# Rotational kinetic energy of a fly wheel.

## 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=$$\frac{1}{2}$$I$$\omega$$2
I=mr2
a=r$$\omega$$2
$$\tau$$=Fr , where $$\tau$$ = 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?

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gneill
Mentor
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.

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
Mentor
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
Staff Emeritus