Question

The motor of an engine is rotating about its axis with an angular velocity of 120 rev/minute. It comes to rest in 10 s, after being switched off. Assuming uniform angular deceleration, find the number of revolutions made by it before coming to rest.

Answer 1

The initiai angular velocity = 120 rev/minute = $\left(4\pi \right)$ rad/s.
Final angular velocity = 0
Time interval = 10 s.
Let the angular acceleration be a. Using the equation $\omega ={\omega }_0+\alpha t$ we obtain
$\alpha =(-4\pi /10)$ rad/s${}^2$
The angle rotated by the motor during this motion is
$\theta ={\omega }_{0}t+\frac{1}{2}\alpha t^2=\left(4pi\frac{rad}{s}\right)\left(10s\right)-\frac{1}{2}\left(\frac{4\pi }{10}\frac{rad}{s^2}\right)(10s{)}^2$
$=20\pi rad=10$ revolutions.
Hence the motor rotates through 10 revolutions before coming to rest.