Calculating power from a prescribed rotation

[JTC]

Hi,

Forgive me for this trivial question. I am confused.

Let's say I have a gyroscopic device in which the rotor is set to spin at a prescribed angular velocity.
Next, put it on an ocean surface in which the ocean waves induce a precession.
These two rotations, then induce a moment (induce a nutation), M (I name this torque, because my question is about this).

Power is the angular velocity times the moment.

Now suppose I set up the equations -- and input the precession and spin -- and get a system in which I compute the angular velocity corresponding to the nutation.

So how do engineers calculate power. It seems I can calculate the induced angular velocity or the induced angular moment (one or the other), but now do we calculate the power: I have one or the other, but not both.

In other words, in my naive understanding, I can generate an angular velocity. If I restrain the angular velocity, I can get an induced moment. But if it is free to rotate, how does one compute the power?

I must be missing a big step.

 

[Baluncore]

Power is the angular velocity times the moment.

A system will have an initial total energy that is distributed amongst potential and kinetic state variables. Changes to the system over time will result in energy flowing between the state variables of the system. You must account for the total energy because energy is conserved. Time is not important to the double entry book keeping.

Power is fundamentally the rate of flow of energy. Time is then important because there must be an “engine” that converts or transfers energy between state variables. You must install an engine with a sufficient power rating to handle the required maximum energy flow. The cost of an engine is usually proportional to power, but you only have to install and pay for the engine once.

Power is not conserved. You must pay for the energy you use, not for the power.