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May
18
comment How can I determine whether the mass of an object is evenly distributed?
If you are allowed to go beyond rigid inertia, there are plenty of methods to debunk simple frauds such as dmckee's counter example. You could compare the thermal conductivity between two closely neighboured points to that between two antipodes, or observe its deformation when compressed infinitesimally. Or x-ray the thing, duh.
May
9
awarded  Yearling
May
9
comment Topological band theory
Well, physicists have a tendency to regard everything as continuous on all $\mathbb{R}$ and work with low-order pertubations as long as nothing seems to go wrong, don't we? Without really checking how mathematically sound this is...
May
8
comment What is a “measure equation” as mentioned by this TeX Users Group guide?
@ChrisWhite: that's debatable. IMO, rough empirical relationships are almost always much more efficiently conveyed by graphical means, whereas the purpose of equations is to make exact mathematical statements. There, units are nothing but noise that makes the algebra cumbersome. — But may the astronomers choose what they like best, as long as I don't need to decipher such equations in solid-state papers I'm happy...
Apr
30
comment If a balloon is continuously filled with air and stays at a constant shape and size will there be any empty space in the balloon?
So what you're asking is basically: if you press enough gas molecules into a constant volume, would it always remain a gas?
Apr
4
revised Simulations of Planetary Motions
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Apr
4
answered Simulations of Planetary Motions
Mar
30
comment Conservation of Linear Momentum at the point of collision
"With non-zero velocities and non-zero masses this constant will be non-zero." Non-sequitur. It will in fact be zero for equal masses and opposite velocities, which "happens" to be also the only case in which "At the point of collision, both particles have velocity zero" is possible. So even with zero-duration collisions, there would be no contradiction here.
Mar
30
revised How electrons act under rotating magnetic field?
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Mar
30
revised How electrons act under rotating magnetic field?
added 1264 characters in body
Mar
30
answered How electrons act under rotating magnetic field?
Mar
26
comment Does the sun rotate?
@JerrySchirmer: infinitesimally close to zero? I don't think so. Classically, $\{\vec{0}\}$ (or any singleton set) is a null-subset of the set of angular momentum vectors, so one might say the probability is in fact exactly zero. Quantum-mechanically, there are only finitely many states of quantised angular momentum when the energy is limited, so the probability is ridiculously, but not infitesimally small.
Mar
7
comment Can the solar system really fit in a thimble?
At least for the second version of the statement, it's also wrong in a much more fundamental way than the answers already pointed out: there aren't actually any empty spaces between the electrons and the nucleus! Rather, the electrons fill up that entire space. It's only "right" to say that atoms are mostly empty when you focus on the nuclei, which are in fact localisable in a very small subvolume of the atom.
Mar
5
comment What causes insects to cast large shadows from where their feet are?
With a smoothened pike it wouldn't really be a shadow anymore, though, just a less brightly-lit, possibly fuzzy area. Only for the limit of $r_{\mathrm{pike}}\ll r_{\mathrm{dip}}$ do you get the actual sharp circular shadows this question is about.
Mar
5
comment What causes insects to cast large shadows from where their feet are?
Refraction is merely a special way to look at photon propagation that only works for smooth (differentiable) surfaces. To describe something like this phenomenon you first have to do some ugly limit discussion (of course, most physicists would not make that step explicitly). On the other hand, Fermat's principle works directly (as it corresponds to the more fundamental Feynman-path propagation of the photons) and can thus be used to describe the circular shadow right away.
Mar
5
revised What causes insects to cast large shadows from where their feet are?
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Mar
5
comment What causes insects to cast large shadows from where their feet are?
I disagree: "as it gets nearer to the foot" would lead to some messing around with Snell's law, which is physically far less enlightening than Fermat's principle. — Right – as I said, the foot itself doesn't matter. What matters is that there's a "pike" where a whole bunch of light rays have their quickest path (and therefore none of them gets much energy).     As for "why would it bend left", I think it's clear that this is just an example ray, like the straight one.
Mar
5
answered What causes insects to cast large shadows from where their feet are?
Jan
22
comment Why do tuning forks have two prongs?
@Nathaniel: all freely-vibrating–string instruments have their harmonics stretched to some degree, not just pianos. It's only most obvious in small pianos, because the strings of these have a particularly big thickness-to-length ratio.
Dec
7
comment Why cant one see tidal effects in a glass of water?
@vsz: that, I think, is really the most important point, why don't you add it as an answer?