# Questions tagged [conservation-laws]

The statement that a property of a system does not change if the system is isolated.

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### Which symmetries lead to the ladder operators of the harmonic oscillator?

It seems like symmetries usually lead to ladder operators. For example in a central potential problems the conservation of angular momentum leads to angular momentum ladder operators being used in the ...
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### Conservation of linear vs. angular momentum in two similar cases

I have a question that eludes my understanding: Imagine we have a bullet of mass $m$ and a rigid pendulum with a bob of mass $M$ hanging from a rigid rod of negligible mass hanging from the ceiling ...
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### Could we deduce energy, momentum and angular momentum conservation laws from only Galilean relativity?

In Newtonian physics we could deduce conservation of energy, momentum and angular momentum from Newton's three laws. But by Noether's theorem, conservation laws could be deduced from symmetries. Could ...
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### Charge conservation in ohmic material - Apparent paradox

Consider an ohmic material with constant conductivity, which obeys the relation: $$\vec J = \sigma \vec E$$ where $\vec J$ is the current density and $\sigma$ is the conductivity. Applying the first ...
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### Kinematics of a two-body decay [closed]

I suspect a flaw in the reasoning below, but am unable to pinpoint it: Is there something inconsistent in terms of the application of conservation of momentum and energy? Thanks for any hints in ...
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### Do bodies stick together after an inelastic oblique collision?

My question is particularly about an oblique collision case. (For example a body having velocity along x axis approaching another with velocity along y axis) From what I know, in perfectly inelastic ...
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### Does moving the idler in a wheel and disk CVT conserve energy or momentum? [closed]

Consider the wheel and disk CVTs (continuous variable transmissions) below. Configuration A comprises a CVT disk coupled to the "system under control" 's', whereby a control wheel 'cw' ...
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### Proving conservation of supercurrent

I am trying to prove that the supercurrent $J^\mu = \gamma^{\nu \rho} F^A_{\nu \rho} \gamma^\mu \lambda^A$ is conserved in ${\cal N}=1$ SUSY Yang-Mills theory ( basically trying to reproduce equation ...
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### 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 ...
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### Can impact offset of an electron on an ion affect the resulting particle velocities?

A free electron, of mass $m_e$ and velocity $v_e$ collides with an ion of mass $m_i$ and velocity $v_i$. When they recombine, a photon of exactly the ionization energy $E_i$ will be emitted, moving in ...
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### Why do basketballs with more air in them bounce more than ones with less air?

I thought it this because more air means more pressure, so there will be more pressure when the ball is deformed and it will gain more kinetic energy as it rebounds. However, some sources say that ...
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### Does Noether's theorem apply to a strict on-shell symmetry of the action that holds on every integration region?

I've worked through different proofs of Noether's theorem and read various posts about it on this site. Some important takeaways, among others from this and this post by Qmechanic were Every off-...
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### How can we choose two different mass moment of inertias for the same momentum calculation?

I am working on answering part (a) and here is what I got: By conserving linear momentum, we have that $$mv_0 =(3M)v_f \hspace{3mm}\implies \hspace{3mm} v_f =\frac{1}{3}v_0$$ Now, in order to conserve ...
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### Why does the mass term not violate particle number conservation in a free theory?

The Lagrangian of a free real scalar field theory is $$\mathcal{L} = \frac{1}{2} \partial_{\mu} \phi\; \partial^{\mu} \phi \; - \frac{1}{2} m^2 \phi^2.$$ If we decompose $\phi$ in terms of the ...
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### How can a free electron and an ion in a plasma recombine without violating conservation of energy and momentum?

This question is the inverse of How does ionization of gas molecule affect the translational kinetic energy of the molecule? The answer to that question is that a molecule cannot spontaneously ionize: ...
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### Symmetry transformation exact meaning

In whatever text/review I happen to come across (like for example From Noether’s Theorem to Bremsstrahlung: A pedagogical introduction to Large gauge transformations and Classical soft theorems, ...
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### Finding the Noether current

I'm currently reading "QFT for the gifted Amateur by Lancaster and Blundell, and in a lot of the problems I'm a bit unsure of how to do them, an example asked "Consider a system ...
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### Energy and momentum conservation for light reflection [duplicate]

There is a radiation pressure which means that when light reflects from a surface, the surface will get some momentum/energy. If so, what is the balancing change on the light/radiation side if light ...
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### Field equations for systems violating local conservation rule

Is there a modified gravity theory which only allows for some weaker form of local conservation rule? Like in Einstein's gravity, equating $G_{\mu\nu}$ with $T_{\mu\nu}$ naturally leads to ...
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### Proof for conservation of angular momentum in rotating frame of reference

imagine a simple situation such that an object is rotating on a table about a rope as seen in the below figure now if i pull on the rope from the center , the radius of circular motion of the object ...
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### Understanding kinetic energy [closed]

Let's assume I am on a boat and I throw rocks (image courtesy from Wikipedia): From my point of view, throwing the first rock and throwing the second rock appears to make no difference. It is the ...
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### How is Noether’s theorem actually applied?

Noether’s theorem roughly states that the existence of a symmetry group for a given system implies a conservation law for that system. All well and good, except that I’m shaky on exactly how you ...
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### Noether's theorem for supersymmetry [duplicate]

I know that Noether's theorem states that all symmetries of the universe correspond to some conservation law. If supersymmetry were true, would there be a new conservation law? In other words, does ...
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### Tsiolkovsky rocket equation assumptions

From what I understand, the elementary derivation of the Tsiolkovsky rocket equation makes the assumption that mass is lost as a linear function of time. Why do we make this assumption? Does it follow ...
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### Confusion in conservation of momentum [closed]

Two masses $m_1$ and $m_2$ are attached to the two ends of a rope that is sent through a pulley. Then a mass $M$ is dropped onto the mass $m_1$ from a $h$ height. So when the law of conservation of ...
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### Does the direction of an angular velocity vector always stays constant with no force involved [duplicate]

Are there cases where there is a rigid body that rotates somehow and the direction of the angular velocity vector changes in the lab system?
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### "Momentum" of spinning disc from collision -- conserving momentum of input momentum?

I have an application for which I have concluded a collision lets conserve momentum. Examples of the type of scenario in which I believe my conclusion applies: a waterwheel blade hit by a ball (wheel ...
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### Energy created by gravity

So just a thought experiment: I take my rocket and fly through space. Meanwhile I pick up some piece of debris that experiences no (big) gravitational pull. I attach it with an infinitely long rope to ...
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### Challenging Cauchy's Stress Tensor: Objectivity and Generalization of Divergence Theorem

I'm investigating the limitations of the Cauchy stress tensor model in classical continuum mechanics, specifically focusing on its compliance with the principle of material frame indifference (MFI) ...
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### Rolling in opposite direction to linear motion

In this blog about a cylinder rolling up a frictionless incline, the author concludes that the cylinder will still be spinning clockwise at the top of its ascent up the hill and will then descend with ...
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