All Questions
10,535 questions
37
votes
6
answers
41k
views
Blowing your own sail?
How it this possible? Even if the gif is fake, the Mythbusters did it and with a large sail it really moves forward. What is the explanation?
- 479
37
votes
3
answers
26k
views
Deriving the Lagrangian for a free particle
I'm a newbie in physics. Sorry, if the following questions are dumb. I began reading "Mechanics" by Landau and Lifshitz recently and hit a few roadblocks right away.
Proving that a free ...
- 473
36
votes
6
answers
14k
views
Why is superdeterminism generally regarded as a joke? [closed]
Before anything, I'm sorry for being an outsider coming to opine about your field. This is almost always a stupid decision, but I do have a good justification for this case. I've been reading about ...
- 1,972
36
votes
4
answers
30k
views
Any good resources for Lagrangian and Hamiltonian Dynamics?
I'm taking a course on Lagrangian and Hamiltonian Dynamics, and I would like to find a good book/resource with lots of practice questions and answers on either or both topics.
So far at my university ...
36
votes
4
answers
22k
views
What exactly is a virtual displacement in classical mechanics?
I'm reading Goldstein's Classical Mechanics and he says the following:
A virtual (infinitesimal) displacement of a system refers to a change in the configuration of the system as the result of any ...
- 37.4k
36
votes
5
answers
4k
views
Is there a physical system whose phase space is the torus?
NOTE. This is not a question about mathematics and in particular it's not a question about whether one can endow the torus with a symplectic structure.
In an answer to the question
What kind of ...
- 58.3k
35
votes
3
answers
12k
views
Clarifying the actual definition of elasticity. Is steel really more elastic than rubber?
Yes, I know it's steel. It's everywhere on the web and I did google. But I seek enlightenment.
My physics textbook defines elasticity as:
Property by virtue of which a material regains its shape.
...
- 551
35
votes
3
answers
11k
views
Lagrangian and Hamiltonian EOM with dissipative force
I am trying to write the Lagrangian and Hamiltonian for the forced Harmonic oscillator before quantizing it to get to the quantum picture. For EOM $$m\ddot{q}+\beta\dot{q}+kq=f(t),$$ I write the ...
user56199
35
votes
2
answers
5k
views
Symbols of derivatives
What is the exact use of the symbols $\partial$, $\delta$ and $\mathrm{d}$ in derivatives in physics? How are they different and when are they used? It would be nice to get that settled once and for ...
- 52.4k
34
votes
3
answers
7k
views
Are double pendulums eventually periodic?
I've often heard it said that the motion of a double pendulum is non-periodic. (This may be related to the fact that it's a chaotic system, but I'm not sure about that.) But this does not seem ...
- 2,999
34
votes
3
answers
6k
views
Why is Noether's theorem important?
I am just starting to wrap my head around analytical mechanics, so this question might sound weird or trivial to some of you.
In class I have been introduced to Noether's theorem, which states that ...
- 510
34
votes
5
answers
18k
views
How was the formula for kinetic energy found, and who found it?
My questions mostly concern the history of physics. Who found the formula for kinetic energy
$E_k =\frac{1}{2}mv^{2}$
and how was this formula actually discovered? I've recently watched Leonard ...
- 1,249
34
votes
4
answers
5k
views
How can earthquakes shift the earth's axis?
One often comes across news articles that claim that an earthquake shifted the earth's axis.
http://news.google.com/?q=earthquake%20shifted%20OR%20shifts%20earth%27s%20axis
If you ignore the ...
- 8,850
34
votes
7
answers
5k
views
The usage of chain rule in physics
I often see in physics that, we say that we can multiply infinitesimals to use chain rule. For example,
$$ \frac{dv}{dt} = \frac{dv}{dx} \cdot v(t)$$
But, what bothers me about this is that it raises ...
- 8,040
33
votes
4
answers
4k
views
If free electrons have classical trajectories, then why don't bound electrons around the nuclei have it too?
I have read this question:
Changes to chemical properties of elements due to relativistic effects are more pronounced for the heavier elements in the periodic table because in these elements, ...
- 29.3k
33
votes
4
answers
6k
views
Physical and Geometrical interpretation of Differential Forms
I have a doubt about the physical and geometrical interpretation of differential forms. I've been studying differential forms on Spivak's Calculus on Manifolds, but my real intent is to use those ...
33
votes
10
answers
7k
views
What is the Earth truly rotating about/revolving around?
Earth rotates on its axis and revolves around the sun, the sun revolves around the galaxy, the galaxy is also moving. So Earth's net rotation as observed from a fixed inertial frame consists of all ...
- 1,398
32
votes
9
answers
5k
views
Does amplitude really go to infinity in resonance?
