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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Can spin angular momentum be understood as orbital angular momentum in extra dimensions?

It is to my understanding that in Kaluza-Klein theories the mass of particles can be understood as linear momentum in the extra dimensions. Let's consider in $\mathbb{R}^{1,3}\times{}B$ space-time a ...
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38 views

Angular momentum needn't always change in multiples of $\hbar$?

I read the following claim in Slichter's popular book, Principles of Magnetic Resonance (after Fig. 4.3, it's p100 in this version.). Despite the title, the author claims it in a quite general manner ...
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1answer
60 views

Total magnetic moment in an atom

I have a doubt regarding the calculation of total angular momentum of electron in an atom. Which is the right way to do it? Method 1: Total magnetic moment $$ \begin{align} \vec{\mu_J} &= ...
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33 views

What does Weinberg–Witten theorem want to express?

Weinberg-Witten theorem states that massless particles (either composite or elementary) with spin $j > 1/2$ cannot carry a Lorentz-covariant current, while massless particles with spin $j > 1$ ...
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1answer
19 views

When conserving angular momentum, about which point(s) should it be calculated?

In my physics problem I have a ball fired at a non fixed bar, which is moving at some velocity, causing them both to stick together and the bar-ball pair to rotate about the new center of mass. About ...
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2answers
69 views

What is the point of the reduced Planck's constant $\hbar$ (h-bar)? - Why don't we just have Planck's Constant $h$?

I know that $ħ$ is $h / 2π$ - and that $h$ is the Planck Constant ($6.62606957 × 10^{-34}$ $Js$). But why don't we just use $h$ - is it that $ħ$ is used in Angular Momentum Calculations?
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28 views

Difficult Atwood's machine problem - Finding $L(t)$ [on hold]

The whole problem was: You have got a turnable disc of mass $m$ and radius $r$. The rope around the disc has mass $M$ and length $l$. At time $t=0$ the disc is not turning. The height difference ...
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46 views

Angular momentum in an accretion disk

I need to plot the time evolution of the total angular momentum in an accretion disc. This confuses me because I thought this should be constant, since angular momentum has to be conserved? I'm given ...
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1answer
88 views

Half integer eigenvalues of orbital angular momentum

Why do we exclude half integer values of the orbital angular momentum? It's clear for me that an angular momentum operator can only have integer values or half-integer values. However, it's not clear ...
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3answers
54 views

For the Uncertainty Principle, Do the Units of the Two Complementary Quantities have to Equal Js?

I know that the Uncertainty Principle is: $△P•△Q=ħ/2$. But do the units on the Left Hand Side of the equation always have to equal 'Js', i.e. Energy x Time (the same is the Plank Constant, $h$) or is ...
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3answers
457 views

Conservation of Angular Momentum, as related to a flywheel

Trying to work out some pesky flywheel dynamics for a project I'm working on, would love some for your assistance to better understand the underlying concepts. For a given flywheel (thin-walled ...
4
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3answers
876 views

$\hbar$, the angular momentum and the action

Is there anything interesting to say about the fact that $\hbar$, the angular momentum and the action have the same units or is it a pure coincidence?
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1answer
23 views

Rotational dynamics about a point or an axis?

In several books and sites, its written that torque is calculated about an axis and angular momentum is calculated about a point. In MIT's Angular momentum lecture pdf, Angular momentum has been ...
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2answers
104 views

Quantised Angular Momentum?

So when learning about the Bohr model of hydrogen and de Broglie waves, it was shown that treating the electron of hydrogen as a de Broglie wave results in the relationship $$L=n\hbar, \qquad ...
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1answer
25 views

Question about central force,and acceleration of the tangent velocity due to a radial velocity and angular momentum conservation

I am a bit confused, and I'll appreciate some help. Let's say that a particle is moving under the influence of a central force. Let's say that its initial velocity, has both: tangent component and ...
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2answers
41 views

Finding $M_{ij}$ from $J_{i} = -\frac{1}{2}\epsilon_{ijk}M_{jk}$ of the Lorentz group

I cannot understand why if $$J_{i} = -\frac{1}{2}\epsilon_{ijk}M_{jk}$$ then $$M_{ij}= -\epsilon_{ijk}J_{k}.$$ Here $M_{ij}$ is the generator of the 4 dimensional Lorentz algebra (although I have ...
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1answer
37 views

Tidal locking of a planet to a satellite

As in the case of Pluto and its moon Charon, both the bodies are tidally locked to each other, will the Earth ever be tidally locked to the Moon? Is there any effect on the rotation of the Earth ...
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3answers
416 views

Are there planetary systems where the planes of orbits vary greatly?

