Dorky Poll: Conservation

Yes, it definitely has to be angular momentum. That's why we space scientists have to play such interesting games stealing angular momentum from handy passing planets in order to get spacecraft into the orbits we really want. It also explains why it's so bloody difficult to de-orbit a spacecraft.

i kinda like conservation of momentum. who doesn't like collisions? or billiards?

Conservation of Ream.

Conservation of Mass because it means business and you can't argue with it.

> #4:
Unless said mass gets converted into energy...

Conservation of probability in QM. "Probability" seems almost the opposite of "conservation law." The fact that probability has to obey a conservation law is like the triumph of order over chaos.

Conservation of angular momentum. The best part of freshman physics:

http://www.youtube.com/watch?v=545GwnupKAE

Angular momentum. What would we do without cool things like accretion disks to watch?

Angular momentum. What would we do without cool things like accretion disks to watch?

Conservation of angular momentum, for two reasons. First, quantum mechanics. Gotta have QM.

Second, conservation of angular momentum is enforced by Noether's theorems plus vacuum isotropy. Noether requires a continuous symmetry or one approximated by a Taylor series. Parity is a discontinuous external symmetry (coupled to translation and rotation). There is no reason why angular momentum should be conserved by chemically identical, oppposite geometric parity atomic mass distributions.

Thermodynamics constrains an angular momentum conservation violation to below 10^(-13) relative, about 10^(-15) relative expected. It is measurable if it is there to be observed. How much fun would that be?

Conservation of effort. My math prof used to say if you save effort in a proof in one step, it's just coming back to haunt you elsewhere. In fact I had to notice over and over again, the only way to really shorten an argument or a proof is either being sloppy or to recast it such that another already proven statement can be used. I guess I'm just not dorky enough for your polls ;-)

I go with angular momentum, too. You can see demonstrations of it every day if you watch the TV weather report. The weatherguy might or might not know why air circulates around highs and lows the way it does, but there it is.

The hamiltonian of freezing water has a special continuous symmetry : it is scale-invariant. At the freezing point, there are many very small pieces of ice continuously turning into water and back. The size of these ice pieces is distributed according to a power law. (phase transition in the Ising model).
By Noether's theorem, some quantity must be conserved in freezing water.
I have no clue what quantity this is, but it it my favourite conserved quantity.

I guess I'm not as sophisticated as most, but I'll say Energy.

Besides being one of my favorite Feynman lectures, I've found that there are a lot of problems where you can get a quick feel for the answer by using energy conservation.

Risking a double post: Charge conservation. I didn't think much of it until I learned that it was related to gauge invariance, and then there's the whole CPT mess to work through.

Justin @7:

That demonstrates torque = dL/dt, not L = constant, so it is not an example of angular momentum conservation. Flipping the wheel over while sitting on a frictionless stool, or spinning like an ice skater or diver, those are conservation of angular momentum.

Mark @12:

Circulation of air around a high or low is a result of looking at accelerated motion in an accelerated (rotating) frame of reference. Storm systems are just a Foucault pendulum made up of a fluid. Conservation of angular momentum applies when the earth's rotation changes to compensate for the rotation of a large storm.

What this discussion demonstrates is that effects associated with angular momentum are visually interesting (there is nothing like seeing the effects of a cross product and an inertial tensor become real) but not well understood. For example, I know that I can't explain properly how to do a "cat twist" or turn a somersault into a twist in diving even though I 'know' how they work.

Angular momentum is definitely the coolest, but linear momentum is the one where students can actually see and understand it.

Conservation of linear momentum, I just love momentum for some inexplicable reason.

Conservation of meetings. Actually, they're more like entropy: you can never decrease them, you can only hope to hold them constant.

Does anyone have a copy of Robert Forward's nonfiction book Future Magic (Avon Books, June 1988), who can provide us with his back-of-the envelope calculation of how much energy could be liberated if we could violate the Law of Conservation of Angular Momentum, and annihilate a sing;e quantum of spin? I remember it as humongous, and of science fiction interest...
# ISBN-10: 0380898144
# ISBN-13: 978-0380898145

If it were not for Conservation of Baryon Number, of course, we would not be here to discuss the matter.

Energy, because you can use it as a shortcut in many kinds or problems.

Baryon number minus lepton number, which potentially plays a role in the story of why there's more matter in the universe than antimatter, but which might turn out not to be conserved at all... it's a conservation law with nice open questions associated to it.

I'll go with lepton number, since one of my favorite topics to teach about is (are?) neutrinos.

I'll go with lepton number, since one of my favorite topics to teach about is (are?) neutrinos.

OK, I'll play: my favorite conservation law from elementary Newtonian physics is conservation of center-of-mass (sometimes called center-of-momentum) motion. This is the conservation law that says that the center of mass of a system moves with constant velocity -- or equivalently, that one can move to a frame in which this point is fixed. Even though this conservation law looks just like a modest rearrangement of the law of conservation of momentum, it's really a different thing. For example, if you consider the classic elementary physics problem of person standing in the middle of a frictionless disk (or ice-covered pond), it is conservation of center of mass that says that they can't get to one edge of the disk without throwing something to the other edge; if you only knew conservation of momentum, you might think you could somehow get the person and all their possessions to the same edge of the disk.

This conservation law is related by Noether's theorem to the Galilean symmetry of Newton's equations -- the transformation to reference frames moving with constant velocity. It is a beautiful lesson in elementary physics that we can also see this by noting that transforming to a rotating reference frame does not preserve Newton's laws -- fictitious centrifugal and Coriolis forces appear when we do this. So there should *not* be a conservation law that corresponds to "angle of mass", even though there is an angular momentum conservation law -- and sure enough, there is no such conservation law: the person in the middle of a frictionless surface can change the direction they are facing (by, say, moving something heavy in a circle) without letting go of anything. (This also explains why a cat can land on its feet, even if it didn't start falling with its feet down...)

I.Q. No matter how large the committee gets, the aggregate I.Q. remains the same...

noether's theorem

Angular momentum, 'cause then you get to have fun with spin! Plus, [Lx,L2] = 0.

Kudos to Alex R @27.

That is a *really* nice explanation for how a "cat twist" works. No messy math needed, and it elucidates the contrast between linear and rotational motion really nicely.

I like conservation of energy, but I like it because (as I understand Noether's theorem) it's a mathematical consequence of the symmetry of physical reality with respect to time translation.

I also like it because it's the easiest way to work out that someone just doesn't *get* science.

CCP, I'm not sure whether you're saying angular momentum does not enter into the circulation of air around low and high pressure systems, but if you are, then I think you are overlooking it. Air at a given latitude has a given angular momentum. If it moves to a higher latitude, R is smaller, thus omega becomes larger. Thus it must move in the direction of the Earth's rotation, giving it a higher angular rate than it had before.

@13: Entropy?

@13: Entropy?

CPT? The Laplace-Runge-Lenz vector? Noether charge in gauge theory?