Bicycles with gyroscopic effect "cancelled out"

Factual Questions
61

I’ve referenced the magnets-Feynman video to people multiple times. That also involves completely non-intuitive causes and interactions, which are well beyond the ken of merely scientific people, and needs actual geniuses, I’m told. Every time I ask that question I get responses about virtual photons, and I just admit my limitations and quit. The macro scale torques in a spinning wheel don’t seem to be anywhere near that level.

No one has responded to my questions about the Feynman quotes. I can also try to read that really dry passage that was linked.

62

The magnets video isn’t really about magnets. It’s about how, if you’re asking any kind of “why” question, you need to have in mind what a satisfying answer would be. The difficulty in answering a question about magnets specifically isn’t that relevant, although it makes a good example because it’s an extreme case. The same basic idea applies to any scientific question, though. You can go as deep as you want, past where no one can give you a satisfying answer. One way or another, you have to stop before then.

I tried to answer your question about the chair’s pivot, but you didn’t respond to that one. Can you expand on what you’re having trouble with? Understanding that point is pretty fundamental to everything else in the discussion.

63

“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.”

“I think it’s totally fair. The OP has been presented with completely satisfying explanations of the effect if you assume conservation of momentum .”

So your explanations are completely clear and I’m the problem. Despite the fact that no one has almost even tried to state a clear series of cause-effect relationships about forces that makes the precession happen. It just occurred to me that no one has tried, that I can recall. “This causes this which causes this because of this” is how I get the point across to kids. No one has tried to string the whole thing together, and stating things like “conservation of momentum” lazy and/or dismissive.

64

No, what I’m trying to say is that the series of cause-effect relationships is completely ignorable if you accept conservation of momentum. You don’t have to understand the intermediate steps; you just have to observe the system before and after. If angular momentum is conserved, then the chair must be spinning afterward once the wheel’s axis is vertical. Precisely how this happened can be explained, but only with difficulty.

If you want this detailed explanation, then what you are saying is that conservation of angular momentum is not a sufficient explanation for your purposes. That’s fine, but it’s been tough to pin down exactly what kind of explanation you do want.

65

“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.” Sure.

“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.”
But as I said in my response to the Feynman quote, the entire point is that the wheel spinning on a horizontal axis makes the person in the chair go around. I have no idea why this “raise the wheel over your head” thing has been brought up, and as far as I can tell, no one has tried to explain it.

I’m asking for a connected series of logical statements of causes and effects that makes the wheel go around a different axis. Holding the wheel over your head is cheating, and furthermore, I’m not convinced that being handed a spinning wheel on a frictionless pole will do anything. It has already canceled out its momentum by acting on the thing that pushed it into spinning, and will just coast isolated from then on.

66

You take that back. I’ve been entirely clear that I’ve been trying to find out HOW it works. “Conservation of momentum” is the sort of lazy phrase-throwing that I would embarrassed to use in the classroom." Feynman even pointed out in one of his autobiographical books that phrases have to mean something. “It works by fleeber-blop” is useless.

67

Correct–that will do nothing. You are combining a system with no angular momentum (you, sitting in a motionless chair) with a system with angular momentum (the spinning wheel). The final system has the same angular momentum as the wheel did. Nothing else changes.

However, if you are already holding the wheel, with the axis horizontal, then you have zero angular momentum about the vertical axis. If you twist the axis to be vertical, you must still end with zero momentum, and yet the wheel has some. Therefore something must negate that momentum, in order to sum to zero. You cannot couple it to the ground somehow, since there is the pivot. So the only alternative is that you and the chair start rotating in the opposite direction (but more slowly, since you are more massive than the wheel).

68

Thanks for the effort. This answers nothing for me, unfortunately. It’s a paragraph composed by someone who knows the subject too well, talking to people who already know the point, and makes almost no effort to explain why anything happens. There is no use of any cause-effect relationships. The phrases “so then”, “because”, “causes”, “pushes”, “pulls”, “creates”, etc. are not used. I literally don’t know what his point is even supposed to be.

69

After spending about an hour on the phone with my physics major brother, who is an AP Physics teacher, I am informed that physics classes themselves are to blame. According to him, the classes have developed a way to get the right answers for the effects by inventing concepts like “the torque goes out the axle at right angles to the rotation”, and most people have never had it explained another way. He can’t do it either. This explains why I have been accused of not accepting the idea of the conservation of momentum, although I will point out that even that was not explained through from beginning to end, and even its logic and/or math were not presented in full. If you’re going to say that it’s not your job, then don’t participate in the discussion. Half explanations aren’t useful.

