Questions tagged [angular-momentum]

The conserved quantity arising from a rotational invariance. Combine with rotational-dynamics for the classical mechanics approach and quantum-mechanics for the QM interpretation

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Sequential Stern-Gerlach devices - realizable experiment or teaching aid?

At least one textbook [1] uses sequential Stern-Gerlach devices to introduce to students that the components of angular momentum are incompatible observables. Viz., the $z$-up beam from a SG device ...
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Why are generators defined oppositely in Weinberg's vs. Maggiore's QFT books?

I've been confused about the sign conventions used in Weinberg's QFT book for a long time. Here's my question: The generators $J^{\mu\nu}$ are defined in this book as $$U(1+\omega)=1+\frac{i}{2}\...
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Relativistic rotational squeezing?

I would like to consider a sphere rotating at very high angular speeds, such that the speed in its equator would be relativistic. This is very similar to Ehrenfest paradox situation, except that ...
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Understanding forbidden selection rule $m_J=0$ to $m_J=0$ for $\Delta J=0$

I am seeking to gain a physical understanding of the specific single-photon selection rule which states that for $ΔJ=0$ i.e. ($J = J’$), transitions involving $m_J=0$ to $m_J’=0$ are forbidden. ...
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Does an evaporating black hole violate conservation of angular momentum?

Angular momentum is supposed to be conserved, but when a rotating black hole evaporates the Hawking radiation comes out in straight lines. Doesn't this violate conservation of angular momentum? Does ...
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Quark intrinsic angular momentum and the Proton Spin Crisis

According to recent results regarding the "Proton Spin Crisis", apparently only about 30% of the total angular momentum of the proton comes from the intrinsic angular momentum of its constituent ...
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Interpretation of inequivalent spin structures (on the circle)

I was wondering about the physical interpretation of inequivalent spin structures on a given configuration space. For simplicity, I'd be satisified by only discussing the case of the circle. There ...
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On an Uncertainty Relation for Angular Variables

I'm looking for a proof of the Angular Momentum - Angle uncertainty relation $$\frac{\Delta L \Delta \theta}{1-(3/\pi^2)\Delta \theta^2} \geq \frac{\hbar}{2}$$ which does not involve solving the ...
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Protoplanetary disks, angular momentum and prograde orbits

Very similar question at Astronomy SE: https://astronomy.stackexchange.com/q/6183/4042 Given a typical protoplanetary disk made up of the usual planetary system stuff, dust and gas and whatnot, ...
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Lagrangian of the Euler equations - why are Lin constraints required?

The following equation describes the motion of a rigid body rotation, such as a gyroscope: $$ \frac{d\textbf{L}}{dt} ={\bf{\tau}}= \textbf{r}\times m\textbf{g}= {\omega}\times \textbf{L}$$ where $...
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Goldstein Classical Mechanics exercise 5.17 (3ed) conceptual

I am having difficulty understanding a concept in the "Heavy symmetric top" type of problems. I will include all of my efforts as to hopefully have someone easily point out what it is that I'm missing....
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Does the spin1/2 rotation operator rotate spin in real space?

in quantum mechanics, the rotation operator for spin one half is $R_{\alpha}\left(\hat{\boldsymbol{n}}\right)=\mbox{exp}\left(-i\frac{\alpha}{2}\boldsymbol{\sigma}\cdot\hat{\boldsymbol{n}}\right)$. ...
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Uses of the Angular Momentum 4-Tensor

The angular momentum 4-tensor has 6 independent components, three angular momentum components and three new guys. Some call these new guys the 'boosts', but since they are the conjugate momentum of ...
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What type of fields are continuous spin representations?

Continuous spin representations (infinite dimensional representations of the Lorentz group) are pretty rarely discussed, and usually not in that much mathematical details. And usually it is done in a ...
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Spin via Change of Phase

Thinking of spin as arising from a change in the phase of a wave function: The angular momentum is defined by the change of the phase of the wave function under rotations, which may come from the ...
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How does pulling backwards on the pedals cause the bike to move backwards?

