Average Power Input for Wheel with Rotational Inertia

AI Thread Summary
The discussion focuses on calculating the average power input to a wheel with rotational inertia as its speed increases from 0 to Wf over a time interval T. The net torque is defined as IWf/T, leading to an initial attempt to calculate power using P=torque*angular velocity, resulting in P=(IWf^2/T). However, this approach only evaluates power at a specific moment rather than averaging it over the entire interval. The correct method involves integrating power over the time interval and dividing by T to find the average. Participants highlight the importance of considering power at various points in time to accurately determine the average input.
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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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