In zero gravity, a moving object will stay in motion until it's stopped or slowed by something else, correct? If you were to create a turbine in zero gravity, could you start it spinning very fast using an extremely small amount of thrust, then just let it keep moving on its own inertia until it needs another little bit of thrust to counteract the friction from the brushes?
Lets break it down;
In zero gravity, a moving object will stay in motion until it's stopped or slowed by something else, correct?
Zero gravity AND zero atmosphere, yes. Either on their own, this is not necessarily true, and honestly in this case the atmosphere is the more important issue.
Really, even in zero grav and zero atmo, it's still technically false for anything spinning that doesn't satisfy cylindrical symmetry along the axis of rotation, since gravity waves, but for all practical purposes...
could you start it spinning very fast using an extremely small amount of thrust,
In a vacuum, if it was very light or the thrust was constant for a long time, yes. Acceleration is still a function of both force and mass (which for rotational cases becomes the moment of inertia, i.e. a function of both the mass, AND it's distribution relative to the axis of rotation), so a tiny force won't instantaneously get you up to high speeds, but in a vacuum, the absence of friction would allow such a thing if the force is constant for long enough. Of course, if it's in a vacuum, I'm not sure turbine is the right name for it, since a turbine is an object that generates rotation from the movement of a fluid (be it a gas or a liquid).
then just let it keep moving on its own inertia until it needs another little bit of thrust to counteract the friction from the brushes?
Anything that draws power from the turbine will slow it down; whether that's in the form of atmosphere being moved out of the way, or brushes causing friction, or the current drawn from it, that will be constantly braking it. Since you specified a tiny thrust, it's quite possible that said braking would be greater than the thrust, and hence it would eventually slow down even under conster thrusting.
HOWEVER, one possibility here is using the turbine as a
flywheel instead; note the second case they list. If you got your spinning object up to very high speeds in a vacuum without tapping it, you would then in effect be able to use it as a mechanical battery, tapping it for higher power over shorter time frames.