I was recapping the forced oscillations, and something troubled me. The equation concerning forced oscillation is:
$$
x=\frac{F_0}{m(\omega_0^2-\omega^2)}\cos(\omega t)
$$
I don't understand why this ...
- 677
32
votes
11
answers
5k
views
In reverse time, do objects at rest fall upwards?
I want to develop a game where time runs backwards, based on the idea that physical laws are reversible in time. However, when I have objects at rest on the earth, having gravity run backwards would ...
- 422
32
votes
6
answers
8k
views
Why are Killing fields relevant in physics?
I'm taking a course on General Relativity and the notes that I'm following define a Killing vector field $X$ as those verifying:
$$\mathcal{L}_Xg~=~ 0.$$
They seem to be very important in physics ...
- 1,573
32
votes
7
answers
8k
views
Why can you hammer a hole into an underwater ceramic cup?
Hammering a nail into a ceramic cup causes it to shatter when dry but not when submerged in water. Is there an intuitive explanation for this? And does it have anything to do with the Rehbinder effect?...
- 12.6k
32
votes
2
answers
5k
views
Is there a limit as to how fast a black hole can grow?
Astronomers find ancient black hole 12 billion times the size of the Sun.
According to the article above, we observe this supermassive black hole as it was 900 million years after the formation of ...
- 7,455
31
votes
5
answers
12k
views
Artificial gravity on rotating spaceship?
One of the possible ways to simulate gravity in outer space is to have a rotating spaceship, so that the centrifugal force experienced provides a gravity-like force.
My question is: shouldn't this ...
- 25.3k
31
votes
4
answers
6k
views
How do I show that there exists variational/action principle for a given classical system?
We see variational principles coming into play in different places such as Classical Mechanics (Hamilton's principle which gives rise to the Euler-Lagrange equations), Optics (in the form of Fermat's ...
- 965
31
votes
3
answers
3k
views
Does topology have any role in classical physics?
I've seen many applications of topology in Quantum Mechanics (topological insulators, quantum Hall effects, TQFT, etc.) Does any of these phenomena have anything in common?
Is there any intuitive ...
- 12.6k
31
votes
4
answers
4k
views
How can transverse waves on a string carry longitudinal momentum?
In general, if a wave carries energy density $u$ with velocity $v$, it also carries momentum density $u/v$. I've seen this explicitly shown for electromagnetic waves and (longitudinal) sound waves.
...
- 105k
31
votes
6
answers
8k
views
Noether Theorem and Energy conservation in classical mechanics
I have a problem deriving the conservation of energy from time translation invariance. The invariance of the Lagrangian under infinitesimal time displacements $t \rightarrow t' = t + \epsilon$ can be ...
- 10.3k
31
votes
3
answers
7k
views
Will a falling rod stay in contact with the frictionless floor?
Question
A uniform rod of mass $M$ is placed almost vertically on a frictionless floor. Since it is not perfectly vertical, it will begin to fall down when released from rest.
I have seen solutions ...
- 1,431
31
votes
3
answers
7k
views
Are there examples in classical mechanics where d'Alembert's principle fails?
D'Alembert's principle suggests that the work done by the internal forces for a virtual displacement of a mechanical system in harmony with the constraints is zero.
This is obviously true for the ...
- 5,398
31
votes
3
answers
5k
views
Spontaneous symmetry breaking in classical mechanics, quantum mechanics and quantum field theory
I wondered if someone could help me understand spontaneous symmetry breaking (SSB) in classical mechanics, quantum mechanics and quantum field theory. Consider a Higgs-like potential, with a local ...
- 15.3k
30
votes
4
answers
73k
views
Difference between momentum and kinetic energy
From a mathematical point of view it seems to be clear what's the difference between momentum and $mv$ and kinetic energy $\frac{1}{2} m v^2$. Now my problem is the following: Suppose you want to ...
- 1,191
29
votes
9
answers
26k
views
Book about classical mechanics
I am looking for a book about "advanced" classical mechanics. By advanced I mean a book considering directly Lagrangian and Hamiltonian formulation, and also providing a firm basis in the geometrical ...
29
votes
3
answers
3k
views
Why doesn't a fly fall off the wall?
Pretty simple question, but not an obvious answer at least not to me. I mean you can't just place a dead fly on the wall and expect it to stay there, he will fall off due to gravity. At first I ...
- 991
29
votes
2
answers
9k
views
Invariance of Lagrangian in Noether's theorem
Often in textbooks Noether's theorem is stated with the assumption that the Lagrangian needs to be invariant $\delta L=0$.
However, given a lagrangian $L$, we know that the Lagrangians $\alpha L$ (...
