A wheel free to rotate about its axis that is not frictionless is initially at rest. A constant external torque of +44 N·m is applied to the wheel for 23 s, giving the wheel an angular velocity of +520 rev/min. The external torque is then removed, and the wheel comes to rest 120 s later. (Include the sign in your answers.)
a) Find the moment of inertia of the wheel.
b) Find the frictional torque, which is assumed to be constant.
Torque = Intertia x angular acceleration
Inertia = (mr^2)/4
This is the inertia for a solid disk
angular acceleration = angular velocity/time
The Attempt at a Solution
So heres my attempt I started by changing the 520 rev/min to...
520 rev/min * 1 min /60 sec = 8.67 rev/sec
8.67 rev/sec * 2 pi rads/1 rev = 17.33 pi rads /sec
After that I wanted the angular velocity so I did...
17.33 pi rads/sec / 23 seconds = 2.368 rads / sec^2
With the angular velocity I found the angular acceleration to be...
a = 2.368/23 sec = .1029 rads / sec^2
I know I'll have to use that to solve for the Torque (I think)
What I'm really stuck on is getting a) The moment of intertia of the wheel.
I = (mr^2)/4
I don't know where to get the r from, and maybe that equation is wrong overall which is another thing I am confused about.
If I can get that I believe I would just use the angular acceleration I got and the Intertia to get the Torque.
Any help towards the right direction would be greatly appreciated, thanks :)