Inspired by this question, are there any known planetary systems with largely varying planes of orbit? For example a system where two planets have perpendicular planes?
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5answers
6k views

Why aren't there spherical galaxies? [duplicate]

According to the Wikipedia page on Galaxy Types, there are four main kinds of galaxies: Spirals - as the name implies, these look like huge spinning spirals with curved "arms" branching out ...
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2answers
39 views

How are the components of the spin vector defined?

How do we distinguish between the $x$, $y$ and $z$ spin components? More precisely: how do we define the $z$ component? (according to what, it is the $z$?) for measuring the $x$ component how ...
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2answers
109 views

Physical interpretation of applying a unitary operator to a state

When we apply one of the Pauli matrices $\sigma_y$ on one of its eigen-vectors $| \odot \rangle$, what does the eigen-value tell us about $| \odot \rangle$? Is this considered a measurement of $| ...
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3answers
30 views

Commutation Relationship

For the Hamiltonian of the hydrogen atom, does the square of angular momentum, $$L^2 = L_x^2+L_y^2+L_z^2$$ commute with Hamiltonian operator, $$H = \frac{1}{2m}(p_x^2+p_y^2+p_z^2) + V(r)~?$$ Should ...
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2answers
42 views

Flipping a bottle

I tried to do this experiment recently at school and my house. I started the experiment by having three same type of bottles with the labels A,B and C. Bottle A has been fully filled with water, ...
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0answers
29 views

Need to Zero Angular Momentum

I'm writing a molecular dynamics simulation and need to zero the angular momentum of a collection of particles. For each particle I know the location, mass and velocity. My rotational physics is a ...
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1answer
107 views
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3answers
599 views

Why does spin have a discrete spectrum?

Why is it that unlike other quantum properties such as momentum and velocity, which usually are given through (probabilistic) continuous values, spin has a (probabilistic) discrete spectrum?
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1answer
61 views

In 2-dimensional and 3-dimensional universes, stellar systems and galaxies are flat and disky. But what about in 4-dimensional universes?

I just watched that interesting video: https://www.youtube.com/watch?v=tmNXKqeUtJM In 2 dimensions a cloud of particles rotating in a plane is flat by definition since it's in 2 dimensions. ...
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1answer
32 views

Spin operators commutation

Why do the spin operators $ S_{x1}$ and $S_{x2}$ of two particles along the $x$-axis commute i.e $S_{1x}S_{x2}-S_{2x}S_{1x}=0 $ ?
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Rotational wave funtion of a nucleus

The rotational hamiltonian of an axially symmetric rotor is, in the intrinsic frame of the body, where the moment of inertia is diagonal, $$\mathcal{H} = \frac{\hslash^2}{2I} \left(J^2 - I_3^2\right) ...
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1answer
50 views

Does angular momentum of our planetary spin explain the natural 'log e' explanation (the spiral pattern) of my fossil gastropod collection? [closed]

If so, where is the momentum conserved? Any shell may shatter if from a recent land or sea shell. Is a fossil the same way, just waiting for decompression?
3
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2answers
91 views

Introducing angular momentum for the first time to a class

What is the best way to introduce the notion of angular momentum to a class without making it appear an unnecessary and artificial construction?
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3answers
869 views

motion in the body-fixed frame?

