Questions tagged [conservation-laws]

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

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Higher form symmetries and massive gauge fields

I have seen all kinds of questions and answers about how to identify a higher-form symmetries, but they all seem rather abstract. What I would like to do is investigate two very simple examples. ...
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Why is angular momentum conserved in a central field?

I am trying to understand how a gyroscope works, which in the broad strokes is due to conservation of angular momentum. I understand the case when the angular momentum passes through the origin of ...
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State an equation for conservation of mass and use it to show that fluids of constant density are incompressible

I have the following question: State an equation for conservation of mass and use it to show that fluids of constant density are incompressible My solution (1): My solution (2): I don't know how ...
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Intuition for the time/energy connection?

I find the following analogy reasonably intuitive: translational symmetry : conservation of linear momentum :: rotational symmetry : conservation of angular momentum In contrast, I find the analogy ...
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Momentum conservation when virtual photon decay into lepton pair

I know the fact that one photon can not decay into electron-positron pair. at the CM frame, the momentum of electron + positron is zero. However, the momentum of a photon can not be zero. Though, I ...
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Constant expectation values for spin components of Dirac particles

My question is largely related to this one: Spin expectation values in Dirac theory It regards a free Dirac particle, with spin z+ in its rest frame, and moving with momentum in the x direction as ...
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Mass conservation in fluid dynamics

I am trying to derive the mass conservation equation: In one of the step we are given the equation to find Fluid mass gained through a small element of the surface 𝑑𝑆 in a time 𝑑𝑡 is: I don't ...
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Least Action in General Relativity

For an affinely parameterised geodesic we can form the Lagrangian: $$ \mathcal L = g_{ab}\dot x^a\dot x^b = \text{constant} $$ The Lagrangian is constant by the fact that the geodesic parallel ...
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Validity of continuity equation $\frac{\partial \rho }{\partial t}+\nabla \cdot \left(\rho \vec{V}\right)=0$

$\frac{\partial \rho }{\partial t}+\nabla \cdot \left(\rho \vec{V}\right)=0$ When is the continuity equation valid? And how can i find it mathematically? Is it valid only for newtonial fluids?, ...
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Kinetic energy produced in an explosion

If there is a train moving at 2 m/s with a cannon attached to it loaded with a ball, and then the ball is launched from the train, how would one find the kinetic energy produced by the explosion if ...
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Landau Lifshitz pseudotensor — energy density

Landau-Lifshitz stress-energy pseudotensor $t^{ik}$ is defined in such a way that, combined with matter stress-energy tensor $T^{ik}$, it leads to continuity equation: $$ \frac{\partial}{\partial x^k} ...
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Can you used a tethered “boot” to move in space?

Preface: On Earth, with the help of gravity, I can easily tie a wrench to a rope, then spin it around, lasso-style, and let go at any time to send the wrench and rope flying away from me in the air. ...
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Intuitive argument for why $\Delta m=0$ for transitions with light polarised in $z$-direciton?

The selection rules have $\Delta m =0$ for light polarised in the z-direciton trying to excite an atom. Mathematically it is clear that $\langle n, l, m_l| z |n, l, m_l \rangle = 0$ unless $\Delta m=0$...
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Conservation of Energy with Chemical and Kinetic Energy

There is a rocket $R_1$ that is traveling with velocity $V$ with respect to another rocket $R_0$ of the same mass. $R_1$ has $J$ joules of kinetic energy with respect to $R_0$. $R_0$ has fuel onboard ...
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Throwing a baseball at a car and it staying there [closed]

I was recently asked the following question in a physics contest: For some odd reason, you decide to throw baseballs at a car of mass $M_i$, which is free to move frictionlessly on the ground. You ...
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Conservation of angular momentum of disk and block

This problem appeared on the 2021 $F=ma$ Test that was held three days ago. However, I'm having trouble understanding other solutions. Exact wording of problem: "A uniform solid circular disk of ...
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Physical intuition behind the equation of continuity

There is a question in my book The cross sectional area of water falling (streamline flow) from a tap decreases as it goes down. Explain this behaviour on the basis of equation of continuity. I know ...
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How to show that momentum is conserved when tachyon interacts with normal matter?

