Questions tagged [conservation-laws]
The statement that a property of a system does not change if the system is isolated.
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Conservation of angular momentum from Noether's theorem and Lorentz invariance
Noether's theorem has been stated in the form that if the assignment $\phi \mapsto \phi + \delta \phi$, $x^{\mu} \mapsto x^{\mu} + \delta x^{\mu} $ leaves the action invariant, then the quantity $$ f^{...
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Can we detect a cyclic coordinate by just inspecting the Lagrangian?
I'm reading through Susskind-Hrabovsky's Theoretical Minimum. On page 126, where they are talking about cyclic coordinates, an example is given:
Suppose two particles moving on a line with a ...
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Classifying all symmetries of a mechanical system [duplicate]
Given a newtonian mechincal system with $n$ objects, we may think of it as living in $\mathbb{R}^{6n+1}$ ; one dimension is time, $3n$ dimensions for velocities, and $3n$ for positions.
We then have ...
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Conservation of Charge vs. Conservation of Energy
Is conservation of charge ever violated like conservation of energy is violated during cosmological expansion? I am trying to understand this with respect to Noether's Theorem.
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Newton's Third Law of Motion? [duplicate]
Newton's third law of motion states that every action has an equal and opposite reaction. But, on punching a wall, I feel much greater force than on punching an inflated balloon. So, what does it mean?...
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What is the reason that conservation of momentum is conserved in nuclear reactions?
I understand that in nuclear reactions such as fusion or fission, it is known that energy released due to the mass defect to obey the conservation of energy.
However, researching online; I fount ...
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Conservation of angular momentum and its prediction by Newtonian Physics
The situation, in brief, is that newtonian physics is incapable of
predicting conservation of angular momentum, but no isolated
system has yet been encountered experimentally for ...
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Collisions in a System of Bodies
There are three blocks A,B and C, with B and C at rest connected by a light spring and A moving with a velocity v, all three lying on the same horizontal frictionless surface. After some time A ...
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Why is tangential particle momentum conserved in a collision?
In my dynamics class, we learned that the individual momenta of two colliding particles is conserved in the direction tangential to the collision. Why would this be the case?
Consider the diagram ...
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Resolution between off-shell and on-shell views of particle interactions in popular writing
This question is based on this blog post 'Is Dark Matter Lurking in Neutron Decays?' and a following comment I re-read recently. It has something I have seen often in popular writing, which I believe ...
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1answer
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Kinetic Energy in a non-inertial frame
This is the question I was solving:
A ball of mass m is released from A inside a smooth wedge of mass m as shown in figure. What is the speed of the wedge when the ball reaches point B?
This was ...
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What is the maximum theoretical efficiency of conversion of potential energy to kinetic energy and vice-versa?
Am looking at different techniques available for identifying sources of energy.
As part of it, have the following question :
What is the maximum theoretical efficiency of conversion of potential ...
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Where is the momentum going?
When a ball of mass $m$ collides elastically having velocity $v$ with a wall, then it retraces itself with the same velocity. Impulse on the ball due to wall is $2mv$ and since there is no external ...
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Properties of centre of mass
Can we prove that if, for a system of particles, the centre of mass is at origin then the summation of $xy$ over all the particles of the system is zero, where $x$ and $y$ are the respective ...
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Do the determination of conserved quantity in QM can use other operator instead of Hamiltonian?
The conserved quantity in quantum mechanic determine by
$$\frac{d}{dt} \langle Q\rangle = \frac{-1}{i\bar{h}}\langle\psi|[H,Q]|\psi\rangle+\langle\psi|\frac{dQ}{dt}|\psi\rangle$$
First: From the ...
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Best representation of a proton in non-static spacetimes
The classic way to represent a proton in flat spacetime is to use a simple point charge,
$$J = (e \delta(r), 0)$$
But if we're using an arbitrary metric (let's assume still globally hyperbolic ...
