Questions tagged [conservation-laws]
The statement that a property of a system does not change if the system is isolated.
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How do conservation of energy and relativity hold if spacetime is discrete?
I understand the principle of conservation of energy and momentum in classical physics. I am aware of the fact that such conservation laws arise due to fairly deep mathematical symmetries in the ...
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3answers
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Probability current density confusion
As we all know, the probability current density in quantum mechanics is defined as: $$\textbf{J}=\dfrac{\hbar}{2mi}(\Psi^* \nabla \Psi-\Psi \nabla \Psi^*)$$ For simplicity let us work in one dimension ...
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Why does the speed of a ping pong ball increase when the space in which it can bounce decreases?
I was playing table tennis the other day when I my ball fell off the table. I placed my paddle above it in order to slow it down, and then I brought the paddle to the ground so that the ball would ...
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Conservation of Momentum on Noether's Theorem for Relativistic Classical Fields
Consider an infinitesimal translation (α = 0, 1, 2, 3)
$$x'^{\mu} = x^{\mu} + \frac{\delta x^{\mu}}{\delta a^{\alpha}} \delta a^{\alpha}$$
where $\delta a^{\alpha}$ is a parameter from transformation ...
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1answer
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In a closed system (body), is it possible to stop fast moving body with internal forces? [closed]
We know closed system cannot generate unidirection motion of itself. is it possible for system to stop or slow by itself with internal motion when it is moving very fast. Example: A space ship is ...
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2answers
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Do Maxwell's equations contain any information on the time evolution of the current density $J$?
The answers to Can the Lorentz force expression be derived from Maxwell's equations? make clear that Maxwell's equations contain only information on the evolution of the fields, and not their effects ...
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Is conservation of angular momentum responsible for rotating a rigid body when it slows down an internal wheel?
Suppose that there is a rigid body, such as a satellite, which contains inside it a wheel that is spinning at a constant rate. This means that the satellite has a certain, constant, angular momentum ...
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Covariance of Noether's charge in GR
If we consider a theory of GR (the standard Einstein-Hilbert action) and a complex scalar field, we can easily see that we have a global $U(1)$ symmetry for the scalar field. Now, via Noether's ...
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How to identify internal and external forces acting on a system of particles?
In my Physics textbook there is sample problem in which a firecracker placed inside a coconut of mass M, initially at rest on a frictionless floor, blows the coconut into three pieces (A, B and C) ...
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What is the mathematical implication of constant temperature and/or energy/momentum in the following identity?
Question:
What is the mathematical implication of constant temperature $(T)$, constant energy/momentum $(E)$ and constant ration of $(E/T)$ shown by the subscripts in $(1)$*?
$$T \left( \frac{\...
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Collision of constrained spheres
In a standard collision of two spheres, if one wants to be general for inelastic, rough rotating spheres, there are two coefficients of restitution used. The coefficient of restitution in the normal ...
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Position Based Dynamics - Cloth Balloon Constraint
I am attempting to implement the cloth balloon constraint from section 4.4 of this paper:
https://matthias-research.github.io/pages/publications/posBasedDyn.pdf
It is my understanding that after ...
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3answers
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What kind of system would conserve momentum but not energy?
In my physics book (chapter 9 - center of mass, linear momentum and collision), it is written
Momentum should not be confused with energy. In some cases momentum is conserved but energy is definitely ...
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1answer
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Want to clear some doubts on Conservation of momentum [closed]
I was doing a question on SHM and i came across something pecular..In that Question Conservation of momentum eqn was written then differentiated to find the eqn of acceleration. Are we allowed to do ...
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1answer
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Coefficient of restitution for a perfectly inelastic collision
The coefficient of restitution is defined as the ratio of the differences in velocities of colliding objects after and before the collision: $$k_{COR}=\frac{v_{1,after}-v_{2,after}}{v_{1,before}-v_{2,...
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Interpretation of Gauss's theorem applied to Maxwell's equations: $\dfrac{d}{dt} \int \rho \ dV + \int \mathbf{j} \cdot \mathbf{n} \ dS = 0$
Using Maxwell's equations and Gauss's theorem, we get
$$\dfrac{d}{dt} \int \rho \ dV + \int \mathbf{j} \cdot \mathbf{n} \ dS = 0,$$
where $\rho$ is the electric charge density and $\mathbf{j}$ is the ...
