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age 20
visits member for 2 years, 2 months
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2h
comment What do people actually mean by “rolling without slipping”?
@Muphrid I think I will. But come to think of it, that the center of the disk travels $2 \pi/9$ is perfectly expected, so maybe the statement is true if "travels one circumference" refers to the center of the disk.
3h
comment What do people actually mean by “rolling without slipping”?
(with "s" being the arc length movement of the point of contact with the curve)
3h
comment What do people actually mean by “rolling without slipping”?
@Muphrid I included the overall distance travelled by the point of contact! I'm just looking at rolling without slipping on curved surfaces and many online solutions write $r d\theta=ds$, but I'm pretty sure (citing my example above) the correct version is $rd\theta=(1-kr)ds$, where $k$ is the curvature of the surface. Actually I derived that formula using the "a point in contact with the ground is momentarily stationary" condition. I'm mostly posting this for a sanity check.
3h
comment What do people actually mean by “rolling without slipping”?
@Muphrid, see: mathandcode.com/img/diskrollnoslip.gif would you agree that this example shows that your bolded sentence isn't true on non-flat surfaces? It illustrates a circle radius $8/9$ rolling inside a circle radius $1$. The circle rolls an angle of $2\pi/8$ while its point of contact with the ground travels a distance $2\pi$ and the center of the circle travels a distance $2\pi/9$ (not $2\pi/8$).
19h
comment Why is cross section inversely proportional to wavelength for interstellar scattering?
Hookean springs have $F\propto x$, though $x$ and $F$ are different units. The unit conversion is introduced in the constant of proportionality $k$. $F=kx$.
2d
comment Do bad clocks measure proper time?
Could you copy the definition of good versus bad "in the sense of MTW §1.5"?
Nov
22
comment How does a giant walk-in fridge maintain a thin temperature gradient at the entrance?
@WetSavannaAnimalakaRodVance Thanks for that!
Nov
21
comment How does a giant walk-in fridge maintain a thin temperature gradient at the entrance?
Is there a wind curtain? (A box/rail above the door which blows a wall of air down. They're present at many store entrances)
Nov
20
comment What is the physics of a spinning coin?
related: physics.stackexchange.com/questions/68676/… and mathandcode.com/disk I wanted to solve this problem in full generality. So my solution is undoubtedly more complicated than it needs to be. But you should be especially interested in "Partial constraint 2"
Nov
20
comment What would be the consequences of time not being “relative”
And his struggle was before he abandoned galilean relativity. You're correct that if you assume galilean relativity you can conclude that special relativity is wrong. But it seems like you're trying to show that special relativity is inconsistent in its own right?
Nov
20
comment What would be the consequences of time not being “relative”
-1 for, if no other reason, making the quote sound like it supports your post. He states in the next paragraph it was only thought by Einstein to be a contradiction when assuming Galilean relativity ("he had been assuming that the ordinary Newtonian law of addition of velocities was unproblematic")
Nov
19
comment How is strong time dilation consistent with weak tidal forces?
Mentioning spin: wired.com/2014/11/metaphysics-of-interstellar Thorne: "I went home, slept on it, did a calculation, and found that if you have a black hole that spins rapidly enough, and a planet that is very close to the last stable circular orbit, you could get the time dilation he wanted. It just amazed me." (Not that it changes your answer, just that in the movie Gargantua is in a stable circular orbit with realistic [but absurd] time dilation)
Nov
15
comment Problem in Euler-Lagrange imply Newton
@MedSaâdAlami, so certainly that term doesn't vanish. But, if it did vanish, what would that get you? (Also, $\theta=a \cos(\omega t)$ does not solve the simple pendulum problem, it solves the simple harmonic oscillator problem.) For reference I think the proof of Newton's laws from the principle of least action is given in L&L as equation 5.3. It's so simple because the first step in this would be writing $L$ in the form 5.1.
Nov
15
comment Problem in Euler-Lagrange imply Newton
@MedSaâdAlami Newton's equations are specifically written as $m\ddot{x}=-U'(x)$, where $x$ is a coordinate in your Euclidean system. If you want to prove Newton's equations, then, you'd better choose to write $L$ in terms of Euclidean coordinates first. (The pendulum adds an extra degree of complication, therefore, because there is now a force of constraint when you move back to Euclidean coordinates!)
Nov
12
comment What's the largest mushroom cloud possible from a coffee cup/grenade sized nuclear bomb?
@crclayton I'm almost certain that $1450 ft$ is just the height of the bomb when it went off!
Nov
11
comment Second derivative of dirac delta expression
@doetoe actually, scratch that, I guess it is a bit obvious they're artefacts, and only the $k=0$ behavior (which doesn't exist) is the important part.
Nov
11
comment Second derivative of dirac delta expression
@doetoe How can you be sure that they're just artefacts? (though I think you're right, since the $\sqrt{2 \pi}$ seems too specific). The process works exactly (no artefacts) for $\delta^{(n)}(x)$
Nov
11
comment Why do we have to use an integral in this scenario to figure out $v_{max}$?
In that equation $M$ is the mass enclosed in a Gaussian surface about the center of the Earth. If I remember correctly, the field turns out to go like $GmMr/R^3$ where $R$ is the radius of the Earth.
Nov
9
comment Is the explanation of special relativity in Stephen Hawking's “The Grand Design” flawed?
@bright.magus it's shorthand for $t$ arbitrarily larger than the duration of the experiment.
Nov
9
comment Is the explanation of special relativity in Stephen Hawking's “The Grand Design” flawed?
There are a lot of commonly understood tools in special relativity that have to be sorted: Filling space with clocks at $t=-\infty$ and collecting all the data at $t=+\infty$. So you can talk about "the location at time $t$ in frame $X$" and make perfect sense of it. So saying "two persons can't see the same ray of light" is a bit off.