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# Gyroscopic precession Watch

1. Hey, I'm having a little trouble understanding some ideas about precession. Here's my understanding:

If a spinning wheel is held out horizontally (along the y axis), then it has angular momentum pointing along the y axis. Because weight acts down, a torque is induced which adds angular momentum in the x direction. This causes the angular momentum vector to change direction and rotate around the xy plane.

Firstly, have I said anything particularly stupid there? If I have, could you please explain it and correct me.

Secondly: this doesn't seem consistent. At some point the angular momentum will be oriented along the x axis (having precessed 90 degrees). But that's the direction that the torque generated by weight is in origionally. I know that the torque always acts 90 degrees to the lever arm, my issue is that if it wasn't precessing a torque in this direction would cause the wheel to drop, yet when it's precessing and has an angular momentum that has rotated to be entirely in this direction, it still stays up.

I'm probably getting confused by vector products or somesuch, but a bit of help would be nice.
2. Bump. (Also, I have a vague idea of what might be the right answer, but I'd prefer someone to express it properly than for me to babble as above.)
3. (Original post by lerjj)
Hey, I'm having a little trouble understanding some ideas about precession. Here's my understanding:

If a spinning wheel is held out horizontally (along the y axis), then it has angular momentum pointing along the y axis. Because weight acts down, a torque is induced which adds angular momentum in the x direction. This causes the angular momentum vector to change direction and rotate around the xy plane.

Firstly, have I said anything particularly stupid there? If I have, could you please explain it and correct me.

Secondly: this doesn't seem consistent. At some point the angular momentum will be oriented along the x axis (having precessed 90 degrees). But that's the direction that the torque generated by weight is in origionally. I know that the torque always acts 90 degrees to the lever arm, my issue is that if it wasn't precessing a torque in this direction would cause the wheel to drop, yet when it's precessing and has an angular momentum that has rotated to be entirely in this direction, it still stays up.

I'm probably getting confused by vector products or somesuch, but a bit of help would be nice.
What about the torque due to the rotation?
4. (Original post by Phichi)
What about the torque due to the rotation?
Not sure I understand- why would rotating cause a torque? You need a force to be applied surely, and the only external one acting is weight.
5. (Original post by lerjj)
Not sure I understand- why would rotating cause a torque? You need a force to be applied surely, and the only external one acting is weight.
I was referring to the initial force to cause the rotation and increase in angular momentum. Nevertheless, are you taking the x and y directions as both horizontal? The z being downwards, towards the earth?
6. (Original post by Phichi)
I was referring to the initial force to cause the rotation and increase in angular momentum. Nevertheless, are you taking the x and y directions as both horizontal? The z being downwards, towards the earth?
Yes, weight acting along z axis, lever arm initially aligned along y axis. Then the torque due to the weight is in the x axis (is that correct?). I suppose my question is that since a torque in the x axis would usually cause the spinning wheel to fall (rotate in yz plane), why doesn't this still happen?

EDIT: the setup is shown here:http://hyperphysics.phy-astr.gsu.edu/hbase/rotv2.html but I'm still confused to the reasoning.
7. (Original post by lerjj)
Yes, weight acting along z axis, lever arm initially aligned along y axis. Then the torque due to the weight is in the x axis (is that correct?). I suppose my question is that since a torque in the x axis would usually cause the spinning wheel to fall (rotate in yz plane), why doesn't this still happen?

EDIT: the setup is shown here:http://hyperphysics.phy-astr.gsu.edu/hbase/rotv2.html but I'm still confused to the reasoning.
The torque is directed in the x axis initially, which causes the angular momentum to rotate around the xy plane.
8. (Original post by Phichi)
The torque is directed in the x axis initially, which causes the angular momentum to rotate around the xy plane.
I get that part. My issue is that when there is no initial angular momentum, the torque creates angular momentum in the x axis that causes it to rotate in the yz plane.

This means I should associate a component of angular momentum in the x axis with falling, and since this component increases (for the first 90 degrees anyway) of the precession, why doesn't the gyroscope fall?
9. Have you got half an hour to watch a video?

as the chap says, gyros can be particularly confusing and probably video is the most natural medium to explain them imo.

note that he's using a gimballed gyro which lets the centre of mass of the gyro remain stationary which isn't the case with a gyro supported at one end of an axle, it allows you more control over the forces than leaving it to the weight of the gyro - also he uses cylindical coordinates (2nd part) which are a bit more convenient than (x,y,z)

---
if you're still interested there's an (in)famous TV lecture by the late prof Laithwaite with a lot of gyro demos... but the prof gave some ropey explanations, there's a page now which has correct explanations. (afaict) - http://www2.eng.cam.ac.uk/~hemh/gyro...yroscopes.html the links there to the videos of the Laithwaite lecture have died but you can see it on the RI website http://www.richannel.org/christmas-l...the-jabberwock
10. (Original post by Joinedup)
Have you got half an hour to watch a video?

as the chap says, gyros can be particularly confusing and probably video is the most natural medium to explain them imo.