Also, before you jump in and say, “but the torque vector does point out the axle”, just don’t bother. I also understand that there are mathematical explanations of torque that are valid, and that it’s possible to defend the idea that the math is the true definition, but I’m trying to explain this through concepts. I maintain, and he agrees, that it should be possible to explain something as macro-scale and Newtonian as a stupid bike wheel should be explainable similarly to “This pushes here and causes this which pulls this and causes this and energy is input continually here by this, and if we think about all that for a minute, we see that these cancel out and the overall force is this direction.”

Apparently almost no one ever does this, which shocks me. Yes, I have unintuitive things in my AP Chem class that I have to sort of hand-wave, but they are official Deep And Dark things that almost literally no one understands, like why there are only 2 electrons per orbital, or why the energy levels are the sizes they are. I have to flatly state that I was never told, and the answers are apparently so Math that the students should be grateful I’m not trying to explain them any more deeply. Once we’ve gotten past that, I endeavor to create cause-effect relationships that are logical enough to be retained and understood, not just memorized.

“If you twist the axis to be vertical, you must still end with zero momentum, and yet the wheel has some. Therefore something must negate that momentum, in order to sum to zero. You cannot couple it to the ground somehow, since there is the pivot. So the only alternative is that you and the chair start rotating in the opposite direction (but more slowly, since you are more massive than the wheel)” I will admit this finally makes something out of the Feynman quote, which I maintain is still a paragraph so densely packed that it only communicates to someone who has been through the course, and that’s my trying to be charitable and consider that Feynman outranks me on the science scale by a factor of about a million. If it were a quote from just someone on the internet, I would think the person doesn’t actually know what he/she’s talking about, or has little practice in communicating details. The paragraph and the explanation quoted here still don’t seem to be even addressing the idea of precession, though. And before you jump in and yell that it does, no one has tried to clearly articulate how it does. They just keep pointing at the paragraph.

70

Let me give it a try, I’ll try to first do it without vectors and then with vectors, though qualitatively, not quantitatively and hopefully make both clearer.

First let me make a point about linear momentum though, to help justify part of the Feynman explanation. Linear momentum is conserved. If I bounce two carts against each other on a frictionless track, I can calculate the resulting velocities using the conservation of momentum and energy. But what if I make a stationary buffer on the track and bounce the cart off that? Now momentum seems to not be conserved. I have momentum towards the buffer, and then I have momentum away from the buffer. That’s a change of twice the magnitude of the momentum in question. What gives?

Well what happens is the momentum of the Earth changes. Or more simply, the Earth-cart system has conserved momentum by various elements of the Earth (without the cart) system gaining momentum.

If I stand with my feet firmly planted on the ground and hold the spinning wheel I can, with surprising effort if the wheel is spinning fast and/or is heavy (i.e has a lot of angular momentum) change the direction of the axle. But in that situation I’m transferring some of that momentum to the Earth minus wheel system.

The swivel chair isolates me, at least in part, from the Earth system. I can’t impart momentum around the vertical axis to the Earth, because trying to do so just cause me to spin on the chair swivel. I’ve made myself one of the cars on the frictionless track.

Now initially the system of me on the chair seat and the wheel only has angular momentum around the horizontal axle of the wheel, but I can use force to twist that axle out of the horizontal. We can view that momentum as the sum of momentum around that original horizontal axle, which is now just a reference direction, a similar reference axle that is vertical.

To conserve angular momentum there needs to some element zeroing out the angular momentum around the vertical axis that I put into the wheel. That element is the whole system, me, the wheel and the chair seat, rotating in the opposite direction.

If the wheel was rotating away from me at the top, and I twist it so the top tilts to the right, there is now some small clockwise motion to the wheel when viewed from above. So I, the chair, and the wheel have to swivel anticlockwise on the chair. If I twist it the other way, the chair swivels the other way. If the rotation of the wheel was opposite, the swiveling would happen in the other direction.

Now let’s say that instead of one wheel there are two equal wheels parallel on the axis I’m holding and I spin those up in opposite directions. Now, when I twist the axle and look down from above, one wheel has gained a component around the vertical reference axis that is clockwise, but the other one has gained a component that is counter-clockwise. There is no need for the wheels, me, chair system to swivel, because those two changes cancel each other out.

