The Mystery of the Speeding Grinding Wheel
What is the average angular acceleration of a grinding wheel that speeds up from 2.0 rad/s to 11.0 rad/s in 5.5 seconds?
The average angular acceleration of the grinding wheel is:
a. 9.6 rad/s
b. 4.8 rad/s
c. 1.6 rad/s
d. 0.33 rad/s
To calculate the average angular acceleration of the grinding wheel, we can use the formula for angular acceleration:
Angular acceleration (α) = (Final angular velocity - Initial angular velocity) / Time taken
Given:
Initial angular velocity (ωi) = 2.0 rad/s
Final angular velocity (ωf) = 11.0 rad/s
Time taken (t) = 5.5 seconds
Plugging in the values:
α = (11.0 - 2.0) / 5.5 = 1.63 rad/s²
Therefore, the correct answer is option 'c': 1.6 rad/s
So, the average angular acceleration of the grinding wheel as it speeds up is 1.6 rad/s².