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

 

[PJC01]

Hello there,

Thank you for bringing up this interesting topic. I can provide some insight into the concept of gyroscope precession and its relation to angular momentum and energy.

Firstly, let's define what a gyroscope is. It is a spinning object with a fixed axis of rotation, often in the form of a disc or wheel. When a force is applied to a gyroscope, it will experience a torque, which causes it to precess or rotate around a different axis.

Now, let's look at the concept of angular momentum. This is a property of a rotating object that is a combination of its rotational speed and mass distribution. In a gyroscope, the angular momentum is initially in the horizontal direction, as the disc is spinning around its fixed axis. However, when a torque is applied, the direction of this angular momentum changes, causing the disc to precess.

So, where does the angular momentum in the vertical direction come from? It is actually a result of the conservation of angular momentum. When the disc precesses, its angular momentum in the horizontal direction decreases, but it is conserved by increasing the angular momentum in the vertical direction. This is similar to the concept of a spinning top, where the spinning motion causes it to stay upright.

Now, let's talk about the energy involved in precession. As you correctly pointed out, there is no change in gravitational potential energy during precession, as the motion is confined to the horizontal plane. However, there is a transfer of energy from the spinning motion of the disc to the precessing motion. This is known as kinetic energy transfer, where the energy of the spinning disc is converted to the energy of precession.

I hope this helps to clarify your understanding of gyroscope precession and its relation to angular momentum and energy. Keep exploring and asking questions, it's the key to scientific discovery.