I saw this video by George Hart recently: https://www.simonsfoundation.org/2014/03/20/mathematical-impressions-the-bicycle-pulling-puzzle/ Hart attached a string to the pedal while it was on the ...
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Why is the angular momentum defined as the cross product of linear momentum and the radius?

I first searched why is Torque defined as a cross product and a lot of people answered that it is defined as a cross product because angular momentum is defined that way and it is only logical that ...
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Spin of higher string excitations

I am trying to better understand spin in string theory. There is already a good post here: Ssecond and third level excitations of open string But I have these questions: 1) Why would the second ...
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Why does a spinning disc turn before it fades?

I have recently gotten into disc golf, and an interesting phenomenon happens when you throw a disc hard. If you throw a disc right hand back hand, so that the disc spins clockwise, at high velocities ...
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Possible values of the total orbital angular momentum quantum number $L$

I'm reading Gerhard Herzberg's "Atomic spectra and atomic structure" (can be accessed on archive.org, the relevant part is from p.82-87) and I don't quite grasp how to determine the possible values of ...
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Linear momentum of a rotating system

So say we have a thin rod resting horizontally on a flat frictionless surface. The rod is pinned at its center, and a small mass collides perfectly inelastically with one end of the rod after moving ...
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Ground state of an odd, deformed nucleus: intuition for what happens to the $j_x$ and $j_y$ of the odd particle

This is something that relates closely to my long-ago PhD research, and it's a point that I never satisfied myself thoroughly on. I have a copy of a standard text that covers this general topic, de ...
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General Commutator for Spherical Tensors (reformulated)

Edit: I think what I was looking for wasn't very well understood, so I'm reformulating my question to make it clearer. Hope this helps. In the book of "Angular Momentum: An Illustrated Guide to ...
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Why does the neutron have spin 1/2 and not 3/2?

The neutron is thought to consist of three tightly bound quarks, each with spin 1/2. Simple addition of angular momentum would tell us that the resulting system (neutron) could have either spin 1/2 or ...
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Dzhanibekov effect in quantum systems

Dzhanibekov- or Tennis racket effect is what happens when an object with three diferent moments of inertia doesnt spin around the axis with highest or lowest moment of inertia. The object starts to ...
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Minimal value of angular momentum in a close binary

I just noticed something interesting with the angular momentum of a close stellar binary. This question is somewhat related to another question of mine, but the question here is clearly different : ...
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Does the event horizon of a black hole need to be an oblate sphere?

Suppose two black holes where rotating around each other, perhaps spinning into each other, at a distance such that their event horizons merge into one event horizon. It seems to me that the event ...
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Is there an intuitive interpretation of the shape of the angular momentum eigenstate?

I was watching a MIT lecture video on angular momentum eigenstate. Toward the end of the lecture, the professor had shown some plots of the first few spherical harmonics, in an attempt to explain ...
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Angular momentum of the vacuum

I'm studying quantum field theory from "An introduction to Quantum field theory" by Peskin and Schroeder and from "A modern introduction to quantum field theory" by Maggiore. I've read from "An ...
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What variable is the conjugate momentum for angular momentum?

From the definition of conjugate momentum for a generalized coordinate we get that the conjugate for angular momentum should be proportonal to its integral with respect to time. According to my ...
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Equivalency of conditions involving angular momentum of a rolling ball hitting a wall

(59th Polish Olympiad in Physics) A ball of mass $m$, radius $r$ and a moment of inertia $I = \frac 25 mr^2$ is rolling on the floor without sliding with the linear velocity $v_0$. It hit the wall ...
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What is the relationship between the angular speed and the diameter of the eye of a water vortex?

In a water vortex formed in a plastic bottle, what is the relationship between the angular speed of the water and the diameter of the hole in the cap? I would have expected that according to the ...
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When Did Structures Begin to Orbit in the Universe?

In Big Bang Cosmology, I am familiar with the radiation era, and the moment of last scattering, but I am just not familiar with the physics of orbits, or of the “falling outward,“ if you will, that ...
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Why are some things attracted to you but others repelled by you in rotating reference frames?

