Rotating wheel, proving that power is proportional to square of torque

[djfusion777]

I have a mechanics question.

"A wheel starts from rest and rotates with constant angular acceleration about a fixed axis.

1) Prove that the power at any given time is proportional to the square of the net torque about the axis.

2) Prove that the power at any given angular displacement is proportional to the 3/2 power of the total torque about the axis at that angular displacement"

I know that Torque = r x F

Power in this case is rate of change of rotational Kinetic Energy, Ek = 1/2I (omega)^2 where I = moment of inertia.

No idea where to go from here, any help much appreciated!

 

[blochwave]

That's not the only thing torque equals. This problem doesn't mention force, it does mention angular acceleration though, hmmmmz...

A decent place to start, since you have an expression for Ek and you know you're looking for something dealing with the rate of change of Ek, is to find that rate of change of Ek, eh?

 

[tiny-tim]

ignore force, go for angular momentum

See http://en.wikipedia.org/wiki/Torque:​

torque can be defined as the rate of change of angular momentum

Does that help?

 

[blochwave]

I wouldn't take that approach, I was thinking torque=I*angular acceleration, then take the time of derivative of Ek, and you're about one substitution away from beautiful victory