How many revolutions

Question

A fan rotating with an initial angular velocity of 1500rpm is switched off. In 2.00s, the angular velocity decreases to 450rpm. Assuming the angular acceleration is constant, how many revolutions does the blade undergo during this time?

Answer 1

The angular acceleration ∝= (450-1500)/2= -525 rpm/sec = -1583 rad/sec². The angle rotated in this period = .5*1583*2²= 3166 radians or 504 revolutions.