Question

Part complete 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 90 rad/s. the wheel is run at that angular velocity for 29 s and then power is shut off. the wheel decelerates uniformly at 1.8 rad/s2 until the wheel stops. in this situation, the time interval of angular deceleration (slowing down) is closest to:

Answer 1

As we know from the equation of kinematics

$w = w_0 + \alpha * t$

here it starts from rest

final angular speed will become 90 rad/s in time interval of t = 10 s

now we will have

$0 = 90 + (-1.8)* t$

$t = 50 seconds$

So it will stop after 50 seconds of constant deceleration.