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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2
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2answers
33 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 ...
0
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3answers
38 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 ...
0
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1answer
32 views

Eigenvalues of Angular Momentum in Quantum Mechanics

The eigenvalue equation of the $L^2$ operator is given by $$L^2f_l^m = \hbar ^2l(l+1)f_l^m$$ Side: So a determinate state for some observable $Q$ is a state where every measurement of $Q$ returns ...
35
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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 ...
0
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0answers
39 views

Allowed Values of Angular Momentum for a Rotating Mass

I am attempting to calculate all possible values of angular momentum, $L_z$, which can be found by making a measurement on the following system: A small mass, $M$, is attached to the end of a rigid, ...
-1
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0answers
26 views

Rotation of a rigid body [closed]

There is a pen of length l = 12cm, which initially is in vertical position and falls by rotating through the center Q which coincides with the extreme of the pen on which it was initially standing. ...
0
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1answer
30 views

Spin operator eigenstate in Fock space

I am creating an operator group from representation of spin 1 operators $$J_{x} = \frac{1}{\sqrt{2}}\left(\begin{array}{ccc} 0 & 1 & 0\\ 1 & 0 & 1\\ 0 & 1 & 0 \end{array} ...
0
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0answers
34 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 ...
1
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0answers
9 views

Pivotal door - how is the load distributed?

A pivotal door, where instead of the door hung or cantilevered from the hinges screwed to the frame, the door is hung using a top and bottom pivot. The bottom pivot assembly's the floor-spring is ...
2
votes
2answers
119 views

What motion can emerge in a still universe? [duplicate]

I consider a very large non homogeneous cloud of dust in isolation. No external gravitational interactions. It is initially completely still and start collapsing under the its own gravity. Can the ...
2
votes
1answer
123 views

Rotating black holes and naked singularity

In the book The science of interstellar by Kip thorne can be found the following: There is a maximum spin rate that any black hole can have. If it spins faster than that maximum, its horizon ...
20
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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 ...
7
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3answers
168 views

What is the origin of spin of celestial objects?

In an older question from June 2011, Why does each celestial object spin on its own axis?, apparently revived by the system, a user is asking about the origin of the rotation of celestial bodies. The ...
5
votes
2answers
102 views

Ground state of Spherical symmetric potential always have $\ell=0$?

I was given a problem where I have a spherically symmetric potential (the exact form is not relevant to this question, I think - but anyway is it 0 for $r\in[a,b]$ and $\infty$ everywhere else) and I ...
0
votes
1answer
46 views

Where did I go wrong in ket vector in quantum mechanics? [closed]

Consider a system of total angular momentum j = 1. The operator jx is given by: What are the possible values when measuring jx? My attempt: The eigenvalues after calculation are -1, 0, 1. Now I ...
2
votes
2answers
66 views

Why does dot product equal to one? (Pauli spin matrices)

I was reading these lecture notes (NB: PDF): For spin-1/2, the rotation operator $$ R_\alpha^{(s)}(\mathbf n)=\exp\left(-i\frac{\alpha}{2}\vec\sigma\cdot\mathbf{\hat n}\right) $$ can be ...
2
votes
0answers
32 views

Do coupled angular momentum eigenstates depend on angle between particle positions?

Suppose we have two particles with positions $\vec r_1$ and $\vec r_2$. The corresponding coupled angular momentum eigenstates would be expressed via Clebsch-Gordan coefficients as (according to this ...
1
vote
4answers
166 views

Does the angular momentum vector operator $\hat{\vec{J}}$ have no eigenstates?

Angular momentum projection operators $\hat J_z$ and $\hat J_y$ don't commute, as don't the other combinations of different projections. But this means that there's no such state in which the whole ...
3
votes
4answers
119 views

Why Does Angular Velocity Increase as Radius Decrease?

Suppose a child were to ask you why a tetherball (picture below) seems to speed up as it wraps around the pole. How would you explain this to them? Certainly you wouldn't say something like, "Angular ...
0
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3answers
77 views

Help with Conservation of Angular Momentum Question

An ice skater executes a spin about a vertical axis with her feet on a frictionless ice surface. In each hand she holds a small 5kg mass of which are both 1m from the rotation axis and the angular ...
0
votes
0answers
36 views

Torque, angular velocity, keeping track of the rotation of a sphere

I'm trying to simulate a rotating sphere due to a torque on a specific point on the sphere. Say the sphere is connected to a string (so variable length) on the bottom, on $(r, \theta, ...
1
vote
1answer
71 views

Can the angular momentum of any rigid body (symmetrical or asymmetrical) be found this way?

Can the angular momentum of anybody regardless of whether its symmetrical about the center of mass or not be found by finding the angular momentum about its center of mass and summing it up with the ...
0
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1answer
60 views

Working towards finding Clebsch-Gordan coefficients for a single electron

I'm really confused about a problem involving a single electron which eventually wants me to calculate Clebsch-Gordan coefficients. I think this is probably because, I've only ever seen examples done ...
0
votes
1answer
31 views

Two-Body problem confusion regarding equations of motion

I'm reading John Taylor's Classical Mechanics text, and I'm a little confused about something in chapter 8, which deals with the two-body problem with central forces. The issue is with the equations ...
8
votes
3answers
391 views

What do the Pauli matrices mean?

