The Mystery of the Speeding Grinding Wheel

19 May 2024

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.