Questions tagged [conservation-laws]

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

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Why doesn't pulling in your arms on a rotating stool violate conservation of energy? [duplicate]

From what I understand, pulling in one's arms on a rotating stool would decrease the radius, thus decreasing the moment of inertia. If we decrease the radius enough to halve the moment of inertia, we ...
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Accessible States in the Ergodic Hypothesis

According to Wikipedia, the ergodic hypothesis is the assumption that all accessible microstates are equiprobable over a long period of time. My question is about the precise meaning of "...
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Are Van Der Waals Forces related to the Van der Waals Equation?

In a physics class, I learned about Van Der Waals forces that allow geckos to stick. Do they have any relation to the Van Der Waals Equation relating gas pressure to temperature and volume?
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Why do internal forces not affect the conservation of momentum?

How is momentum conserved? I know that the condition is that no external resultant force should act on the interacting objects. But how is the momentum conserved if the objects surfaces touch and ...
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Law of Conservation of Time? [closed]

So, it may or may not seem to be stupid, but if we think that there is a person named John who travels back in time by any means, and he met his past lets say him small John then the past small John ...
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Stopping Distance in Conservation of Momentum Investigation

In a set of old textbook materials from Merrill Physics from the mid 90s, there is a page on Fitch Inertial Barriers put near construction zones. Three cars are going to collide into a set of these ...
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Consequence of diffeomorphisms invariance in General Relativity

Let's consider a theory with gravity and matter field(s) $\Phi$. The action of this theory is the following: \begin{equation} S[g,\Phi] = S_g[g]+S_m[g,\Phi] = \frac{1}{16\pi G}\int_Md^4x\sqrt{-g}R+\...
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Noether's theorems and General covariance

Given the action $$ A = \int_{M} d^{4}x \ \mathcal{L}(\phi, \nabla \phi) $$ where $\mathcal{L}$ is a lagrangian density, or if you prefer $\mathcal{L} = \sqrt{-g} \mathcal{\tilde{L}}$ and $\mathcal{\...
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Noether charges as generators of symmetry transformation in classical Hamiltonian field theories

I would like to prove that Noether charge $Q$ is a generator of the same symmetry as the one that due to the Noether's theorem led to the current $j^\mu$ and charge $Q$ in classical field theory (I ...
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How much of the universe will get flatter in how long?

So I learned recently that star systems are relatively flat due to the conservation of angular momentum. On how large a scale does this degree of flattening apply. i.e will the universe eventually ...
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Conservation of momentum of airplane in runway

On exercise 4.6 from Klepper's Book "Intro do mechanics" there is a plane on a landing lane. It has its engine off but is braking with force $F_b$. Also, it is attachted to a sandbag that ...
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Example of time-dependent constant of motion in classical mechanics

In classical mechanics text, when learning about Poisson brackets, one gets $\frac{df}{dt} = \{f,H\} +\frac{\partial f}{\partial t}$, where $H$ is the Hamiltonian of the system and for $\frac{df}{dt}=...
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Equation in Field Quantization Greiner

Hello, I dont understand the red part. Shouldn't it have minus instead? Sorry for lack of formatting, I only have a phone.
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Newton's third law and cannons

A cannonball firing from a cannon is often given as an example of Newton's third law. The explanation goes like this: The cannon exerts a force on the cannonball and thus the cannonball exerts an ...
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Different symmetries or no symmetries in string theory?

I was reading the book "A Fortunate Universe" by Geraint Lewis and Luke Barnes and something caught my attention: At page 195 the authors say that universes with different symmetries could ...
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Calculating final velocity of two colliding protons?

In an isolated system of two colliding protons [ say, proton1(p1) and proton2(p2)]; initially p2 is at rest, and p1 is moving with uniform horizontal velocity $\vec{u_1}=a \hat{i}$ m/s. First way of ...
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Angular momentum vectors

Hi I am trying to learn the concepts of angular momentum but I don't understand why in the formula for torque the radius from the line of action of the force is regarded as a vector surely distance is ...
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What term describes the trajectory space splitting behavior when parametrizing a pendulum?