All the introductions I've found to Pauli matrices so far simply state them and then start using them. Accompanying descriptions of their meaning seem frustratingly incomplete; I, at least, can't ...
4
votes
1answer
119 views

Misuse of $\mathbf J^2$ in classifying Poincare reps

$SO(1,3)$ has an infinite number of representations, classified by the Casimir invariant $p^2$. $SO(3)$ also has an infinite number of representations, classified by the Casimir invariant $\mathbf ...
2
votes
0answers
89 views

Para and ortho hydrogen angular momentum values

In Wikipedia, it is said that: Orthohydrogen, with symmetric nuclear spin functions, can only have rotational wavefunctions that are antisymmetric with respect to permutation of the two protons. ...
3
votes
2answers
113 views

What is the cause of planetary rotation. Not orbital rotation [closed]

I am a senior in high school, sixteen years old. I think differently than most in my class. Recently, I have been thinking about alternative causes for the rotation of our planets. My current thought ...
0
votes
0answers
11 views

Equation of motion for Rabi resonance method

I am reading this article about Rabi and Ramsey resonance measurement, and I have trouble understanding what happens with the magnetic moment $\vec{J}$ when the oscillating magnetic field is added. ...
1
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2answers
73 views

Does a ball spin more from left to right than it does from right to left?

I swear that in a manual on tennis published by the German Tennis Association (Deutscher Tennis Bund) it stated as fact that all things being equal a ball will move more from left to right than from ...
4
votes
1answer
314 views

Angular momentum in curved spacetime

It is known that the angular momentum components are also a representation of the $SU(2)$ generators. Given a non-trivial spacetime, say a black hole of some kind or AdS space, how can one define the ...
5
votes
1answer
85 views

How much effort would be required to fix the Earth's rotation?

Given that the earth's rotation has been slowing down by very slight amounts over time, forcing us to introduce leap seconds and so forth into our clocks and calendars, I would like to ask if this ...
3
votes
1answer
63 views

Why does matter gather as discs around massive objects? [duplicate]

Why do discs, like rings of Saturn and the spiral shape of our galaxy form around massive objects, instead of just a (spherical?) cloud of matter?
0
votes
1answer
24 views

J-coupling constants and nuclei with zero total angular momentum

The Wikipedia page on J-couplings states that Scalar or J-couplings (also called indirect dipole dipole coupling) are mediated through chemical bonds connecting two spins. It is an indirect ...
2
votes
0answers
92 views

How to compute the normal ordered angular momentum of a Klein-Gordon real scalar in terms of ladder operators?

I'm trying to compute the angular momentum $$Q_i=-2\epsilon_{ijk}\int{d^3x}\,x^kT^{0j}\tag{1}$$ where ...
0
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0answers
35 views

Interpretation of angular momentum in semi-classical vector model

My Professor said that when we calculate the total angular momentum of multiparticles, in this case i.e. 2 particles, we can add total angular momentum by thinking this way, if both spins allign they ...
1
vote
2answers
106 views

Why does the Earth rotate on its axis?

I know that the earth moves around the sun because of the gravity force, because the spacetime around the sun is curved. But why does the earth rotate on its axis, and which parameters can affect ...
4
votes
2answers
80 views

Can a Storm make the day longer/shorter?

I've read that changes in jet streams can affect the speed that the Earth rotates on its axis, thus making the day longer or shorter?
0
votes
1answer
80 views

Are the Pauli matrices closed under commutation?

I tried to make a group multiplication table for the Pauli matrices, but I keep getting multiples in front of the elements. What am I doing wrong? I thought the Pauli matrices formed a group that was ...
0
votes
0answers
28 views

Could we imagine spin as rotating probability densities (orbitals) in a kind of expanded orbital model?

I know there is no spin in orbital model. And it is always said there is no visualization for the spin. But why not just let the oribtals rotate with 4D quaternions in some 3D dynamic model?
3
votes
2answers
377 views

What is meant by the spin of a particle? [duplicate]

I have been studying that electrons have quantum number called spin quantum number(s), this number can have either +1/2 or -1/2 value. If s=+1/2, the spin is clockwise and if s=-1/2, the spin is anti ...
0
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1answer
30 views

How is angular momentum conserved when torque is zero?

According to law of conservation of momentum , angular momentum of a particle is conserved when its torque is zero . Please make it easier for me to visualise this condition .
4
votes
1answer
49 views

Why is the specific notation used for term symbols useful?

This has bugged me for a long time. Term symbols describe electronic states of atoms which have well-defined total electronic angular momentum $J$ as well as total spin and orbital angular momenta ...
1
vote
1answer
27 views

What is the 'triangle selection rule' in spectroscopy?

This paper states that However, the multiphonon relaxation bridging the $^5\!D_1$ and $^5\!D_0$ levels is a well-known exception because it is formally forbidden by the triangle rule and occurs ...
0
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0answers
35 views

Quadrupole moment of a valence proton

The state of an unpaired nucleon in the nuclear shell model is given by the quantum numbers $l$, $s$, $j$ and $m_j$ resulting from coupling $l$ and $s$ when we add spin-orbit interaction. In chapter 5 ...
1
vote
2answers
97 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 $| ...
1
vote
1answer
47 views

Precession in the vector model of angular momentum - quantum mechanics?

The vector model of angular momentum in quantum mechanics says that, for example, the angular momentum vector $\mathbf{L}$ precesses about its projection on the $z$ axis, like this: We can add ...
1
vote
0answers
42 views

Can we prove Conservation of Angular Momentum without assuming internal forces are central?

The only proof I've seen of Conservation of Angular Momentum assumes that the internal forces of the system act along the line joining particles i and j (i.e. - all internal forces are central.) Can ...
0
votes
1answer
61 views

Correct approach for calculating excited states of circular quantum dot under effective mass approximation

From Asnani, Mahajan et al, Pramana Journal Of Physics 73 #3 (2009) p574-580 "Effective mass theory of a two-dimensional quantum dot in the presence of magnetic field", which can be seen here: ...
0
votes
1answer
70 views

When two objects roll down an incline, does the velocity increase?

I know the basics of rotational motion but this question just confused everything: The answer to the question is A. But why? My problems: If first, I treated both the disks as two particles, ...