This is really basic, I'm sure: For rigid body motion, Euler's equations refer to $L_i$ and $\omega_i$ as measured in the fixed-body frame. But that frame is just that: fixed in the body. So how ...
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2answers
85 views

A student of mine wants to build a Gyroscopic Inertial Thruster

I work as a tutor with students in their first three semesters. One of my more eager students is obsessed with this thing: A Gyroscopic Inertial Thruster Here is a Wikipedia Article on that. I was ...
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0answers
17 views

Force-free motion of a Symmetric Top

How do we know the direction of the angular momentum vector L for force-free motion of a symmetric top? Additionally, how do we know that it is constant? I know that L=r x p, and that p is constant, ...
1
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1answer
42 views

Why does orbiting matter form an acretion disk? [duplicate]

Why does matter in orbital motion around a central body tend to form an accretion disk, as opposed to some other configuration like a sphere? I know this has something to do with angular momentum ...
12
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1answer
135 views

Are the orientations of spin-axes and binary/planetary orbits random or is there any relationship with the Galactic plane?

In an answer to another question, a claim has been made that orbit/spin orientations are random (at least within our own Galaxy), except perhaps towards the Galactic centre. I have dabbled in this ...
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0answers
28 views

Most general gyroscope motion [duplicate]

In Kleppner & Kolenkow's Introduction to Mechanics (Amazon link), the general gyroscope motion including nutation was derived using the approximation condition $\Omega T \ll 1$ where $\Omega$ is ...
2
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6answers
1k views

How does a spinning electron produce a magnetic field?

I learned in my undergraduate physics class that atoms have magnetic fields produced by the orbit of electrons and the spin of electrons. I understand how an orbit can induce a magnetic field because ...
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1answer
70 views

What are phase conventions in angular momentum and rotation calculations?

I work with complicated angular momentum calculations related to atomic physics; nevertheless, I never need to use anything related to a phase convention (apparently because it's taken care of in a ...
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3answers
109 views

Angular momentum

The satellites are revolving around a planet in circular orbits by themselves (no external source to maintain their speed). Are we able to make them revolve in elliptical orbits by themselves? Do ...
1
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1answer
28 views

Addition of angular momenta, coefficient in the |10> state

In Griffith's text, they apply the lowering operator on the |$11\rangle$ state to get the |$10\rangle$ state. They show this result in two forms on pg. 185: $S_{-}\left(\uparrow\uparrow\right) = ...
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2answers
50 views

Does electron in an $s$-orbital have angular momentum?

I've read on science forum that electron in orbital $s$ has no angular momentum and would fall into nucleus, so hydrogen atom would not be possible. Electron has mass and speed after all right? So how ...
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0answers
38 views

Is it possible to reverse gravital direction of center of a mass by gyroscopic movements?

I am sorry that I don't know exact terms to define my question in physics. I watched a few videos that showed moving objects by its own like cubli (gyroscopic moving parts by means of mini motors and ...
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4answers
1k views

If angular momentum is conserved, what's wrong with this scenario?

I understand that, in a given system with no external torques applied, angular momentum is conserved. However, consider the following situation: Let's say the earth revolves around the Sun in a ...
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9answers
2k views

Physical meaning of the angular momentum

Still reading Classical Mechanics by Goldstein, I'm struggling on a very basic notion: angular momentum. I physically understand it as the momentum of an object rotating around something given a ...
0
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3answers
51 views

Conceptualization and modelling of spin

I'm trying to get a decent understanding of the bell inequality, and so am trying to understand spin both conceptually and mathematically. When I picture spin, I imagine a sphere rotating about its ...
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1answer
71 views

Where do $L_+$ and $L_-$ live, if not in $\mathfrak{so(3)}$?

This question is continuation to the previous post. The lie algebra of $ \mathfrak{so(3)} $ is real Lie-algebra and hence, $ L_{\pm} = L_1 \pm i L_2 $ don't belong to $ \mathfrak{so(3)} $. However, ...
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2answers
1k views

Why the galaxies forms 2D plane (or spiral-like) instead of 3D ball (or spherical-like)?

Question: As we know, (1) the macroscopic spatial dimension of our universe is 3 dimension, and (2) gravity attracts massive objects together and the gravitational force is isotropic without ...
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1answer
62 views

Why does the raising and lowering operator not affect total angular momentum?

My notes define: $$ L_{\pm} = L_{x} \pm i L_{y} $$ and states: $$ [L_{z},L_{\pm}] = \pm \hbar L_{\pm} $$ I'm fine with this as it's easy to show the result with some ugly algebra. It then says: ...