In response to a question someone asked, I wondered how a gyroscope works? Specifically, why does it do what it does? One classic experiment is done at many science museums, like the Exploratorium. Get a bicycle wheel, tie a string/rope to one side of the axle, spin the wheel vertically, and hang it on the string. It doesn't fall down, it stays upright, but "precesses" around (as if it were going around a corner).
Think about a small piece on top of the wheel. When you hang it, that piece is being pushed away from the string.
But it's already moving. When you add the inertia to the force that's trying to make it fall, you change it's direction of motion slightly. So now it's path is going to "precess" around the string a bit.
The same logic applies to the bottom, in the reverse, but the effect is added so top and bottom work together to cause the wheel to turn.
BUT, you might ask, what about the sides? Fair enough, and I had to think about it a gazillion times. Turns out that they TRY to precess, but the 2 sides cancel each other out.
OKAY, you say, what about when it's standing up?
Another fair question.
-- First, you can't ever stand it up perfectly straight.
-- Even if you could, it's not made perfectly.
-- And in the event you did, it would just balance until it stopped.
But when it's just a bit off, it spins around. Exactly the same thing is happening, but the forces are less, so the precession proceeds more slowly. If you watch carefully, as it becomes less and less straight up, it spins (precesses) faster, because the gravity trying to topple it is stronger. Hanging it, as in the bicycle wheel and string above, is the extreme case.
I could go on, but I think this horse is as dead as I can get it.