Gyroscope precession

I have a system diagrammed and explained in the image below.

Experimentally I believe the wheel will rotate around the pivot point where the cable is attached in a counter-clock motion if observed from above. However, theoretically why this would be so is confusing me. It seems to me that all linear forces (weight and tension) cancel and the only force not canceled is the torque force. But if I understand this torque force in the same way that I understand, say, a wrench being applied to a nut, then the the arm $\vec{r}$ and the force $\langle 0, -mg\rangle$ would only contribute to a rotational motion in the $yz$-plane.

Clearly the analogy must be bad and the part that's screwing it up is the fact that unlike the nut, this system has momentum. But I thought the momentum due to rotation was not of the system at the pivot where the cable was attached but rather was of the rotation of the wheel about its center. I don't see how that transfers over to momentum about the pivot where the cable is attached.

Am I fundamentally misunderstanding something here?

[Edit: As I think about this, maybe a better question to ask is, since the wheel spins around the pivot point where the cable is attached, there must be some force causing this motion. I assume it's a centripetal force since the motion seems roughly circular, so where does this force come from? Still, my thought is that it can't be the torque force because that's supposed act perpendicular to the plane of motion and here the torque is not in the right direction for that.]

• Dec 29, 2015 at 6:12