Question

A fan rotating with an initial angular velocity of 1000 rev/min is switched off. In 2 seconds, the angular velocity decreases to 200 rev/min. Assuming the angular acceleration is constant, how many revolutions does the blade undergo during this time.
A) 10
B) 20
C) 100
D) 125
E) 1200

Answer 1

The average angular acceleration of the fan is

$\alpha_{\rm avg}=\dfrac{\Delta\omega}{\Delta t}=\dfrac{200\frac{\rm rev}{\rm min}-1000\frac{\rm rev}{\rm min}}{2\,\rm s}=-6.67\dfrac{\rm rev}{\mathrm s^2}$

The number of revolutions after time $t$ is given by

$\theta=\omega_0t+\dfrac{\alpha}2t^2$

Acceleration is assumed to be constant, so $\alpha=\alpha_{\rm avg}$ and over the 2 second interval we have

$\theta=\left(1000\dfrac{\rm rev}{\rm min}\right)(2\mathrm s)+\dfrac{\alpha_{\rm avg}}2(2\,\mathrm s)^2=20\,\mathrm{rev}$

so the answer is A.