- 2,930
29
votes
5
answers
6k
views
Classical proof of the gyromagnetic ratio $g=2$
I was reading Representing Electrons: A Biographical Approach to Theoretical Entities, by Theodore Arabatzis.
At a certain point, where he is explaining the history of the magnetic moment of the ...
29
votes
0
answers
778
views
Extended Born relativity, Nambu 3-form and ternary ($n$-ary) symmetry
Background: Classical Mechanics is based on the Poincare-Cartan two-form
$$\omega_2=dx\wedge dp$$
where $p=\dot{x}$. Quantum mechanics is secretly a subtle modification of this. On the other hand, the ...
- 6,727
28
votes
3
answers
4k
views
Lagrange's equation is form invariant under EVERY coordinate transformation. Hamilton's equations are not under EVERY phase space transformation. Why?
When we make an arbitrary invertible, differentiable coordinate transformation $$s_i=s_i(q_1,q_2,...q_n,t),\forall i,$$ the Lagrange's equation in terms of old coordinates $$\frac{d}{dt}\left(\frac{\...
- 12.3k
28
votes
2
answers
24k
views
What is the difference between configuration space and phase space?
What is the difference between configuration space and phase space?
In particular, I notices that Lagrangians are defined over configuration space and Hamiltonians over phase space. Liouville's ...
- 2,342
28
votes
2
answers
6k
views
Why does the classical Noether charge become the quantum symmetry generator?
It is often said that the classical charge $Q$ becomes the quantum generator $X$ after quantization. Indeed this is certainly the case for simple examples of energy and momentum. But why should this ...
- 7,994
28
votes
10
answers
5k
views
Will a ball slide down a lumpy hill over the same path it rolls down the hill?
Suppose I have a lumpy hill. In a first experiment, the hill is frictionless and I let a ball slide down, starting from rest. I watch the path it takes (the time-independent trail it follows).
...
- 53.7k
28
votes
6
answers
56k
views
Why does my door shut faster when the window is open?
I've noticed that if I shut my door when the window is open in a room, the door will tend to shut faster. If I shut the door when the window is closed with a normal force it will not fully close as if ...
- 431
27
votes
5
answers
5k
views
Newton's law requires two initial conditions while the Taylor series requires infinite!
From Taylor's theorem, we know that a function of time $x(t)$ can be constructed at any time $t>0$ as $$x(t)=x(0)+\dot{x}(0)t+\ddot{x}(0)\frac{t^2}{2!}+\dddot{x}(0)\frac{t^3}{3!}+...\tag{1}$$ by ...
- 27.2k
27
votes
7
answers
7k
views
Is it possible to recover Classical Mechanics from Schrödinger's equation?
Let me explain in details. Let $\Psi=\Psi(x,t)$ be the wave function of a particle moving in a unidimensional space. Is there a way of writing $\Psi(x,t)$ so that $|\Psi(x,t)|^2$ represents the ...
27
votes
3
answers
24k
views
Derivative with respect to a vector is a gradient?
I've encountered in some books (and even completed an exercise from the Goldstein by using it), a strange notation that seems to work exactly like a gradient, I have tried to look for an explanation ...
- 443
27
votes
3
answers
32k
views
Constructing Lagrangian from the Hamiltonian
Given the Lagrangian $L$ for a system, we can construct the Hamiltonian $H$ using the definition $H=\sum\limits_{i}p_i\dot{q}_i-L$ where $p_i=\frac{\partial L}{\partial \dot{q}_i}$. Therefore, to ...
- 27.2k
27
votes
4
answers
2k
views
Are there undecidable statements in classical mechanics?
Do Gödel's incompleteness theorems have any significance or application to axiomatic theories of classical mechanics like Newton's for example?
- 864
27
votes
5
answers
17k
views
Why is the bell, well, bell shaped?
What is the significance about the bell shape, when its hit at the rim it rings/produces sound better than other shaped objects? If so could anyone explain a little bit on it.
EDIT: From the ...
- 373
27
votes
1
answer
19k
views
Constants of motion vs. integrals of motion vs. first integrals
Since the equation of mechanics are of second order in time, we know that for $N$ degrees of freedom we have to specify $2N$ initial conditions. One of them is the initial time $t_0$ and the rest of ...
user17116
26
votes
21
answers
5k
views
What happens when a car starts moving? The last moment the car is at rest versus the first moment the car moves
Imagine a car that's at rest and then it starts moving. Consider these two moments:
The last moment the car is at rest.
The first moment the car moves.
The question is: what happens between these 2 ...
- 371
26
votes
5
answers
4k
views
What does it mean that physics no longer uses mechanical models to describe phenomena?
I've just started reading Sommerfeld's Lecture on Mechanics, with no background in physics (only in math). Can you explain to me what the author means with the bold sentence?
Mechanics is the ...
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