Note that my understanding of general-relativity is rudimentary. If I understand right, it means that basically any reference frame can be considered stationary, but there may be random gravitational ...
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What are the assumptions behind “term symbols”?

In multi-electron atoms, the electronic state of the optically active "subshell" is often expressed in "term symbols" notation. I.e. $^{2S+1}L_J$. This presumes that the system of electrons has ...
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3 Axis Gyroscope with forced Precession and Limits of Motion

I am working a problem concerning a 3 axis gryoscope, the spinning mass is a magnet (dipole). This is part of a optical sensing device. The inner gimbal is for pitch rotation, and the outer gimbal is ...
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Why do control moment gyroscopes exhibit “torque amplification”?

There are a number of articles that describe the benefits of using control moment gyroscopes (CMGs) over reaction wheels in inertial navigation applications. One of the primary benefits of using a CMG ...
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Do particles also have intrinsic linear momentum (linear analogue of spin)?

We know from quantum mechanics that microscopic particles have spin, which is a kind of intrinsic angular momentum. The particle has angular momentum without physically rotating. In a similar way, do ...
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1answer
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Rod hits rod - angular and linear momentum

I've been analyzing "ball hits a rod in space" type collisions, where speeding ball transfers part of its kinetic energy during elastic collision to the motionless rod, making it gain linear ...
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Physical interpretation of the definition of angular momentum in classical mechanics

To what I understand, the following is a valid way to introduce the angular momentum $\mathbf L$ in the Lagrangian system of a rigid body. We can consider the extended configuration space to be $M\...
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What will eventually happen to a coin spinning in space?

There were some answer comments at Is it possible to make the Sun spin a coin in space? that could be a question in their own right, so here it is. Posit that we have a coin in space, on both faces ...
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What generates a neutron star's magnetic field?

Is the magnetic field of a neutron star generated by the minuscule amount of protons and electrons left or the spin of the neutrons? If its because of the spin of the neutrons, how come they are all ...
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2-dim angular momentum in quantun mechanics

I just studied the theory of angular momentum in non-relativistic quantum mechanics, which defined angular momentum as generators of Lie group $SO(3)$. And by using the Lie construction relationship, ...
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How to decompose Cartesian into spherical tensor with Wigner-Eckart theorem?

I'm solving a question that required me to work with a Cartesian tensor, $A_i$, with Wigner-Eckart theorem. The book was Sakurai Modern Quantum Mechanics with information given in related posts: Ra....
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1answer
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About obtaining eigenvalues for angular momentum with ladder operators

$$ \newcommand\<\langle \newcommand\>\rangle $$ I'm following Griffiths' intro QM text, 2nd edition. We have defined the angular momentum operator and obtained the commutation relations $[L_i, ...
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1answer
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Why do we need to symmetrize the stress-energy tensor?

An elementary definition of the stress-energy tensor $T_{\mu\nu}$ in terms of the Lagrangian for flat spacetime is $$T^{\mu\nu}=\frac{\partial \mathcal{L}}{\partial(\partial_\mu\phi)}(\partial^\nu\phi)...
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Angular momentum of a single particle

I have to answer the following question: Consider the decay $\rho^0\to\pi^+\pi^-$. The rho meson has angular momentum 1, what must the orbital angular momenta of the pions be, given that they are ...
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Lagrangian formulation of classical spin chains

Is there a way to construct a Lagrangian formulation of the classical dynamics of a spin chain - say a Heisenberg or XY chain? The Hamiltonians here are obvious.
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1answer
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Why does mass (gas) transfer between binary stars cause them to move apart?

Some binaries, like Algol binaries, move monotonically apart from each other as one steals gas from the other. Why? On a naive level, shouldn't friction and such cause the two stars to move (rotate?,...
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1answer
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$SU(2)$ vs $SO(3)$ in Quantum Mechancs

When we're talking about spatial rotations is quantum mechanics, why do we need to resort to $SU(2)$? Why isn't $SO(3)$ enough? I've read that $SO(3)$ isn't simply connected, and I've read about ...

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