A grinding wheel is initially at rest. A constant external torque of 52.5 N· m is applied to the wheel for 18.4 s, giving the wheel an angular speed of 605 rev/min. The external torque is then removed, and the wheel comes to rest 101 s later. Find the moment of inertia of the wheel.
Torque = I * a
The Attempt at a Solution
Since Torque is equal to external torque + frictional torque, i decided to calculate what the acceleration would be without frictional torque to remove that variable. So I calculated the acceleration first, 605rev/min * 1 min / 60 sec = 10.08333 rev/s. 10.083333 rev/s divided by 18.4 sec is 0.548 rev/s^2, * 2pi = 3.44 rad/s^2. Then 10.083333 rev/s divided by 101 sec = 0.0998349835 rev/s^2. Multiplied that by 2 pi to get 0.62728 rad /s^2 and then added it to the original acceleration to get 4.0705 rad/s^2, the angular acceleration without friction. Then 52.5 = 4.0705 * I, to get 12.9 kg*m^2. This isn't right.
I'm assuming this strategy doesn't work. How else can I do it? Thanks for any help.