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Possible proof that the universe can not have infinite mass? [duplicate]
I was thinking about the possibility of the universe having infinite mass, but then it occurred to me that it would then perhaps violate conservation of mass. Here is my thought process:
Assuming ...
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Quantum and classical correlation functions [duplicate]
Are quantum and classical correlation functions the same? To the best of my knowing they are derived differently. But when people speaks about correlation functions they always refer to the classical ...
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Gyroscopes and Conservation of Angular Momentum
Let's begin by insisting that angular momentum is conserved everywhere and at all times. Since it is a vector quantity, direction matters.
Consider a gyroscope on the end of shaft, the other end of ...
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Physical interpretation of a PDE
I'm not a physicist and I would like to understand the physical meaning of the following equation:
$$u_t (t,x)=-\Delta^2 u(t,x)+f(t,x).$$
This is a $4^{th}$ order parabolic equation similar to the ...
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Steady flow of the relativistic dust - stress-energy tensor
Given relativistic dust (p=0) in flat spacetime. The dust moves in one direction along coordinate $x$ only. Consider this flow is steady. So for an observer at rest at fixed point of $x_0$ $v(x_0)$ ...
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1answer
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Equation in Current vector in a Klein Gordon Equation
I'm trying to get the current vector $J^\mu$ of a Klein-Gordon equation:
$$\Psi^* \Box \Psi =\Psi^* \partial^{\mu} \partial_\mu \Psi= \partial^{\mu}(\Psi^*\partial_\mu \Psi)-\partial^\mu \Psi^*\...
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Collision of Rolling body
When a rolling body collides with a wall elastically,its torque is zero.But direction of velocity of particle is reversed.So will the angular momentum be conserved?
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Reversibility, Entropy and Information in Quantum Mechanics
I suspect that I harbor some misconceptions about these topics. A first item is that QM processes are time reversible. So, in principle, the entropy must remain constant. (??).
A second item is the ...
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Conserved charges generate transformations
Focussing on classical mechanics of a point particle, WLOG since it captures the relevant information for field theory and generalises to the quantum case, how do we show -- in general -- that ...
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Verifying completeness of constants of motion
I can find constants of motion by looking at the null space of the Poisson Bracket operator $ \{H, \cdot\} $ over a polynomial space by brute force with symbolic algebra (code).
This scales terribly ...
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2answers
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Prove the Total Mechanical Energy of the System is Conserved via Differential Equations [closed]
Consider the dynamics of a particle P shown: Particle in 3D space with Radius r
Newton's second law states that:
$$\frac{d}{dt}(m\dot r) = \mathbf F$$
where, $\boldsymbol{r}$ is the position vector ...
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1answer
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Linear momentum of a system remains conserved, but with respect to which frame of reference?
I have studied that linear momentum of a system remains conserved. But i can't figure out with which reference of frame it is conserved. Is it conserved with respect to system reference frame or in a ...
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Do the balls keep moving forever?
In a hypothetical world where there is no friction, and all collisions are elastic would an object in lateral motion be perpetually moving and never come to a stop?
Assumptions:
Perfect vacuum: zero ...
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Conservative or non conservative convection
I want to describe the convection of a species $B$ by another species $A$. Meaning that $A$ is bringing $B$ with it, and there is no other velocity associated to $B$. So I have 2 conservation ...
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5answers
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The impulse on a wall
If a ball was thrown to a wall, How could we calculate the impulse on the wall ?
For example, if I throw a $2kg$ ball with $ 4m/s$, and it returned with the same speed but in the opposite direction, ...
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Is potential energy always inversely proportional to separation?
This is a question from Class 11 Physics NCERT.
The answer is that only graph (v) is correct and the reason given here is that potential energy varies inversely with separation. But does that always ...
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How to show that translational invariance in $y$ of implies that it's an eigenstate of $p_y$?
Let us consider a particle on a plane with uniform magnetic field $B=B\hat{z}$, and hence with the Hamiltonian $H=\frac{1}{2m}(\vec{p}+e\vec{A})^2$. I am concerned with finding the energy eigenstates, ...
