Question

A machinist turns the power on to a grinding wheel, at rest, at time t = 0 s. The wheel accelerates uniformly for 10 s and reaches the operating angular velocity of 58 rad/s. The wheel is run at that angular velocity for 30 s and then power is shut off. The wheel slows down uniformly at 1.4 rad/s2 until the wheel stops. In this situation, the total number of revolutions made by the wheel is closest to:

Answer 1

hint:there is three situation...
1.there is a constant angular acceleration..use \[\theta=\omega _{0}t+1/2\alpha t ^{2}\] and \[\omega=\omega _{0}+\alpha t\]
2.there is no acceleration..use \[\theta=\omega t\]
3.there is constant angular retardation..use\[\omega ^{2}=\omega ^{2} _{0}-2\alpha \theta\]