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Conserved quantity associated with Permutation Symmetry?
Based on my crude understanding of Noether's Theorem, for each symmetry in physics, there is a conserved quantity associated with it. If so, what is the conserved quantity associated with permutation ...
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Conservation laws in Newtonian mechanics
Newton's third law is equivalent to conservation of momentum.
Assuming conservative systems, we get conservation of (mechanical) energy.
Assuming central forces, we get conservation of angular ...
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Is it possible to change the momentum of a system without actually doing any work on the system?
Consider a rigid wall somewhere in free space. Now imagine two balls of the same mass and same speed headed towards the wall from two opposite directions. Now they go on to hit the wall and rebound ...
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1answer
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Conserved quantities for the system consisting of an uniform spinning top
A uniform top of mass $M$ with its lower end fixed to the ground is rotating on its axis of symmetry with angular velocity $\Omega$, initially in a vertical position ($\theta=0, \dot \theta=0$). The ...
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1answer
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Definition of charge with Hodge star
I understand the definition of charge given by
$$ Q = \int_{\mathbb{R}^{D-1}} \text{d}^{D-1}x J^0. \tag{1}$$
In Carroll’s Spacetime and Geometry book (pg. 455) he writes
Start by imagining that we ...
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Global and gauge charges
I have seen several questions regarding the difference between global and gauge charges, but I don't really get the physical implications.
The sQED lagrangian is:
$\mathcal{L}=-\frac{1}{4}F_{\mu \nu}^...
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Why is angular momentum conserved in this case?
I was doing the following problem:
A solid cube of wood of side $2a$ and mass $M$ is resting on a horizontal surface. The cube is constrained to rotate about an axis $AB$. A bullet of mass $m$ and ...
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What happens if you spin a coin in space?
Will the coin spin forever or will it be de-accelerated by the gravitational force?
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Is possible to derive electromagnetic terms in energy balance from a molecular prespective?
In 'Physical foundations of continuum mechanics', A. Ian Murdoch shows that,
starting from the Newton's law of a single molecule, modeled as a material point inserted in a system of material points, ...
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1answer
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Is the $p + p \to K^+ + K^+ + n + n$ process allowed in the SM?
In an exercise it asks to prove why certain processes cannot happen in the Standard Model. One such process is the following:
$$ p + p \to K^+ + K^+ + n + n $$
This process conserves baryonic number ...
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1answer
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In general, conservation laws do not hold whenever the center of mass of the system is moving?
I am currently studying Classical Mechanics, fifth edition, by Kibble and Berkshire. Problem 3 of chapter 1 is as follows:
Consider a system of three particles, each of mass $m$, whose motion is ...
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1answer
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Does the law of conservation of momentum also hold for position and acceleration?
The following is the law of conservation of momentum (in terms of velocity):
$$m_1\mathbf{v_1} + m_2 \mathbf{v_2} = m_1 \mathbf{v_1}^\prime + m_2 \mathbf{v_2}^\prime.$$
Does the law of conservation of ...
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1answer
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Why can't we take the surface as part of a system when conserving linear momentum?
In a problem I'm facing, friction acts on the system that I wish to apply conservation of linear momentum. Why can't I take the surface as a part of system and conserve momentum? As the surface is ...
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1answer
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Will a rotating rigid disk precess in microgravity?
Given a wheel like a disk with some angular velocity $\omega$, will it precess in microgravity?
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Continuity equation in QM
I found this question in a quantum mechanics exam:
What is the physical interpretation of the continuity equation $\frac{\partial\rho}{\partial t}+\frac{\partial j}{\partial x}=0$? Here $\rho(x,t)$ is ...
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Flight mechanics of a quadcopter, yaw, conservation of angular momentum, linear momentum counterpart?
I have been trying to understand how a quadcopter yaws. Referring to the figure below which is bird's eye view of a quadcopter:
image credit : https://www.youtube.com/watch?v=iQAPkN7OWus
While the ...
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7answers
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What is the second conserved Quantity of the Pendulum?
