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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Direct measurement of $\mathbf S^2$

For concreteness, consider two spin-1/2 particles with spin vectors $\mathbf S_i=(S_i^x,S_i^y, S_i^z)$. The total Hilbertspace is four-dimensional, and as a basis we can take the (simultaneous) ...
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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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What is the Landé g factor?

What is the Landé g factor? I know that it gives the relation between magnetic moment and angular moment, but i wanted to know why are those magnitudes related to each other and why is the magnetic ...
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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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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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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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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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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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207 views

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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120 views

Is the moment of inertia calculated about an axis, or about a point? And must the point be at the center of mass?

I know that, $$L=I\omega$$ where $L$ is the angular momentum vector, $I$ is the inertial tensor, and $\omega$ is the angular velocity. Now here are my doubts :- Before I was taught the moment of ...
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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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1answer
63 views

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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389 views

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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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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Identical Particle Wavefunctions

Consider the process $$\rho^0\rightarrow\pi^0+\pi^0$$ The $\rho^0$ has $J=1$ whilst the two pions have $S_{tot}=0$ and thus require $L_{tot}=1$ by conservation of angular momentum. Consequently this ...
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Precession on a heavy rod: Angular momentum and torque contradiction

Say I got a so massive rod and a relatively light spinning flywheel. Fixing an end on a pivot, and the disk on the other endpoint, as expected, the rod would undergo precession. If we call the plane ...
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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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154 views

Where this relation for general non rigid motion comes from?

In Goldstein's Classical Mechanics book in the chapter about the dynamics of rigid bodies the equation $$\dfrac{dL_i}{dt}+\epsilon_{ijk}\omega_jL_k = N_i$$ is presented. Now, in one exercise, we are ...
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589 views

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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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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The Spin Term of the Angular Momentum Tensor in Relativistic Quantum Mechanics

In Relativistic Quantum Mechanics, an Angular Momentum Tensor is defined ($J_{\nu \mu}$). This tensor is divided into two terms, one responsible for the spin angular momentum ($S_{\nu \mu}$) and one ...
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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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Does spin angular momentum change with reference frame?

I am guessing that the angular momentum of a particle measured by different inertial observers (no gravity) is different. At the same time, since quantum spin is an intrinsic property, Is it true ...
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How does friction cause a spinning top to fall?

I am wondering how friction can create a torque to change the angular momentum and cause a spinning top to tilt, like in the diagram of a close up of the rounded tip of a top while the angular ...
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Angular momentum of a cylindrical system in general relativity

The definition of energy and enegry flux of a cylindrical symmetric system in general relativity is given by Kip Throne in Phys. Rev. 138, B251 and generalized by Chandrasekhar in Proc. Roy. Soc. Lond....
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If there are eigenstates of $L_z$ in a degenerate subspace, are there also eigenstates of $L^2$?

The question arises from an exercise but tackles deeper understanding of angular momentum operators. Suppose we have a 2D harmonic oscillator and an infinite square well in the third dimension: \...
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1answer
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Wicks contractions of stress-energy tensor and plane partitions

I am working out the number of wick contraction of a number $n$ of stress-energy tensor in 4D CFT. The strategy is as follows: For 1 stress energy tensor $T_{\alpha\beta}$, you have only one ...
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Why does the parallel axis theorem apply in this case?

Next, the wheel is flipped over, so the angular momentum of the wheel is now negative. Obviously, the person must start rotating counterclockwise to conserve angular momentum. Since the person is ...
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Rotational potential energy on a system of two masses

On a homework assignment, we were given the following problem: This system is held at equilibrium according to the configuration in the image; initially the body B is at rest, and the body A is ...
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Difference in rotation of the atmosphere at different levels

The atmosphere near ground level rotates at the same rate (on average) as the earth's surface because of drag effects beween air and ground, and continues to rotate because of inertia. Correct? My ...
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Is angular momentum independent of axis (if axis is parallel)?

I have been told this is true for the moon on this question: Angular momentum of orbiting + rotating body but I don't understand why it should work. Surely the axis must be chosen such that the ...
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Addition of Angular Momenta--Why the naive approach fails

Edit: Physical Set-up: Below, we've basically defined a map from $SU(2)$ to $SU(3)$. However, there's another way to define a map from (a neighborhood of $1 \in$) $SU(2)$ to $SO(3)\subset SU(3)$, ...
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Thermodynamic formulation of pefect fluid with spin

The spin phenomena in an asymmetric spin-related Einstein-Cartan candidate solution is due to microscopic spin of small volumes of a globally "ordinary" perfect fluid. The only description I have ...