In the wheel on a string demonstration it’s not the gravity that makes it precess it’s the torque applied by the axle . In a spinning gyroscope, if the axle was perfectly vertical there would be no precession. All parts of the gyro would feel the same forces of gravity. But the axle in real life can’t be perfectly vertical due to numerous factors (air currents and vibrations, etc) The axle will start to tip in some direction. This will apply the torque to the wheel which will change the orbit (or the path of rotation) by 90 degrees. Which will move the axle to a different orientation which will apply the torque in a different direction, which will move the axle, which will move the torque and on and on.
I think the piece you’re missing is that this is a continuous effect. It’s not that the effect is happening in discreet 90° chunks. All of the points on the wheel are feeling torque from the axle, each with a slightly different vector. So all of the points are acting in unison to affect the axle which affects all of the points etc.
Not really fair. It’s one thing to be able (or unable) to explain something given an underlying set of abstractions. It’s another to start asking for explanations about deeper problems concerning those abstractions.
The interesting thing about gyroscopic effects is that they are explicable using nothing deeper than basic principles of mechanics but are nonetheless hard to explain.
Your example would be the equivalent of asking “why do things have mass”? Not a fair comparison.
I should add, I’m not saying I can give the intuitive explanation that the OP is seeking. It may well be beyond me. But at the moment I don’t have the time to even think about whether I can or not.
I think it’s totally fair. The OP has been presented with completely satisfying explanations of the effect if you assume conservation of momentum. Now, that is essentially where we have to stop: any deeper than that and you have to get into Noether’s theorem, etc. We might be able to give a partial explanation for this particular manifestation purely in terms of linear momentum, but that hasn’t really improved matters in terms of how deep we’re willing to go. We’re down to the symmetry of the universe and can’t go any further.
Chemistry is built on a much higher and more rickety stack of abstractions. Nothing at the AP level is remotely satisfying, and no explanation gets “close to the metal” in the way that conservation laws do.
That is not covered in the test. It involves answers that are unintuitive and largely math, as I said. This precession case doesn’t seem to be one of those. Are you saying it is? Then why are we discussing it in this manner?
Conservation of angular momentum is something we just accept for any basic mechanics course. It can be shown to result from more fundamental principles, but like quantum mechanics and chemistry, it’s beyond the scope of those courses.
You’ve been given a few examples where, to conserve angular momentum, off-axis forces must exist when changing the axis of rotation for a spinning object. We can give more examples, but the ones already should be sufficient. If you’re still not satisfied, then you’re asking for something that wouldn’t be a part of a basic mechanics course. That’s fine too, but then you shouldn’t act like there’s something particularly special about this case vs. chemistry or any other subject.
There’s part of the problem here. I do not accept that I’ve been given an adequate explanation if I accept the idea of conservation of momentum. I’m well aware of the idea, but the instructors on these videos keep assuming something somewhere and not fully explaining the precession process. Because it makes sense to you doesn’t mean they did an awesome job. I can have discussions with AP kids that would completely bypass the Intro kids, because we keep skipping steps in the explanations, because we already understand them. I maintain that’s what’s happening here. When the student is able to assimilate and retain information, and is actually paying attention, and asking furthering questions, it is the job of the instructor to find the details and logical cause-effect processes that make the concept work for the student. The student is doing his/her part.
" Angular momentum around a vertical axis cannot change because of the (frictionless) pivot of the chair" so the momentum can’t change around a vertical axle even though the friction is negligible? What?
" the system (wheel, ourself, and chair) cannot have a vertical component, so we and the chair have to turn in the direction opposite to the spin of the wheel, to balance it." So the chair and the person rotate in the opposite direction of the wheel, even though they’re on axes at 90 degrees to each other. What?
My further point is the difficulty in using only text like that to communicate this. I’m sure it was very clear in Feynman’s mind, and it might be in yours, but if I tried to teach class only in this way, I’d have a lot more crossed eyes than I do already.
So your examples are sufficient, and it’s clear to you, and I’m too dumb to get it. I never argued against the idea of conservation of momentum at all, but this is the 2nd time you’ve said that I don’t even know what that is.
