# Understanding gyroscopes

Considering the typical situation of a rotating bicycle wheel held by one end of its axle by a rope tied to the ceiling: gravity torque is the time derivative of the angular momentum, and in this case is perpendicular to the angular momentum vector which makes it revolve without changing its magnitude (it precesses).

My question is the following: the wheel stops turning eventually because of the friction in the string (it also slows down its own rotation because of friction in the bearing but let's ignore it), but could you clarify how, step by step? Is it because the gyroscope creates a torque on the string axis, but it's reduced by the friction torque, and as a result the friction torque translates back into a residual "gravity torque" (in other terms, the gyroscope "gives up" on a certain amount of gravity torque it can't counteract because of the string)?

To progress toward my actual problem in several dimensions, what if the friction torque is in fact torque given by another gyroscope on the same solid?

• I am having a hard time figuring out what it is you are trying to describe, could you upload an image of the system? Also, what are "gravity torque" and "friction torque," I have never heard of such things. – Kyle Kanos Feb 26 '14 at 18:12
• Thanks for your answer. I updated the description with a link to one of many videos that take pretty much the same example everytime. As for the torques, I should probably have been more precise in saying those are torques generated by the weight of the wheel on the one side and by the friction in the torsion of the string on the other. – Mister Mystère Feb 26 '14 at 22:43
• As usual there is much to be gained by reading 'It Has to Go Down A Little, In Order to Go Around'- Following Feynman on the Gyroscope. The short-short version is that our usual classroom explanation is incomplete, and shows that a slightly more complete version reproduces much more of the dynamics. – dmckee --- ex-moderator kitten Jul 17 '14 at 14:14

## 1 Answer

I'm guessing that you understand clearly the effect of precession here. The reason why the wheel starts to fall down is that when we explain the change in angular momentum of the wheel, we say that the angular momentum vector only changes in direction- right? But the angular momentum vector of the wheel doesn't only point outwards; it also points upwards (it has an upwards and an outwards component). The outwards component is the one that most people keep in mind- it's due to the rotation of the wheel about its center. But the upwards component of angular momentum is due to the rotation of the wheel about the rope.

When considering the torque on the wheel, we can assume that the only thing the torque will do is change the direction of the outwards component of angular momentum (when there's no friction). So, we 'blame' this change of angular momentum on the torque exerted by the wheel's weight, and everything's fine. However, due to friction, the wheel's rotation about the rope slows down, resulting in a change in magnitude of the upwards-pointing component of angular momentum. This equates to a downwards pointing torque on the wheel, which will make it begin to fall.

I had a lot of trouble understanding the phrasing in your question- I hope this is what you were doubtful about. As for your second questions, I have no idea what you meant ("What if the friction torque is in fact torque given by another gyroscope on the same solid?").

Hopefully I was of some help, though.

• For some reason I just saw your answer. Thanks a lot, I didn't see it that way. As for the part even more difficult to understand (sorry about that, but that's a difficult subject to grasp, questions are not clear because my mind's not clear about that), I'm talking about coupling 2 gyroscopes together. My ongoing problem about gyroscopes has 3 of them, orthogonal, on the same platform - and I'm wondering if the torques all cancel out. – Mister Mystère Nov 6 '14 at 0:09