So I was thinking about this post I made earlier: What is the second conserved Quantity of the Pendulum? In which a pendulum appears two have significant properties. It's Kinetic Energy and its Phase. ...
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Conserving angular momentum in elementary decay/reaction

I am trying to understand how to conserve angular momentum in a elementary decay/reaction. Consider the elementary reaction: $$ K^{-}(J = 0) +p(J = 1/2) ~\to~ \Omega^{-}(J = 3/2) + K^{+}(J = 0) + K^{...
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Difference between strong interaction and weak interaction?

I was looking at a straight forward answer on internet which I am unable to find. Can there be a strong interaction in which transformation of one quark flavour into other takes place(Eg. up quark -&...
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About the helicity current

In the paper https://arxiv.org/abs/1912.11034 authors introduce a new conserved current for the massless Dirac fermions. This Lagrangian $$ \mathcal{L} = \frac{i}{2} (\bar{\psi} \gamma^{\mu} \partial_\...
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Differential with respect to constant in Canonical Tranformation

I'm reading canonical transformation from Classical Mechanics by Goldstein. It says, considers a situation in which the Hamiltonian is a constant of the motion, and where all coordinate $q_i$ are ...
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Covariant conservation of the energy-momentum tensor

In order to derive the geodesic equation of motion from the covariant conservation of the energy-momentum tensor we have to do the following procedure: $$ T^{\mu\nu}_{\space\space\space\space;\mu}= \...
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Conserved quantities quantum field theory

In classical field theory, due to Noether's theorem, corresponding to every continuous symmetry there is a conserved current/charge. However, to arrive at this conclusion one has to assume that the ...
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Is it necessary that if we concider a system then always work done by internal forces would be equal to zero? [duplicate]

I am getting confused in between these two cases: Case 1: When we solve pulley-block problems using work-energy theorem then the work done by tension force gets cancelled out because in one block ...
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If net $F=0$ on a system then KE of the system may change due to internal forces or due to internal work done

While explaining Centre of Mass, my teacher told this exact statement that "If net $F=0$ on a system then KE of the system may change due to internal forces or due to internal work done." ...
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Velocity of centre of mass of two particles is v and the sum of the masses of two particles is m [closed]

The total kinetic energy of the system: (A) will be equal to 1/2 mv^2 (B) will always be less than 1/2 mv^2 (C) will be greater than or equal to 1/2 mv^2 (D) will always be greater than 1/2 mv^2 The ...
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Why is it that when you break a brick it hurts less than when you don't break the brick? [duplicate]

Why is it that when you break a brick it hurts less than when you don't break the brick? Consider the brick has a maximum force it can endure $F_\text{max}$. If you hit the brick and it doesn't break ...
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How do I investigate the effect of height of the fall of a marble on the size of a crater in sand?

What do I need? What would the most effective method be to reduce the uncertainty of my outcome? Should I record the mass and diameter of the marble too or just the height? If I change mass will it be ...
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Unitary Operators and symmetries in Quantum Mechanics

This is regarding symmetries and unitary transformations in quantum mechanics. Consider some infinitesimal continuous transformation given by $T$, where $T = 1 - \frac{iG\epsilon}{\hbar}$. If this ...
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Finding amount of energy transfer for $^4He$ and $\gamma$ [closed]

I'm doing practice questions for an upcoming exam and I became stuck on this one (found on OpenStax here): For the reaction, $n+^3He→^4He+\gamma$, find the amount of energy transfers to $^4He$ and $\...
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Conservation law of colour current in Yang-Mills theories

In a Yang-Mills theory where the fermion fields transform under $\Psi \rightarrow e^{-\theta^A t_A} \Psi$ with $t_A$ generators of a Lie-algebra fulfilling $[t_A,t_B]=f^A_{BC}t_C$ a Noether current $...
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$L_3$ conserved on geodesics?

Let's take a simple $E^3$ space with coordinates $(x,y,z)$ and metric tensor $$ g = \mathrm{d} x \otimes \mathrm{d} x + \mathrm{d} y \otimes \mathrm{d} y + \mathrm{d} z \otimes \mathrm{d} z $$ The ...
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Are these conservation laws always true?

