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 rad/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) 68 s
B) 64 s
C) 62 s
D) 66 s
E) 70 s

Question

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 rad/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)  68 s
B)  64 s
C)  62 s
D)  66 s
E)  70 s

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 \, \text{rad/s} $ is the angular velocity and $ \alpha = 1.5 \, \text{rad/s}^2 $ is the angular deceleration. Thus, $ t = \frac{96}{1.5} = 64 \, \text{s} $.

A Machinist Turns on the Power on to a Grinding 1.5rad/s21.5 \mathrm { rad } / \mathrm { s } ^ { 2 }1.5rad/s2

A Machinist Turns on the Power on to a Grinding $1.5 \mathrm { rad } / \mathrm { s } ^ { 2 }$