And I think I’ll save explaining how vectors make this simpler for another post, as I just realized that one reason they’re almost always used is that physics curricula usually have students use them extensively before getting to this point.

71

I see that you’re addressing the first question. Ah. Ok. Thanks.
I got lost about the “top” of things, but if one wheel rotates the opposite way on the axis with the first one, then there’s no rotation imparted to the holder, as the wheels already cancel each other out. Ok.

What I envisioned was that every spinning object resists changing the point in space that its axle is pointing to, and then resists rotating the axis. I also didn’t know about precession, which I did quickly realize puts a hole in my explanation. Are you saying that the entire idea is wrong, and I should just discard it? 2 oppositely spinning wheels will not resist a twisting motion of the pole, or the falling of a bike they are on?

Also, do I have this right: The wheel on the horizontal axis, handed to me, spun by someone else, on a frictionless hub, will just spin there and give me no force, just coasting, because the reverse force has already been put into the person spinning it from a stop, and therefore the ground they were on. Rotating the axle to the vertical position will change something and now it’s not just coasting, and will need to cancel out the rotation so it conserves momentum by rotating the person and the swivel platform.

Also, I know I’m commenting as an outsider, but how do physics students put up with these “torque points out the axle” explanations? There are clearly interested geniuses in these classes who like to actually understand things, and the idea of sitting there and having people hand-wave these “cheater” methods to get the right effects annoys me to where I’m sure I would be a thorn in the side of the TA. I’m shocked that actual physics people can’t explain precession in terms of “this pushes on this and that pulls on this…” My brother says that probably many professors can’t, and no one tried to teach him that, and he went to an actual respectable technology-oriented college, and majored in physics.

72

If the wheel is vertical and you’re holding the ends of the axles in opposite hands, the direction of rotation is most easily described (I think) by the movement of either the top or bottom of the wheel.

I think that is correct, yes. It’s what makes sense from a “conservation of angular momentum” point of view.

Yes, but if you keep the axis perfectly horizontal you can spin it up yourself on the chair. If you imagine the way you would have to rotate to cancel out the movement you can see that wouldn’t make you swivel.

They have likely already experienced pseudovectors in other relationships, and if it’s the first time they’ll get a description of how and why they work. Let me see if I can put it in terms you can accept for this topic that you are already invested in:

A rotating object, let’s for simplicity’s sake stick with a wheel, has angular momentum. Each individual particle in the wheel has constantly changing linear momentum, that all cancel out in aggregate, so they’re not very helpful for understanding the concepts, only the magnitude.

We add angular momentum to an object by applying a torque, which is a force a certain distance from the center of rotation. For the wheel that center is our axle and we likely apply the force to the periphery. How do we describe the resulting angular momentum? It has a magnitude and it has a direction. The direction can’t directly be described as a vector though. It is either around the axle this way, or that way, and “this way” can only be described relative to something else. You can try different approaches, but somewhat similar to in chemistry and chirality, it turns out that it boils down to a form of handedness.

We can describe the position and orientation of the axle easily enough in 3D space using vectors, but there will be two equally valid vectors for the orientation. We standardize on the one where if we point an extended right thumb in the direction of the axle vector the curved fingers point around the direction of rotation. If we pick this direction and give the vector the magnitude of angular momentum we get a description of angular momentum that is unambiguous and that allows us to use well known vector operations to examine the results of forces on the system.

It’s still not simple though. Doing anything involving rotating objects is rather complicated physics. And the only way to truly grasp it is to apply it, which is, unfortunately, also the approach to take to learn how to just apply rules without understanding them.

If you genuinely want to understand this though, I’d start with learning how to use right hand rules and vectors in electromagnetism. It’s not much less weird and “just how it is”, but the applications are much simpler.

Now I’m also getting the idea that you’d also like a “why is angular momentum” conserved explanation? Or maybe that’s just me. Anyway, I’ve been trying to create one for myself and have come up with some attempts that I think are illustrative of why it’s so hard, but might still help slightly. It’s going to take me a bit to type them out though and to remove the obvious errors. (I might have messed up in this post as well, although I did take out a couple of blunders already.)

