Average Power Input for Wheel with Rotational Inertia

[lzh]

Homework Statement

A wheel with rotational inertia I is mounted on a fixed motionless axle. The singular speed w of the wheel is increased from 0 to Wf in a time interval T.
Net torque=IWf/T

What is the average power input to the wheel during this time interval?

Homework Equations

P=torque*angular velocity

The Attempt at a Solution

P=(IWf/T)*Wf=(IWf^2/T)
This isn't right though, what am I doing wrong?

 

[diazona]

Think about this: what's the power input at t = 0? Or at t = T/2? Or generally, at any time between 0 and T? You only calculated the power input at one particular time, but the problem asks for the average.

 

[lzh]

I was thinking of finding the integral of the power from 0 to T and then divide everything by T. But for some reason the answer is coming out weird.