A machinist turns on the power on to a grinding wheel at time t = 0 s. The wheel accelerates uniformly from rest for 10 s and reaches the operating angular speed of $96 \mathrm { rad } / \mathrm { s }$ The wheel is run at that angular velocity for 40 s and then power is shut off. The wheel slows down uniformly at $1.5 \mathrm { rad } / \mathrm { s } ^ { 2 }$ until the wheel stops. For how long a time after the power is shut off does it take the wheel to stop?
A) 64 s
B) 62 s
C) 66 s
D) 68 s
E) 70 s

Question

Quizplus · Accepted Answer

The time taken to stop the wheel after the power is shut off can be calculated using the formula $ t = \frac{\omega}{\alpha} $, where $ \omega = 96 \mathrm{ rad/s} $ is the angular velocity and $ \alpha = 1.5 \mathrm{ rad/s^2} $ is the angular deceleration. Thus, $ t = \frac{96}{1.5} = 64 $ seconds.

A Machinist Turns on the Power on to a Grinding 96rad/s96 \mathrm { rad } / \mathrm { s }96rad/s

A Machinist Turns on the Power on to a Grinding $96 \mathrm { rad } / \mathrm { s }$