This seems to be a sticking point, so let’s take a different tack here. Let’s say you’re in space and you have a wheel with an axle poking out. You want to get it spinning, so you grab the axle and give it a twist. But, it turns out that the axle is covered with very slippery grease. You can’t get ahold of it at all; you can’t spin it up, and likewise it doesn’t spin you in the opposite direction.
Now, you’re still just floating there in space. You aren’t touching anything else, and while you thought you could give the wheel some angular momentum, it turns out you can’t because of that slippery axle.
Well, the same thing is going on with the chair example. You, the chair, and the wheel aren’t touching anything else except for the base of the chair. There’s a swivel between you and it. There’s no way to transmit angular momentum between the two, which effectively means you’re a closed system. If you start with zero angular momentum on that axis, then no matter how you twist the wheel or anything else, you have to end with zero. And stay at zero at all points in between for that matter.
But that means that when you’ve rotated the spinning wheel to vertical, then you and the chair must be rotating oppositely so that the whole system adds to zero. Something must have gotten you spinning. Well, those forces are exactly those that resist the turning motion in the first place.
This illustrates the limitations of just textual instruction, even for someone as used to explaining things as Feynman was. I will point out that he dealt with students who were literally around the top .001%, though.
“Let us now return to the law of conservation of angular momentum. This law may be demonstrated with a rapidly spinning wheel, or gyroscope, as follows. If we sit on a swivel chair and hold the spinning wheel with its axis horizontal, the wheel has an angular momentum about the horizontal axis. Angular momentum around a vertical axis cannot change because of the (frictionless) pivot of the chair” So it can’t have angular momentum around a vertical axis because it’s so frictionless, even though we’re handed a spinning wheel on a horizontal axis, and the entire discussion is how a vertically spinning wheel can produce a horizontal torque.
“so if we turn the axis of the wheel into the vertical, then the wheel would have angular momentum about the vertical axis, because it is now spinning about this axis.” Of course
“But the system (wheel, ourself, and chair) cannot have a vertical component, so we and the chair have to turn in the direction opposite to the spin of the wheel, to balance it.” If the wheel is now on a vertical axis, then the person/chair system should turn the opposite rotation, and the idea that it would have a vertical component is so out of the question that I don’t know why it would be mentioned. Also, the idea of opposite rotation on the same kind of axis is not what’s being discussed. Edit: if we’re handed the spinning wheel, then I don’t think we rotate the opposite direction even when the wheel’s axis is vertical. It can just spin on its hub and assuming this mythical frictionless type of system, impart no friction or backward torque to the pole or to the person.
As far as I can tell, I keep getting told that the rotation on an axis at 90 degrees inherently conserves momentum, which is so intuitive that it needs no further discussion, even though I can’t think of any other examples, and no one can seem to explain it clearly even with this example.
I claim that the how is irrelevant if you accept conservation of angular momentum, and is to a large extent counterproductive.
I’m reminded of all those perpetual motion machines, like overbalancing wheels. Now, it’s true that in every individual case, if you’re careful enough you can discover the failed assumption. But the real reason they fail is that energy is conserved. And you can throw out the whole lot before inspecting a single one on this basis. You can say that the overbalanced wheel fails because there’s a lower density of weights on the side where they are farther out, or some such–but ultimately those are just irrelevant details, and the real, fundamental reason is that energy is conserved.
Likewise, here, we can say there are additional forces because angular momentum is conserved. Done. That’s all that’s required. And sure, in some particular cases we can trace where all the momentum is doing, and find that when we turn the wheel there is a slight mismatch in forces, and so on–but it’s just details. I can always invent a more complicated system, say something with masses flowing around on a twisty, convoluted path, and it might be beyond your ability to analyze. But the answer is the same thing, if there’s a net angular momentum then there have to be extra forces since otherwise there’s no way for the conservation laws to hold.
I stopped reading after “how is irrelevant.” Can you please stop helping? Your help has reached the point of declaring the question to be pointless. I really didn’t see that coming. Why are you in the discussion if you want to declare that “how” is pointless? That’s the entire point being discussed.
You don’t get to say who participates in the discussion.
