At t = 0 s a flywheel is rotating at 30 rpm. A motor gives it a constant acceleration of 0.9 rad/s^2 until it reaches 70 rpm. The motor is then disconnected. How many revolutions are completed at t = 20 s?

Answer 1

1 rpm = 2pi rad/min = 2pi/60 rad/sec = pi/30 rad/sec = .1047 rad/sec

So, to increase from 30rpm to 70rpm is a change of 40rpm = 4.1888 rad/sec

This will take 4.1888/.9 seconds at .9rad/s^2 = 4.65 sec

During this 4.65 sec, it will complete 1/2 * .9 * 4.65^2 = 9.7 rad = 1.55 rev

The remaining 15.35 sec will complete 15.35*7.329 = 112.5 rad = 17.9 rev

So, the total revolutions = 19.5