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## Homework Statement

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.

## Homework Equations

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 here's 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 :)