Rotational kinetic energy of a fly wheel.

[leoflindall]

Homework Statement

The moment of inertia of a fly wheel about it's axis is 20 kg m². A constant torque of 40 N m is applied to the initially stationary fly wheel. Find it's rotational KE after 3 seconds assuming there is no friction in the system?

Homework Equations

KE=[tex]\frac{1}{2}[/tex]I[tex]\omega[/tex]²
I=mr²
a=r[tex]\omega[/tex]²
[tex]\tau[/tex]=Fr , where [tex]\tau[/tex] = torque.

The Attempt at a Solution

I know I have to work out the angular frequency. Knowing the torque applied to the wheel for a given time I should be able to work out the speed after 3 seconds, but I don't know the radius of the wheel. so I think I need to work out the angular velocity and radius, and then I can work out KE. But I can't see how to do this?

Can anyone give me any advice?

 

[gneill]

Consider an analogous linear problem: A object of mass M = 20 kg is on a frictionless surface. A constant force of 40 N is applied to the initially stationary mass. Find its kinetic energy after 3 seconds.

What would your procedure be?

 

[leoflindall]

Use Newton's second law to work out the acceleration, and then the speed and then use 1/2 m v² for the energy.

I was looking to do something similar, but I don't have the mass of the fly wheel to determine the acceleration, nor the radius to determine the acceratory force from the torque. Unless I have missed something - I don't do a lot of mechanics!

I know I'm missing something simple here!

 

[gneill]

I know I'm missing something simple here!

Yes, the moment of inertia is the analog of mass for rotational motion. Torque is analogous to force. Angular velocity is analogous to velocity.

 

[SteamKing]

You're missing a key equation. The applied torque is proportional to the angular acceleration. T = I a where T is the torque, I is the moment of inertia, and a is the angular acceleration. If you know a and you know how long it is applied, can you find the angular velocity?

 

[leoflindall]

I knew I was missing something, with that equation it's easy.

Thank you

Leo