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Question |
| Asked by: |
Sandy Kidd |
| Subject: |
Gyroscopic Couple |
| Question: |
Gyroscopic couple.
Recently there have been several references, comments relating to gyroscopic couple.
I realise I am now old, and maybe a bit stupid, but would some kind, informed person, explain to me how this couple is generated, and how and why it can be a couple?
Sandy Kidd
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| Date: |
18 April 2005
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Answers (Ordered by Date)
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| Answer: |
webmaster@gyroscopes.org - 18/04/2005 16:55:45
| | | Its a physics term that basically just means the precessional force. I think the word couple was chosen because of the relation between the input and output forces.
i.e. if a force is applied on one axis you get precessional force or couple on another axis.
I've always found the terms "Gyroscopic couple" and "precessional force" are interchangeable.
Glenn
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| Answer: |
arthur dent - 18/04/2005 21:09:30
| | | When a body is acted upon by a force not passing through its centre of mass, this will in general produce linear acceleration and rotation of the body. The rotation can be shown to be caused by equal and opposite forces acting equi-distantly from the centre of mass, and in the same plane. These are called a couple. If the body is already spinning, and a couple is imposed which is not about the original axis of rotation, then a complex motion ensues which is described by the 3 Euler equations (first written down over 300 years ago) and involves resultant rotation in other planes. The Euler equations also describe other situations, and so the latter can be used as analogies for the (gyroscopic) motions. Thus, Poinsot likened gyroscopic motions to the paths of contact (polhodes) of an ellipsoid rolling over a plane. Kirchhoff likened them to the shapes taken up by a slender rod which is twisted in opposite directions at its two ends (try it with polypropylene rope). If the spinning object is not in outer space, but is instead on Earth and restrained at one end (i.e. a top), the imposed couple consists of the weight of the top (acting downwards through its centre of mass) and the reaction force (acting, on the lower end of the top, upwards through the support). The resultant (gyroscopic) couple (acting about the centre of mass) tries to produce the same complex motions as in the outer-space case but is prevented from doing so by the support. The gyroscopic couple will try to rotate the entire system (support + Earth) about its centre of mass but will obviously fail, and the top will instead rotate (precess) around the support. If the support is placed on an air-table, the top+support system will rotate about its centre of mass. Note that ice on ice is not as slippery as people assume (pressure-welding occurs too easily) and will hide this movement. Any 'centrifugal' forces are minute. Also suppressed (due to friction at the support) are more subtle aspects of the gyroscopic movements, such as nutation. This leads to the illusion that the resultant gyroscopic couple acts at right-angles to the imposed (gravitational) couple. Interfering with the precession, by blocking it, causes an immediate diversion of the movement of the top; thus leading some people to claim that the precessing top has no angular momentum about the support. Because all of the forces involved are couples, no rectilinear acceleration can be produced, hence no propulsion (unless the top falls off the support and hits the ground). Note that there appears to be a 'loophole', in the first line of this entry, in that a rectilinear force was said to be able to produce linear acceleration plus rotation. Laithwaite thought that this proved that linear and angular momentum are not separately conserved. That is, if a linear force could produce rotation, then rotation could produce a linear motion. The explanation (as to why Laithwaite was wrong) involves a subtlety, in the definition of angular momentum, which is not properly explained in modern textbooks. It is also one which physics students routinely explore experimentally (using air-tables) in their first year at university. They find that there really is no loophole: the angular and linear momenta always balance: separately, with no interconversion.
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| Answer: |
Nitro MacMad - 19/04/2005 18:11:59
| | | Dear Arthur,
Excellent! Now some of the shed dwellers (well me at least) can get their poorly grounded understandings of their experiments onto a better footing. Couples have always troubled me – but then, I still have to look up rectilinear and orthogonal! Hopefully you will continue in this vein and we can all advance our understanding.
Have any of the first year students of whom you write – or anyone else - got video of the classic top/gyro precessing on a plate on an air bed that could be sent to this site's webmaster so that its rotation around its centre of mass can be seen to be true? This would be of great help for the better understanding of those (well me at least) who’s quadratics and even long division leave much to be desired?
I have mentioned elsewhere that Alex Jones produced what used to be considered a good test of starting to get round the third law. This involves a mechanism that would move – on the obligatory “frictionless” base – outside its own starting dimension. Do you know of any device that does not involve a gyro that can do this?
Kind regards
NM
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| Answer: |
webmaster@gyroscopes.org - 19/04/2005 18:36:10
| | | Dear Arthur,
For about 10 years I searched for something to prove conclusively whether a gyroscopic propulsion can or cannot exist. I would LOVE to see a textbook that has these demonstrations for the first year students, or maybe pictures or videos of them in action. Can you find out which educational suppliers sell the kit to do this? Or is it old kit that has been made in house. Arthur from your point of view it would help to shut us up and from our point of view it would narrow the search (and for some of us we may choose to stop doing this sort of research).
I'll put up a bounty of £300 for the first person to get me video of these demonstrations (open to stundents, lecturers or anyone else) or put me in contact with someone who can get them. The video would instantly be put on the website.
I Just hope that someone out there is listening.
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| Answer: |
Sandy Kidd - 21/04/2005 06:52:50
| | | Arthur,
Thank you for your efforts in trying your best to explain to me why gyroscopic couple is gyroscopic couple, and for what is probably considered to be the accepted reasons.
I have to say Arthur that I am not sold on this at all, and quite frankly I think the explanation, not necessarily yours, is needlessly overcomplicated.
It is only a spinning disc after all.
I am also still struggling with the fact that it is felt that it has to be a couple.
I am inclined to think that it does not explain away a gyroscope’s reactions in an accelerated system where there is neither nutation nor precession.
In other words there is no way, certainly that I can see, and by any stretch of the imagination, that a couple as such, can be generated in an accelerated system
Consider the differential in system rotational acceleration, experienced across the gyroscope, parallel to the axis of system rotation.
It is obvious, that the amount of angular momentum, generated in the uppermost sector of the gyroscope, is considerably less than the amount of angular momentum, generated in the lowermost sector, and not in any way equal, let alone opposite.
Just less, and this is all the differential that is required.
Consequently, I feel I must believe in light of the obvious non existence of a couple in accelerated systems, that a couple is not present in passive systems.
The gyroscope will behave in exactly the same manner, without the need for any couple.
Sandy Kidd
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| Answer: |
Luis Gonzalez - 07/08/2005 16:53:50
| | | Arthur,
I must say that your inability to produce the physics students’ experiments (using air-tables) which prove that angular and linear momentum have no interaction, makes it look like you are not telling the truth. It creates great doubt about your ability in physics and makes one question your motives. Are you trying to hide something?
Luis
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