For quick reference, what are the equations for calculating the moment of a fly wheel? (A disk of mass, not just a weight on a stick, if that matters). I know that there are other things too, like bearing load/friction, drag, etc. Am I missing anything?

And how would I calculate the energy lost if I was to, say, use it to be momentarily loaded with a foam ball? (This may be too much for simple calculations, I’ll guess and test if I have to.) Thanks!

Several things. Moment of a solid disk is 1/2mr^2. Moment of a solid ring is mr^2. Energy loss is easy. Figure out how fast you want your ball to come out and you know its kinetic energy. It had to come from somewhere, right? I’d figure 50% efficiency transferring it from the wheel to the ball to be really safe. Kinetic energy of rotation is 1/2I*omega^2 if you want to figure out how much your wheel slows down. (omega is rotational speed in rads/sec).

Finally, I’ve just uploaded a whitepaper that will calculate the time to spin up a flywheel based on the motor characteristics and flywheel dimensions. Check for it in a few hours.