73

At high speeds motorcycle racers have to do this on sharp turns to counter the tendency of the bike to flip:

Like the OP, I’ve wondered if partially countering the spin of the wheels would allow the motorcycle to remain more upright. Unfortunately, I don’t have any answer.

74

Yes and no. Note in that video that which direction the spin axis is pointing doesn’t change, but rather that the object shifts its orientation with respect to that axis.

75

Seems like gyroscopes that are in precession have a couple. And it looks like there should be a rotation around the center of the couple.
http://www2.eng.cam.ac.uk/~hemh1/gyroscopes/couple.html

76

You mean, the direction of the angular momentum does not change. That is the point of the demonstration. The object itself writhes around quite dramatically. See also the animation of a spinning plate, which obviously wobbles, so that its spin axis is constantly changing.

77

It sounds to me like you’re saying that you want an explanation for a vector phenomenon, but without using vectors. That’s not a question that’s going to end well. Any attempt at answering without using vectors is either going to omit so much detail as to be totally worthless, or it’s going to spend way too long re-inventing vectors and just not calling them vectors. Angular momentum does, in fact, reside in something that is inherently a three-dimensional vector space. There are some arbitrary conventions in how we choose to represent that space, but the space itself is still absolutely a vector space, and if it weren’t, we wouldn’t be talking about angular momentum, but about some other concept (which probably wouldn’t be nearly as elegant).

I suppose that you could represent that vector space in ways that don’t depend on arbitrary conventions, but I doubt that would be useful, because then we wouldn’t be mapping that three-dimensional space onto the three-dimensional space we’re intuitively familiar with. Which, arguably, is a more mathematically rigorous way to deal with the problem, because angular-momentum space is not, in fact, the same three-dimensional space as the one we’re familiar with. But it’d still be less intuitive.

78

Note that I haven’t mentioned vectors at all in this thread. Vectors (or more accurately, pseudovectors) are a mathematical abstraction that makes the calculations easier. And they are useful, but not necessary for understanding angular momentum. Here’s another method:

Take our chair+wheel+person system. We have access to a magic video camera that we can fix anywhere in space. It has a long telephoto lens, so that any perspective is flattened, and it’s also an X-ray camera so we can inspect everything. We position it above the chair, looking straight down at the setup. The man is holding the spinning wheel in front of him, upright from his perspective. Our camera only sees the narrow profile of the wheel.

How do we compute the angular momentum on the vertical axis? Well, we just use our camera: first, we pick a point on the image, which really could be anywhere, but we’ll pick the center for simplicity. And then we divide the scene into chunks of mass, and for each one we multiply the mass by the distance to the center by the tangential speed they’re moving relative to the center. That’s just the definition of angular momentum.

What does that give us? Well, the man and the chair aren’t moving at all, so all those chunks add to zero. The bits on the wheel are moving, but they’re all radial–that is, the bits are only moving directly toward or directly away from the center. So those are zero too, which means the angular momentum of the whole scene is zero.

Our camera shuts off for a moment. We’re told that the man is manipulating the wheel somehow, but that there are no outside influences. No one gave him a shove or anything, and he didn’t throw anything from the chair–it’s all self-contained. The camera starts working again and we have to see what happened.

The man has rotated the wheel to be horizontal–from our camera’s view, it’s to the side. And he’s holding it above his head (it doesn’t matter, but it makes things a bit easier to see). We see now that unlike before, the wheel now has a lot of angular momentum–again dividing it into chunks, we see that they now have a high tangential speed. And they’re all moving in the same relative direction, clockwise, say. So a part of our system that started with zero angular momentum now has some finite amount.

But we know from the laws that the momentum before and after must be equal–that is, zero. And the only other thing in the system is the person+chair. So they must be rotating the other way, so that when we divide up all of their little chunks of mass, they’re circulating in the opposite direction (counterclockwise). They’ll be moving more slowly, since the mass is higher and the radius is similar, but in the end all of those chunks must sum to zero, just like before–it’s only the distribution that’s different.

I haven’t mentioned vectors here, or even an axis really (that’s implicit with the camera setup). Here, angular momentum is just a kind of mass circulation around a point, which we know has to stay constant if there are no outside influences.

79

Yes, it sounds like you get it now: two oppositely spinning wheels cancel each other out and do not exhibit any sort of gyroscopic effect, precession, angular momentum, whatever.

Again, I am not sure if this is really significant for bicycle riding. It is more motorcycling where countersteering technique is used.

81

Reported.