All Questions
Tagged with classical-mechanics conservation-laws
220
questions
-3
votes
1
answer
102
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Noether's theorem by a taste of logic [closed]
I am a mathematician and I asked this question briefly and my question became closed, may be - I don't know - because physicists don't used to apply the method of "proof by contradiction". ...
- 1,409
1
vote
1
answer
55
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Designing a thought experiment on Noether's Theorem [closed]
By Noether's theorem, in classical physics, conservation of total momentum of a system is result of invariance of physical evolution by translation.
So logic says "if" there exists closed ...
- 1,409
0
votes
2
answers
78
views
Generalized momentum
I am studying Hamiltonian Mechanics and I was questioning about some laws of conservation:
in an isolate system, the Lagrangian $\mathcal{L}=\mathcal{L}(q,\dot q)$ is a function of the generalized ...
- 59
-1
votes
1
answer
73
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Continuity Equation for Steady State Flow vs Incompressible flow
Good day guys,
I have been reading on the continuity equations on the slides of my fluid dynamics course.
I was introduced to the following definitions:
Steady state flow: $\forall f \in \text{Flow ...
- 286
1
vote
1
answer
72
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Analogy of Euler-Lagrange-equation and Continuity equation
It seems to me that there is a link between the continuity equation
$$\nabla\rho u + \frac{\partial \rho}{\partial t} = 0$$
and the Euler-Lagrange equation for Lagrangian mechanics
$$\nabla_q L - \...
- 19
3
votes
5
answers
936
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What is the point of knowing symmetries, conservation quantities of a system?
I think this kind of question has been asked, but i couldn’t find it.
Well i have already know things like symmetries, conserved quantities and Noether’s theorem, as well as their role in particle ...
- 311
1
vote
2
answers
78
views
Why isn't there such a thing as "internal momentum"?
The three most well-known conserved quantities in classical physics are energy, momentum, and angular momentum.
Suppose we have a system with no external forces acting on it. We can talk about the ...
- 8,640
1
vote
1
answer
54
views
Sufficient condition for conservation of conjugate momentum
Is the following statement true?
If $\frac{\partial \dot{q}}{\partial q}=0$, then the conjugate momentum $p_q$ is conserved.
We know that conjugate momentum of $q$ is conserved if $\frac{\partial L}{\...
- 41
1
vote
0
answers
53
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Doubt Regarding Noether's theorem for time-dependent systems
I'm having problems showing Noether's theorem when the lagrangian is time dependent. I'm trying to do it not using infinitesimal transformations from the beginning, but continuous transformations of a ...
1
vote
0
answers
26
views
Is the invariance of the Lagrangian under some transformation equivalent to the covariance of the motion equation? [duplicate]
Take the Lagrangian $L=\frac{1}{2}m{{\left( \frac{{\rm{d}}}{{\rm{d}}t}x \right)}^{2}}-\frac{1}{2}k{{x}^{2}}$, for example.
The equation of motion of this system should be given by $m\frac{{{{\rm{d}}}^{...
- 41
1
vote
0
answers
29
views
Energy conservation and Lorentz invariants [closed]
In relativistic collision theory,How can we deduce energy is conserved by using Lorentz transformation?
4
votes
1
answer
951
views
Why does a current loop obey Newton's third but a charged particle doesn't?
My super basic question is, the (magnetic) force between two steady current loops obeys Newton's third but the (magnetic) force between two charges doesn't. This is surprising given that the former is ...
- 1,095
2
votes
1
answer
72
views
Some doubts about action symmetry
We know that Symmetry of the Lagrangian ($\delta L = 0$) always yields some conservation law.
Now, if $\delta L \neq 0$, that doesn't mean we won't have conservation law, because if we can show action ...
- 525
1
vote
1
answer
68
views
How to mathematically prove the balls move at equal speeds after an inelastic collision?
Consider a ball moving at a certain speed. It hits an identical ball at rest. After the collision, both the balls move at equal angles $\theta \ne 90^{0}$ (inelastic collision) with the original line ...
0
votes
1
answer
68
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Why do both objects move with the same velocity here? [closed]
I was solving a homework question:
A body of mass M (Fig. 1.43) with a small disc of mass m placed on it rests on a smooth horizontal plane. The disc is set in motion in the horizontal direction with ...
- 73