The problem is as follows: Show that when tachyons interact with normal particles, then a normal particle can emit a tachyon so that the total energy and 3-momentum are conserved. Does anyone know how ...
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On including conserved charges when maximizing entropy of a statistical system

One approach towards constructing the probability of a state in a system is by maximizing the constrained entropy $$ S[p(n);\alpha,\beta] = -\sum_np(n)\log(p(n))\;+\; \alpha\big(\sum_nE_np(n) -\langle ...
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Steam pressure and constant fuel temperature in steam turbines

I've heard that leaving a steam turbine unsupervised can lead to you losing your life. The reason they state is that the heating medium (or whatever it's called) such as coal or gas, produces variable ...
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What are good quantum numbers for the Hyperfine Hamiltonian?

The hyperfine hamiltonian for an atom with one electron in valence shell is of the form: $ H = H_0 + A_1\vec{S}\cdot\vec{L} + A_2\vec{L}\cdot\vec{I} + A_3\vec{S}\cdot\vec{I} + A_4(\vec{I}\cdot\hat{r})(...
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Prove that the angle formed is 90° at a perfectly elastic collision [closed]

I've read the already asked questions on this but I'm still stuck: Prove that when 2 perfectly elastic particles collide, with one being at rest, the angle formed is 90° Attempt. Given that this is ...
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Do quarks need to be conserved in particle interactions?

Specially, for $p^+ + n \rightarrow \Delta^- + \Delta^{++} + \pi^0$. I see that charge is conserved. All other conservation rules seem to check out. But, when drawing the Feynman diagram there seem to ...
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What happens to the mass of a burned object?

If I were to burn a pile of wood weighing a hundred kilograms and I would have a big sack hanging over the burning pile. In this sack I would catch all the smoke that came from the burning pile, if ...
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Intuitive explanation for why time symmetry implies conservation of energy?

According to Noether's Theorem, every physical symmetry leads to a conservation law. For example, time-translation symmetry (the laws of physics don't change over time) implies conservation of energy,...
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Area Swept by particle under central forces is an approximation

From Kepler's second law, we infer, the conservation of angular momentum is equivalent to saying the areal velocity is constant, And the proof goes like this $$ mr^2{\dot\theta=L} $$ where $L$ is ...
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Shouldn't change in entropy always be 0?

We know that entropy is defined as $$dS=\frac{dQ}T$$ Now in any isolated system, by definition $dQ=0$. So should entropy change in any isolated process or system always be 0?
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EM transitions - selection rules

In atomic physics we say that only transitions with $\Delta l = \pm 1$ are allowed. This is since photons are bosons. But for example in nuclear physics we also consider higher order EM transitions ($\...
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Does hero's engine have an upper limit for the rotational speed under ideal conditions?

This is a simple hero's engine. The source of the gas and the rotating part is seperated by a frictionless bearing. So only the upper part rotates. My question is this: Given ideal conditions ( no ...
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Energy conservation in two-body decays?

Let's consider a generic two-body decay $A \rightarrow B + C$. In the center-of-mass frame (i.e, the rest frame of particle $A$), we know that the four-momentum of particle $A$ can be written as $p^{\...
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Where is this magnetic rail gun getting its energy?

Please watch this youtube video of a magnetic rail gun moving a marble. So as you already know, Conservation of Energy states that "energy can be neither created nor destroyed, but can only ...
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Prove momentum is conserved

I have a question which I do not fully understand about conservation of momentum of the shallow-water equation in conservative form. We are given a velocity $u(x,t)$ and the height $h(x,t) = d + l(x,t)...
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Help deriving simple equation in two dimensional collision - conservation of momentum

I need help deriving this equation using the two given expressions in a two dimensional collision problem which uses the principle of conservation of momentum in the x and y axis. Mass $m_1$ and $m_2$ ...
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How to show that at resonance a damped mass-spring system gains no energy?