note that he's using a gimballed gyro which lets the centre of mass of the gyro remain stationary which isn't the case with a gyro supported at one end of an axle, it allows you more control over the forces than leaving it to the weight of the gyro - also he uses cylindical coordinates (2nd part) which are a bit more convenient than (x,y,z)

---
if you're still interested there's an (in)famous TV lecture by the late prof Laithwaite with a lot of gyro demos... but the prof gave some ropey explanations, there's a page now which has correct explanations. (afaict) - http://www2.eng.cam.ac.uk/~hemh/gyro...yroscopes.html the links there to the videos of the Laithwaite lecture have died but you can see it on the RI website http://www.richannel.org/christmas-l...the-jabberwock
I haven't yet watched his second explanation, but surely his first relies explicitly on conservation of angular momentum, which is not valid because he's exerting an external torque? Is there some reason that this isn't true?

More to the point, what's special about the gyro spinning? Surely conservation of angular momentum would be just as happy to cause a precession to keep L=0 ? I'm missing something here (obviously, as the gyro DOES work as is pretty clear).

I'll watch the second part but I'm not that used to polar cords so there' a risk I don't get it...
11. I'm not actually sure this helped much. I don't think I'm expressing very well what I'm having difficulty explaining. Additionally, I don't understand how this can be understood in terms of conservation of angular momentum because a torque is being very visibly applied in all situations demonstrated.

Can someone explain what is wrong with the notion that gravity usually produces a torque in the x direction (using the co-ordinate system discussed above) which causes a body to fall in the z direction (actually a circle in the yz plane). I don't see why the body spinning makes any difference, because I can consider the total angular momentum to be split into two components, one of which is the original spinning and one of which is the falling motion.

There must be something wrong with this, and I suspect it has something to do with the fact that the magnitude of the angular momentum remains constant in real life, whereas in my scenario you keep a constant component of L in the y direction and then gain L in the x direction (the increase in this component causing it to fall).

I'm basically well aware that one of my assumptions is wrong, and I'm trying to explain my current model (which is clearly inconsistent) in as much detail as possible so that someone can tell me what epiphany I'm supposed to be having. Please point out some reasoning I've said that's wrong.
12. (Original post by lerjj)
I'm not actually sure this helped much. I don't think I'm expressing very well what I'm having difficulty explaining. Additionally, I don't understand how this can be understood in terms of conservation of angular momentum because a torque is being very visibly applied in all situations demonstrated.

Can someone explain what is wrong with the notion that gravity usually produces a torque in the x direction (using the co-ordinate system discussed above) which causes a body to fall in the z direction (actually a circle in the yz plane). I don't see why the body spinning makes any difference, because I can consider the total angular momentum to be split into two components, one of which is the original spinning and one of which is the falling motion.

There must be something wrong with this, and I suspect it has something to do with the fact that the magnitude of the angular momentum remains constant in real life, whereas in my scenario you keep a constant component of L in the y direction and then gain L in the x direction (the increase in this component causing it to fall).

I'm basically well aware that one of my assumptions is wrong, and I'm trying to explain my current model (which is clearly inconsistent) in as much detail as possible so that someone can tell me what epiphany I'm supposed to be having. Please point out some reasoning I've said that's wrong.
If the x-axis is in the direction of the angular momentum, the z axis is the vertical (upwards), and y on the same plane as x, perpendicular. The weight cause a torque along the y axis, which is perpendicular to the angular momentum. This will cause a change in angular momentum, in the xy plane, a precession. I'm confused on your issues? Are you wondering why it won't fall?
13. (Original post by Phichi)
If the x-axis is in the direction of the angular momentum, the z axis is the vertical (upwards), and y on the same plane as x, perpendicular. The weight cause a torque along the y axis, which is perpendicular to the angular momentum. This will cause a change in angular momentum, in the xy plane, a precession. I'm confused on your issues? Are you wondering why it won't fall?
Yes, I'm not quite sure how to articulate what I'm not grasping... I understand why the angular momentum vector has to rotate in the xy plane. But does that actually preclude falling? I mean, it still feels like it ought to fall while it precesses.
14. (Original post by lerjj)
Yes, I'm not quite sure how to articulate what I'm not grasping... I understand why the angular momentum vector has to rotate in the xy plane. But does that actually preclude falling? I mean, it still feels like it ought to fall while it precesses.
The torque will cause rotation in the xy plane. When the angular velocity decreases substantially, torque will no longer hold it up, and it will fall. Perhaps you are not grasping that gravity is doing no work on the wheel initially, it's purely inducing the torque which causes the precession.

Edit: Are you missing the fact there is an upwards angular momentum caused by the rotation of the body about the rope? When the wheel slows, the rotation about the rope will cause the angular momentum, to decrease.
15. (Original post by lerjj)
Yes, I'm not quite sure how to articulate what I'm not grasping... I understand why the angular momentum vector has to rotate in the xy plane. But does that actually preclude falling? I mean, it still feels like it ought to fall while it precesses.
It does in fact dip slightly before it can settle into a stable motion- If you think about energy conservation it has to, so that the lost GPE can compensate for the additional motion around the vertical axis
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