You say that you accept the conservation laws, and I’ve tried to give answers on that basis. But actually I think we can go even simpler than Feynman’s example, because your OP asked something more specific: how does an oppositely spinning wheel cancel out the gyroscopic effect of the first?
And that has an easy answer, following from the definition of angular momentum. You just break apart the system into a bunch of point masses, and add up the mass times the distance from the axis times the tangential speed.
With two oppositely spinning wheels, for each point mass on one wheel, we can pair it with a point mass on the other wheel that’s moving in the opposite direction. Each of these pairs, by definition, has an angular momentum of zero. And so adding them up also equals zero.
So given that the system as a whole has zero angular momentum, there are no additional forces at play when rotating the wheels around. Doing so can’t change the angular momentum of the system as a whole.
So you admit you tried to just invalidate “how” part of the discussion.
I already said that the effect of gyroscopes I had been told was that they want to continue pointing in the the same direction in the universe. This supposedly explained why they can be pushed around and run down strings and still stay upright. There’s clearly more to it than this, but in that conception, another wheel just adds to the stability. This conception is apparently wrong. It does lead to the idea of the torques at 90 degrees to the spin of the wheel, though, which is the current discussion.
I’m now getting blamed for not understanding what has been stated by multiple people to be a very complicated topic, when I am participating and responding coherently, asking pointed questions and not “buy why” and “I just don’t get it”, and blamed by people, I’m gathering, without much practice in explaining things in great detail, which I can assure you is a learned skill.
I’m not blaming you for anything, or calling you dumb, or anything of the sort. But you haven’t been very clear about what kind of answer you expect.
Another Feynman video comes to mind, which is almost totally unrelated to this discussion but is worth watching:
Feynman doesn’t answer the interviewer’s question. He answers a meta-question, by raising another: what kind of answer do you expect from a “why” question?
You have to name a stopping point; a point where you will be satisfied with the answer. If “conservation laws say so” isn’t sufficient, you can say so and we can use that as a starting point. But if that is satisfying to you, but the answers aren’t yet clear, we can work with that as well. But so far it is not clear to me what kinds of answers you would accept–what is the point where you say you need no further explanation, and simply accept a physical principle as true?
Pish tosh. As Cardinal has said, you really aren’t helping. You are confusing what – when giving an explanation – is correct with what is adequate.
If what you are saying were adequate, one could consign the entire field of mechanics to the dustbin and simply replace the entire subject with “energy is conserved”. It is correct but it isn’t useful or adequate because when dealing with objects in life, it helps to understand the details of the way things behave. Sure, ultimately, everything behaves in a way that conserves energy but that is an explanation about as useful as a chocolate teapot.
Cardinal: I want to understand how this object will behave
Dr Strangelove: Energy will be conserved. Now shut up.
Feynman was not being abstruse. It was completely my fault for typing in the text only without the accompanying illustrations. See the link I gave before for an online edition of his lecture notes.
He clearly explains the motion of the particles in a spinning gyroscope, including the actual motion of the axis of a falling gyroscope.
Well, you still want to figure out what happens. It’s just that the fine details are skipped over in favor of using conservation laws or the like. The notes that DPRK linked to has a piece that addresses almost exactly that, in fact:
We may now claim to understand the precession of gyroscopes, and indeed we do, mathematically. However, this is a mathematical thing which, in a sense, appears as a “miracle.” It will turn out, as we go to more and more advanced physics, that many simple things can be deduced mathematically more rapidly than they can be really understood in a fundamental or simple sense. This is a strange characteristic, and as we get into more and more advanced work there are circumstances in which mathematics will produce results which no one has really been able to understand in any direct fashion. An example is the Dirac equation, which appears in a very simple and beautiful form, but whose consequences are hard to understand. In our particular case, the precession of a top looks like some kind of a miracle involving right angles and circles, and twists and right-hand screws. What we should try to do is to understand it in a more physical way.
Now, Feynman is actually saying this as a prelude to a more intuitive explanation of a gyroscope’s behavior. Cardinal may or may not find the explanation satisfying, but in any case Feynman is still only addressing one special case, and doesn’t address the question of having two gyroscopes spinning oppositely.
