Power and Torque

Once it's turning with N=100rpm, power = torque = 0 (neglecting friction, which we must since you haven't told us anything about it).

Realistically, you need to say what run-up time you're looking for (which will probably be the most significant factor in the final torque figure), and give some estimate of the friction.

What JohnDG means is that, if you need the speed to be constant, you're not going to spend energy except for compensate for the friction in the wheels bearings and between them. What is the bearings geometry, type, arrange? Maybe someone can give some tips and estimate it. Besides I agree that the speeding-up time would count with most of the required power installation: if you install a motor that is capable of accelerating the mass to the desired speed under a desired amount of time, it will easily maintain the speed with a lot less energy.

A picture would be nice.

In terms of classical freshman physics it appears to be a very straight forward problem.

Given the change in rotational energy as ΔE= ½IΔω²

Where I= moment of inertia and ω=angular velocity.

By introducing the time component and referring to the definition of power as the rate of doing work then the rate change in energy would approximate the power required to accomplish that change.

ΔΕ/Δt= (½IΔω²)/Δt = Power

If you are going be accelerating your primary wheel with an acceleration wheel then the rate of acceleration will be limited by the force by which the acceleration wheel is pressed against the primary wheel and the coefficient of static friction of the wheels interface. This limiting friction force will define the torque that can be applied to the acceleration wheel before the wheels begin to "slip."

This same method can be used to estimate the power required to accelerate linear systems where the power required is the rate change of the linear kinetic energy(½mv²) of the system. One of the comparisons I have made is the power required to accelerate 1000kg of mass to 1/4 the speed of light in one year to the power that would be required to accelerate that same mass to the approximate heliocentric hyperbolic speed of the fastest human space probes in three days.

Gavilan