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Feb
20
comment A conical pendulum. A textbook claims one can start the circular motion in an unintuitive way
What I had in mind was the centrifugal force, the notorious "fictitious" force that appears in equations of motion when written down in a rotating frame. My thought was that if the centrifugal force were greater than the gravitational restoring force, then the slightly perturbed rotating pendulum would continue to move out. It's possible I'm overlooking something simple, though, especially considering that your experiment isn't confirming this idea. Maybe try again with a shorter string, and slightly larger initial perturbation?
Feb
20
comment A conical pendulum. A textbook claims one can start the circular motion in an unintuitive way
Neat! Your calculation seems correct to me. I would have thought the drill would be spinning faster than that, so I am a bit surprised. I'll have to ponder this some more. Also, ideally, your experiment should use an angular velocity that is not too much different from the pendulum frequency, so that the equilibrium angle is not so large that you enter the nonlinear regime.
Feb
20
answered A conical pendulum. A textbook claims one can start the circular motion in an unintuitive way
Jan
28
awarded  Yearling
Nov
7
reviewed Approve Trajectory of a bomb dropped from an aeroplane
Nov
4
reviewed Edit Why does Einstein's equation of relativity exclude space and time?
Nov
4
revised Why does Einstein's equation of relativity exclude space and time?
rewrote the given equation using MathJax
Oct
10
comment Why do Oreo crumbs float to a single glob at the very center in a glass of milk?
If this were happening at the bottom of the cup, it would be explained in the same way as the so-called "tea leaf paradox" (en.wikipedia.org/wiki/Tea_leaf_paradox). But the fact that it's happening at the surface means something else is going on.
Sep
30
awarded  Explainer
Aug
19
comment How can the black body radiation formula be so general?
@EmilioPisanty yes, the answer could be clarified to give the explicit statement that both free electrons and free positive charges are required for bremsstrahlung, although this is a minor amendment (and could be implicitly understood because of charge conservation).
Aug
16
comment How can the black body radiation formula be so general?
@EmilioPisanty if positive ions are present, free electrons allow for bremsstrahlung, which is often responsible for generating thermal radiation.
Aug
9
awarded  Benefactor
Aug
8
comment Maintaining local thermodynamic equilibrium (LTE) in radiating gas with a broad atomic transition line
Yeah, I'm not sure about the thermal broadening yet, either. But you've definitely clarified some things for me.
Aug
8
comment Maintaining local thermodynamic equilibrium (LTE) in radiating gas with a broad atomic transition line
Ah, this is a promising perspective. I'll think about it some more to see if I agree. Most likely I'll end up giving you the bounty. Thanks for your help.
Aug
5
comment Maintaining local thermodynamic equilibrium (LTE) in radiating gas with a broad atomic transition line
Yes, the relations between the Einstein coefficients are often derived with the assumption of negligible line broadening. If these relations need to be refined for broad lines, that would be good to know. So now, which do you think is the most promising explanation here: the relations between the Einstein coefficients need to be refined, the application of the Boltzmann factor for the level population densities needs to be reconsidered, or both? I'd like to pinpoint in detail how this all works out.
Aug
4
comment Maintaining local thermodynamic equilibrium (LTE) in radiating gas with a broad atomic transition line
Hmm. Perhaps. I appreciate the contribution, although I am also not entirely sure this is the correct explanation. If this could be backed up with a more detailed derivation, or a reference, that would be most helpful.
Aug
3
comment Maintaining local thermodynamic equilibrium (LTE) in radiating gas with a broad atomic transition line
@RobJeffries Thanks, that is another good perspective from which to view my question, specifically "How could you expect LTE in a situation where the radiation field changes appreciable over the width of a line?" Any further help would be greatly appreciated.
Aug
1
awarded  Promoter
Aug
1
comment Why is bandwidth, range of frequencies, important when sending wave signals, such as in radio?
Beautifully explained
Aug
1
comment Shallow water wave question from Acheson's book
I think that the condition $\eta \ll h$ might just be the regime in which the shallow water results are valid. If your initial conditions lead to a situation where this is no longer true, then you can no longer use the shallow water equations. I don't think the condition can be 'derived.'