Consider the problem of a classical pendulum whose state can be described by a function $\theta(t)$ where $\theta$ is measured from the line directly below. We then have that our pendulum's $\theta$ ...
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1answer
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Which body would have a greater force exerted on it?
If mosquito and train each travelling in a straight line towards each other with the same velocity, collide with each other head-on, then which object would under the exercion of a greater force?
Now ...
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A rod lies on a smooth surface and a ball hits it at one end and gets stuck to it
I know how to solve these kind of questions but here since it is an inelastic collision I have some doubts. I checked the solution where they conserved linear momentum as: $(M+m)v=mu$ [$v$ is final, $...
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Do waterfalls conserve momentum? If so, how?
I understand that waterfalls conserve energy, given the fact that the top of a waterfall possesses gravitational potential energy, and as the water is falling from top to bottom, this potential energy ...
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1answer
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Finding mass ratio from the collision of two bodies
I am currently studying Clssical Mechanics, fifth edition, by Kibble and Berkshire. Problem 1 of chapter 1 is as follows:
An object $A$ moving with velocity $\mathbf{v}$ collides with a stationary ...
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1answer
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Is there any deeper reason behind the conservation of mass?
I have read that behind the conservation of energy or momentum is the Noether theorem with its intimidating maths.
Is there any similar deeper foundation behind the conservation of mass?
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Conservation of spin in Non-relativistic limit
Consider electron-positron interaction :
$$e^-e^+\rightarrow\mu^+\mu^-$$
when peskin book come to compute Non relativistic limit of this process said that, because we are in Non relativistic limit we ...
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1answer
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How do I know which Feynman diagram is right? ($s,t,u$-channel)
Following the Lagrangian:
$$\tag{1} \mathcal{L} = \mathcal{L}_{initial}-M^2 \varphi^* \varphi - g\varphi^*\varphi -g\phi^3$$
where $\phi$ is a particle associated with a real scalar field, and $\...
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Is the exchange of momentum between two interacting objects always the same? [duplicate]
The rule is that the total momentum of an isolated system is constant.
I am interested in one question. If you imagine a closed system, there will be two planets, for example: Earth and Mars. They ...
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Why can we still assume momentum is conserved in an inelastic collision?
This is very similar to this question:
How can momentum but not energy be conserved in an inelastic collision?
However, I feel as though an important caveat was not resolved for me which is why I am ...
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0answers
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Is there a formal distinction between Lorentz boosts and the others types of transformations of the Poincaré group?
The doubt arises as space translations can be associated to homogeneity of space, time translations to homogeneity of time and classical rotations to isotropy of space. These properties of space leads ...
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Why don’t astronauts “push” spacecraft?
Perhaps it goes without saying, but according to Newton’s laws “every action has an equal and opposite reaction”. How do astronauts, especially those inside small spacecraft like the Crew Dragon, not “...
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Conservation of left-handed quark current
I'm reading about the Operator Product Expansion in Gelis's A Stroll Through Quantum Fields section 7.4.2. As an example, he's using the product of currents
$$A_1^\mu = \overline{d}_L\gamma^\mu u_L$, ...
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1answer
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During particle-antiparticle annihilation, are the photons expelled perfectly perpendicular?
During particle-antiparticle annihilation, are the photons expelled perfectly perpendicular to the original direction of the particle-antiparticle pair?
There is very little information on the web ...
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Problem with the conservation law in Feynman diagram
I have some problem with the virtual particle process as discussed below.
We have some interactions that have real photon as produced particle. We consider a tree level Feynman diagram for it and the ...
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Gauge symmetry implies global symmetry and quantum gravity
It is folklore that quantum gravity cannot have any exact global symmetry (see Global symmetries in quantum gravity). This follows for example from thought experiments involving black holes (no-hair). ...
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Additions to the stress-energy tensor that leave equations of motion the same
In short:
For a stress-energy tensor $T^{\mu\nu}$, what are possible additions that will leave the tensor equations of motion $\nabla_\nu T^{\mu\nu} = 0$ unchanged?
Context:
Any modification, $T^...
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1answer
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Noether's Theorem and conservation of momentum
So as we all know for a system that has translational symmetry Noether's Theorem states that momentum is conserved, more precisely the theorem states that the quantity:
$$\frac{\partial L}{\partial \...