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Why bending or reorienting the wire does not change the validity of Kirchhoff's junction rule?
Kirchhoff’s junction rule is based on conservation of charge and the
outgoing currents add up and are equal to incoming current at a
junction.
but Bending or reorienting the wire does not change the ...
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2answers
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How did we know that relativistic momentum is conserved in the first place?
From what I understand, people historically did a lot of experiments (or just life experience) realizing that a fast moving object of small mass has the same quantity of "something" that a slow moving ...
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Conservation of linear momentum with mass defect
Suppose we have an insulating container, like a perfect black body, which absorbs all the radiation coming from a radioactive element placed in the center (or some equivalent process like matter ...
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How to check if a generating function produces an identity transformation without substituting the CT equations in the Hamiltonian?
In chapter 9, Goldstein ($3^{rd}$ ed.) includes a discussion and a few "trivial special cases" of Canonical Transformation which keeps the form of the Hamiltonian unchanged and named it Identity ...
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Deriving the Tsiolkovsky Rocket Equation using the rate at which the fuel burns
I'm trying to understand the derivation of the Tsiolkovsky Rocket Equation.
$$\Delta v= \int_{t_0}^{t_1} \dfrac{|T|}{m_0 - t\Delta m}dt$$
The Wikipedia page ...
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Relative velocity, momentum conservation
I am having difficulty in conserving momentum for objects moving with relative velocities. For example:
A block of mass $m$ with a semicircular track of radius $r$ rests on a frictionless ...
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How is linear momentum conserved in case of a freely falling body?
When an object is experiencing free fall, it has a constant acceleration and hence an increasing velocity (neglecting friction). Thus its momentum is increasing. But according to law of conservation ...
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Fields and Conservation of Energy
I am a bit confused about fields, like magnetic fields, and the conservation of energy.
For example, when two magnets are attracted to each other, don't they "exhaust" the field? The moon that orbits ...
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1answer
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Does an atom recoil when photon radiate?
Consider an atom in the excited state radiating a photon and goes to the lower energy state. But photons have a certain angular momentum, the momentum itself is not defined. In this case, will there ...
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1answer
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Supercurrent conservation for super-Yang-Mills in D=3,4,6,10 dimensions
I am following the book by Freedman and Van-Proeyen and this question is related to exercise 6.3.
The supercurrent of a super Yang-Mills theory is given by $\mathcal{J}^{\mu} = \gamma^{\nu \rho} F^...
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1answer
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Why is $\Delta^0$ not decaying weakly?
Given the lower decay I wonder why it happens this way. Wouldn't it be possible to decay via a weak process as well?
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Symmetry reason why magnetic dipole transitions are suppressed
In the theory of light-matter interaction, electric dipole transitions between two atomic states of same parity are forbidden. This is because the Hamiltonian conserves parity. Is there a symmetry ...
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Rigid body dynamics exercise
Yesterday I came across this exercise and I can't really find a way to get the correct answer.
Exercise
A rigid homogeneous rod that weighs $M=5\,\mathrm{Kg}$, has length $l=0.8\,\mathrm{m}$ and a ...
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Energy threshold for photon
I just read https://en.wikipedia.org/wiki/Annihilation#Examples and there is the popular $ e^+e^- \to \gamma \gamma $ reaction described.
Is it always possible to produce a $ \gamma $? A photon does ...
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Why is $J/\psi$ not being able to decay into $\pi^+\pi^-\pi^0$ (Ozi-rule)?
There are already (very similar) questions like What is the precise statement of the OZI Rule? and Why does charmonium (and phi mesons) not decay via quark and antiquark annihilation? but, to be ...
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Why are certain quantities so fundamental to physics? [closed]
Apart from having a qualitative description of quantities such as momentum, work and energy, why are these quantities considered so fundamental? What is the reason to define them in the first place? ...
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Angular Momentum — AP Physics C
Do all of the planets in our solar system have the same angular momentum? If so, why?
I'm not sure if the following is correct: If we could drag a planet radially outward from the sun, then no ...
