha }$
$\Rightarrow =\frac{\left(\frac{100\times 2\pi }{60}\right)}{2\times 0.7}=78.25rad$
$\therefore$ Number of revolutions $=\frac{\theta }{2\pi }=12.5$