Gyroscope Precession: Understanding Angular Momentum & Energy

[transparent]

Hello. I know there are quite a few threads about this, but I couldn't find what I was looking for. This topic has been driving me crazy over the last couple of days. I know the cause behind the precession. It's because the torque due to gravity about the pivot tends to rotate the already present angular momentum vector since it is always perpendicular. This is only possible by rotating the wheel itself, thus causing the precession. What I don't understand is where the angular momentum in the vertical direction comes from, since it was not present initially. There is no torque in the vertical direction. And what about the energy due to precession? Is it because of some change in gravitational potential energy? This seems unlikely since the entire motion of the centre of mass of the disc is in the horizontal plane. Any help will save me from insanity.

 

[Doug Huffman]

Find an old Sperry Gyroscope technical manual.

 

[Matterwave]

Hello. I know there are quite a few threads about this, but I couldn't find what I was looking for. This topic has been driving me crazy over the last couple of days. I know the cause behind the precession. It's because the torque due to gravity about the pivot tends to rotate the already present angular momentum vector since it is always perpendicular. This is only possible by rotating the wheel itself, thus causing the precession. What I don't understand is where the angular momentum in the vertical direction comes from, since it was not present initially. There is no torque in the vertical direction. And what about the energy due to precession? Is it because of some change in gravitational potential energy? This seems unlikely since the entire motion of the centre of mass of the disc is in the horizontal plane. Any help will save me from insanity.

This can be analyzed using the Euler's equations...which I haven't worked with in several years. However, I'd like to point out that there does not necessarily need to be a torque in order for precession to be present. In fact, since the force of gravity acts on the center of mass of the system, it does not, if I recall correctly, present a torque to the system if the system is rotating about its principle axes. The Earth, for example, is in free fall orbit and there are no torques really acting on it, and yet its rotation precesses once every ~10,000 years. There is also a nutation present.

Maybe look here for some more details:
http://en.wikipedia.org/wiki/Euler's_equations_(rigid_body_dynamics)

 

[drragonx]

I'd suggest watching this video.

http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/lecture-24