Question

A machinist turns the power on to a grinding wheel, which is at rest at time t = 0.00 s. The wheel accelerates uniformly for 10 s and reaches the operating angular velocity of 25 rad/s. The wheel is run at that angular velocity for 37 s and then power is shut off. The wheel decelerates uniformly at 1.5 rad/s2 until the wheel stops. In this situation, the time interval of angular deceleration (slowing down) is closest to:

A) 17 s B) 15 s C) 19 s D) 21 s E) 23 s

Answer 1

Hello there.

A machinist turns the power on to a grinding wheel, which is at rest at time t = 0.00 s. The wheel accelerates uniformly for 10 s and reaches the operating angular velocity of 25 rad/s. The wheel is run at that angular velocity for 37 s and then power is shut off. The wheel decelerates uniformly at 1.5 rad/s2 until the wheel stops. In this situation, the time interval of angular deceleration (slowing down) is closest to:

A) 17 s

Answer 2

I have some notes here that might help you answer the problem on your own:

α = dω / dt

Angular acceleration is derivative of angular velocity the same way as linear acceleration is derivative of linear velocity
a = dv / dt

I hope my answer has come to your help. God bless and have a nice day ahead!