Average Power Input for Wheel with Rotational Inertia

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SUMMARY

The average power input to a wheel with rotational inertia I, accelerated from 0 to final speed Wf over a time interval T, is calculated using the formula P = (IWf^2) / T. The initial attempt to compute power at a single moment was incorrect, as it did not account for the average over the entire interval. To find the average power, one must integrate the power function over the time interval and divide by T, ensuring the calculation reflects the varying power input throughout the acceleration period.

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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?
 
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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.
 
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.
 

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