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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 ...
eli morhayim's user avatar
1 vote
3 answers
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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 ...
Giovanni Piacentini's user avatar
2 votes
3 answers
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Two contradictory derivations of Killing equation

In David Tongs lecture notes he derives the Killing equation by showing that the charge $Q=\xi_\mu \frac{\mathrm{d}x^\mu}{\mathrm{d}\tau}$ is conserved $$ 0=\frac{\mathrm{d}Q}{\mathrm{d}\tau}=\frac{\...
Silas's user avatar
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Doubt on conservation of angular momentum for Kepler's laws

Just before proving Kepler's laws, my Professor claimed that if $\vec{F}$ is a central force with center $O$ and it is the only force acting on a point $P$, then the trajectory of $P$ is a curve plane....
Davide Masi's user avatar
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Idealized Newton's cradle

I was wondering about the conditions for an ideal newtons cradle. Under regular circumstances, the collisions are inelastic and a newton's cradle dissipates energy in various forms like heat, friction,...
Ritesh Nandi's user avatar
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Apparent violation of Newton's Third Law in relativistic force transformation

In special relativity, we know that, relativistic force is defined as F = dp/dt, where p = γmv. For forces perpendicular to the direction of relative motion, force transforms as F' = γF. Consider two ...
Kenshin's user avatar
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Which kinds of systems are described by a heat equation?

Every extensive thermodynamic variable has a continuity equation associated to it: $$\frac{\partial \rho}{\partial t}+\vec \nabla \cdot \vec J=0$$ where $\rho$ is the density of said variable and $\...
Lagrangiano's user avatar
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Is there any phenomenon where opposite reaction (Newton's 3rd Law) is not fulfilled?

I'm wondering if there is any case in nature/physics where it has been observed "where there is an action, there is not necessarily an exact equal and opposite reaction". Or is there some ...
Gabe's user avatar
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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". ...
moshtaba's user avatar
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1 answer
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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 ...
moshtaba's user avatar
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How do you solve instantaneous 3 body collisions

A few years ago I built myself a very basic python program that did some very basic collision mechanics between particles with a mass and velocity and it was helpful in learning a few things and ...
Max's user avatar
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1 answer
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Energy of moving Sine-Gordon breather

A few days ago I stumbled across the formula for the energy of a moving breather for the sine-Gordon equation $$ \Box^2 \phi = -\sin\phi.$$ The energy in general is given by ($c=1$) $$ E = \int_{-\...
Ash's user avatar
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1 answer
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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 ...
moshtaba's user avatar
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-1 votes
2 answers
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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 ...
Lagrangiano's user avatar
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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 ...
Leonardo's user avatar
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3 answers
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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 ...
User's user avatar
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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' ...
Mr. Haelscheir's user avatar
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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 ...
baba26's user avatar
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2 answers
82 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 ...
user1255055's user avatar
-1 votes
1 answer
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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 ...
Hugh Perkins's user avatar
3 votes
2 answers
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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 ...
user386598's user avatar
2 votes
1 answer
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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-...
WillHallas's user avatar
2 votes
3 answers
235 views

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 ...
Chris Christopherson's user avatar
2 votes
1 answer
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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 ...
ratchet411's user avatar
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2 answers
66 views

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: ...
Hugh Perkins's user avatar
1 vote
1 answer
62 views

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, ...
schris38's user avatar
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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 ...
Morty Levinson's user avatar
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20 views

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 ...
Damir Tenishev's user avatar
2 votes
0 answers
46 views

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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1 answer
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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 ...
Arnav Agarwal's user avatar
1 vote
0 answers
64 views

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 ...
Maximus's user avatar
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1 vote
1 answer
97 views

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 ...
controlgroup's user avatar
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0 answers
31 views

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 ...
mathman's user avatar
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1 answer
58 views

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 ...
wonderwave's user avatar
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1 answer
63 views

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 ...
Yara Try's user avatar
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-1 votes
1 answer
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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 ...
STOI's user avatar
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2 votes
4 answers
152 views

Why exactly does time translation symmetry lead to conservation of energy? [duplicate]

As far as I know (and I don't know much), Noether's theorem claims that time translation invariance of the laws of physics leads to the conservation of energy. The way I understand it is that if we ...
Parzh from Ukraine's user avatar
5 votes
2 answers
644 views

Theorem in mechanics relating energy flow and momentum

In Feynman's Lecture 27 on Vol. II it is written that There is an important theorem in mechanics which is this: whenever there is a flow of energy in any circumstance at all (field energy or any ...
lalala's user avatar
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1 answer
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Why are there selection rules in electronic transitions?

Why are there selection rules in electronic transitions? What restricts electrons from making transitions to certain states although it is energetically possible?
Tushar Anand's user avatar
1 vote
1 answer
75 views

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 - \...
theta_phi's user avatar
-1 votes
1 answer
108 views

A car collides with a fast-moving bus, which vehicle experiences the greater change in momentum? [closed]

$\textbf{My question:}$ A car collides with a fast-moving bus, which vehicle experiences the greater change in momentum? But when I googled I got conflicting answers from "expert answers": ...
Reuben's user avatar
  • 283
0 votes
1 answer
39 views

Conservation of $y$ component of momentum

Rain with mass $mr$, falling vertically downwards at speed $v$, into a truck of mass $mt$, moving on a horizontal surface at speed $u$ inital, ignoring friction and air resistance. Taking the system ...
Amit's user avatar
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1 vote
3 answers
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How is momentum conserved in this collision with loosely-connected spheres?

There are three identical spheres. B and C are loosely connected with a light inextensible string, and A approaches B directly at some initial velocity $v$. There is no angular momentum. A and B have ...
spraff's user avatar
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0 votes
0 answers
19 views

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?
eitann's user avatar
  • 101
0 votes
1 answer
83 views

"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 ...
user5588495's user avatar
1 vote
2 answers
75 views

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 ...
TheBest_Kappa's user avatar
1 vote
1 answer
104 views

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) ...
Foad's user avatar
  • 373
0 votes
3 answers
77 views

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 ...
KDP's user avatar
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1 vote
1 answer
29 views

Im confused on how conservation of momentum works mathematically for a problem involving a skater throwing two weights from rest [closed]

Here's the question. A 40-kg skateboarder on a 3-kg board is training with two 5-kg weights. Beginning from rest, she throws the weights horizontally, one at a time from her board. The speed of each ...
Groggyboi's user avatar
1 vote
2 answers
139 views

Electrons repel each other forever - why? [closed]

I.e. charge is conserved. How? Why? Background I am coming here with only my intuition, and a desire to learn. My intuition "feels" that if an electron keeps on repelling other electrons, ...
Rabbi Kaii's user avatar

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