# Moment of Inertia and Torque problem

## 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 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...

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 :)

Related Introductory Physics Homework Help News on Phys.org
You have torque and angular acceleration; use that to calculate the moment of inertia of the wheel.

You have torque and angular acceleration; use that to calculate the moment of inertia of the wheel.
Uhm If I use the acceleration I got .1029 rads/sec^2 into the equation T = Inertia x angular acceleration

That would be Intertia = Torque/angular acceleration
Intertia = 44 / .1029
Intertia = 427.6 kg m^2

That didn't get me the right answer and it doesnt look like the right one. Is that what you
ment.

SteamKing
Staff Emeritus
Homework Helper
Your calculation of angular velocity and angular acceleration are incorrect. (Do you really think that angular velocity has units of rad/s^2?)

Your calculation of angular velocity and angular acceleration are incorrect. (Do you really think that angular velocity has units of rad/s^2?)
Ah true...wouldn't the angular velocity and acceleration be this instead then

520 rev/min * 1min/60 sec = 8.67 rev/sec
8.67 rev /sec *2pi rads / rev = 54.454 rads /sec (This would be my actual angular velocity)

So then my angular acceleration would be
a = w/t

This looks right to me, but even if I take this and plug it into Torque = Inertia x angular acceleration the answer for a is wrong.

Ah I finally got the problem, I had to also take into consideration the acceleration of when the wheel was slowing down as well. Add the two accelerations and then use that for
the Intertia.

b) was just using the found intertia to solve for torque

Thanks a bunch to those that helped!