I am having trouble understanding the topic of resonance in vibrations. For a simple spring-mass-damper system, I need to calculate the energy from the drive function and compare it with the energy ...
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Why is the conservation of lepton number a thing?

Since there is no way to tell neutrinos and antineutrinos apart, does conservation of lepton number make any sense? As far as we can tell, the neutrinos and antineutrinos are indistinguishable so from ...
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Frames of Reference and Symmetry in Rotating Systems

Something is symmetric if it is invariant under transformation. If I have a rotating disc, it is said to have rotational symmetry because the conserved quantity in such a system is angular momentum. ...
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Why is angular momentum of object about its axis equal to that of a non-moving parallel axis?

Take for example earth. Earth has angular momentum about its own axis. However, if we ignore the orbital portion, the angular momentum of the earth relative to the sun's axis is the same. Another ...
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Noether's Theorem and Liouville's Theorem

Liouville's theorem states that for Hamiltonian systems the phase space volume $V(t)$ is a conserved quantity, i.e., $\frac{d}{dt}V(t)=0$. This is related to the fact that trajectories in phase space ...
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Why is this decay of the neutral pion suppressed?

I got given a homework problem to check various particle decays, whether they're allowed under the different conversation laws (Baryon, Lepton, charge etc.) Currently im stuck at the following one: $$ ...
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Why is energy lost here?

Let's say a $1 \ \text{kg}$ block is moving. With a speed of $1 \ \text{m/s}$ so its kinetic energy is $\frac{1}{2} \ \text{J}$. Now let's gently place a block of mass $3 \ \text{kg}$. Now as linear ...
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Are heat emissions as bad as greenhouse gasses?

Most of the technology we use generates excessive heat. Like cars, computers, smartphones, batteries etc... All of these needs to be cooled down in some way. Is all this extra heat adding to rising ...
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Intuition for angular momentum

A single object with mass $m$ is rotating around an origin at a distance $r$ and speed of $v$; so its angular momentum is equal to $mrv$; if we decrease its radius (say shorten the rope) its speed ...
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Conserved Charge in Conformal Field Theory

I am reading Introduction to Conformal Field Theory by Blumenhagen and Plauschinn, and do not quite understand how eq. 2.33 for the conserved charge $$ Q = \int dx^1 j_0 $$ is converted to eq. 2.34: $$...
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What exactly happens in a rigid body collision?

Consider a situation in which a body of mass m moving with a velocity v is collided with a similar mass, applying momentum conservation,the initial mass will come to rest and the other mass will move ...
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What symmetries would cause conservation of acceleration?

I have recently been trying to see what consequences Noether's theorem would have if our world was setup with different symmetries. It is a quite elegant result that the invariance of the Lagrangian ...
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Question on how to actually use momentum space Feynman rules in $\phi^4$-theory

The momentum space Feynman rules state that we "integrate over all undetermined momenta" and "impose momentum conservation at each vertex". This is given for example on page 95 of ...
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Have all Noether Charges been enumerated? [duplicate]

Noether's theorem states that every symmetry (of a Lagrangian) is associated with a conserved quantity. Is it possible to know whether or not all symmetries (of the Lagrangians we use) have been ...
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Can someone explain conservation laws in terms of state space?

"Whenever a dynamical law divides the state space into separate cycles, there is a memory of which cycle they started in. Such a memory is called a conservation law." —What is meant by this ...
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Time spent by a comet inside the Earth's orbital (Kepler problem re-visit)

I come across this interesting problem comet-x-earth. It was an exam problem asking the time that a comet will be spent inside the Earth's orbital. I make an illustration for the problem: The comet ...
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If videogames do not conserve momentum, must that mean that they do not have translational symmetry? [closed]

I've heard said many times that symmetries in our universe imply the existence of conserved quantities. One example often given is that translational symmetry implies that momentum is conserved. This ...

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