Imagine a system of particles with the internal force on $i^{th}$ particle due to $j^{th}$ particle being given as $f_{ij}$ From the derivation of law of conservation of momentum and law conservation ...
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How does a rocket travel in a vacuum space? [duplicate]

OK.. let us consider a rocket initially at rest in outer space. Space is considered as vacuum so there is hardly something that rocket can insert a force on. So if the rocket fires up its engines will ...
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Confused about SM neutrinos

I am a bit confused about neutrinos in the standard model. The vertex of the weak interaction charged current, implies that any neutrino interacting through the charged current must be left handed. ...
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Is this Feynman diagram possible or not?

Is this possible or not, and how do you know? I am taking the convention of time being from left to right.
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When exactly does the velocity of a cart change?

I have done many problems where where a small body is thrown from a moving cart and we have to use conservation of momentum to find the final velocities of the cart and the thrown object. To find the ...
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Impulse given to a rotating rod at the centre VS the end

This is a doubt from a question I have solved, I will extract only my queries from it. Case1: let a rod of mass '$m$' lie on a smooth table and impulse $Ft$ is given at one of the ends. (assume the ...
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Why Mandelstam variables in Minkowski do not cover the whole allowed space?

It was mentioned by N.Arkani-Hamed https://www.youtube.com/watch?v=uPrlD0vorzk that Mandelstam variables in Minkowski signature $(+---)$ do not cover that whole allowed space of $s$, $t$, whereas in ...
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Why do inelastic collisions occur in theoretical calculations?

When solving collision problems related to the conservation of momentum in my applied maths course, the question of whether the collision was elastic or not is often asked. A lot of them time (such as ...
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Deriving Laplace-Runge-Lenz Vector

consider a particle in a central potential, i.e. the potential $V$ only depends on the distance $ r = \| \vec{x} \|$ to the origin. The equation of motion thus reads $$ m\ddot{\vec{x}}=-\frac{\partial}...
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Kepler's Second Law: conservation of the energy or of the angular momentum?

Reading from example the old question, Angular Momentum and Kepler's Second Law Considering that now I not remember the proof because starting from the angular moment conservation of $L$ we have ...
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Why does an oscillating mass does not produce gravitational waves (in contrast with an oscillating electric charge)? [duplicate]

I would like to gain insight about this question. I have read it is related with the conservation of momentum, but cannot really differentiate it from the oscillating charge. The monopole radiation ...
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Is there any (locally) conserved charges associated to gauge symmetries?

I'm currently in my second year of master. From what I understand, in QFT, Noether's first theorem implies that for any continuous symmetry (i.e. associated to a $n$-dimensional Lie group $G$, $n\geq ...
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Constants of motion [duplicate]

For any system performing any kind of motion with $n$ degrees of freedom, are $2n-1$ integrals of motion and also $2n$ constants of motion always present? If yes, then is there always a symmetry for ...
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What is the reason for this apparent paradox caused by a massless spring with a locking mechanism?

Imagine that a ball of mass $m$ is launched at a block, which also has mass $m$. Attached to the block, facing the ball, is a massless spring with a massless board at the end. Alternatively, we can ...
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Does the uncertainty principle say that conservation of momentum is violated in quantum mechanics? [duplicate]

The uncertainty principle of Heisenberg says that the uncertainty in the position of a particle multiplied by the uncertainty of the momentum of a particle is always more than or equal to $\frac{\hbar}...
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Equation of Forces for Rocket - The Rocket Equation and Newton's Third Law

Assume a rocket is being vertically accelerated in a homogeneous gravitational field. In the reference frame of the rocket, the burnt fuel is being exhausted downwards with a velocity of $\Delta u$. ...
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Why is the loss of energy maxed in perfectly inelastic collision?

I was doing a physics problem, and it had asked me to find the maximum $K_e$ loss, but I don’t understand why the loss is maxed when the objects stick together (the collision is inelastic).

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