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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Problem with commutator [on hold]

My area is mathematics; however, told me about a problem that can solve with simple math, it says: Using $[\hat{J_{z}},\hat{O}]$, show that $\langle\alpha,j,m|\hat{O}|\beta,j',m'\rangle$ can be ...
3
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1answer
55 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?
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1answer
14 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 ...
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0answers
52 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 ...
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0answers
27 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 ...
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2answers
82 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 ...
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2answers
70 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?
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1answer
69 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 ...
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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
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2answers
360 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 ...
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1answer
21 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
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1answer
46 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 ...
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1answer
22 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 ...
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27 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 ...
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2answers
77 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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1answer
34 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 ...
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30 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 ...
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1answer
56 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: ...
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1answer
60 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, ...
4
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2answers
91 views

How does electron spin change instantaneously without violating inertia principle?

The inertia in one of the main properties of matter. That is why all process in macro world do not happen instantaneously. What I do not understand is how we should apply this general idea of inertia ...
3
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1answer
38 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. ...
2
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0answers
26 views

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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1answer
33 views

Definition respective derivation of angular momentum formula

I am reading An Introduction to Mechanics by Kleppner and Kolenkow (2014). On page 241 is the definition of the angular momentum: Here is the formal definition of the angular momentum $\vec{L}$ ...
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41 views

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 ...
4
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110 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 ...
6
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2answers
432 views

Is there a reason why the spin of particles is integer or half integer instead of even and odd?

It seems to me that we could change all the current spin values of particles by multiplying them by two. Then we could describe Bosons as even spin particles and Fermions as odd spin particles. Is ...
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65 views

Imaginary Angular Momentum [closed]

I recently came across a problem online where it asks you to interpret an imaginary angular momentum about an axis. Apparently there's a chance it has to do with superconducting. What is the correct ...
2
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1answer
50 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: ...
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0answers
19 views

Reason behind the rotation of Earth? [duplicate]

I want to know what is the reason that the Earth rotates on its own axis? What are the forces responsible for the Earth's rotation?
2
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1answer
119 views

Question about atom subshells

So my teacher told me that EACH shell contains 5 subshells (s, p, d, f, g) but what I don't understand is this The 1st shell has only 1 subshell (and not 5 like he said) and the number of ...
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1answer
68 views

Why can't angular momentum be used in flying vehicles?

If angular momentum (L) works like this animation from Wikipedia leads me to believe, why can't we put a large flywheel or several small ones on a chassis, all rotating counter-clockwise around ...
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0answers
24 views

Asymptotics of the Wigner 6j Symbol

So, in doing some numerical computations in QFT, I've run into the following Wigner 6j-Symbol: $ \left\{ \begin{array}{ccc} x & J_1 & J_2 \\ \frac{N}{2} & \frac{N}{2} & \frac{N}{2} ...
3
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1answer
125 views

Conservation of angular momentum in Earth-Moon system

We all know about the fact that tidal friction is slowly slowing down the Earth's rotation about its axis, and that subsequently the Moon is slowly drifting away, in order for the angular momentum of ...
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2answers
292 views

Square of the Pauli matrices and the identity matrix

The square of any of the three Pauli Spin matrices is equal to the identity. Is there any physical meaning to this? Would you expect it? Maybe in the context of the $SU(2)$ group?
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1answer
83 views

Total Angular Momentum of a Hydrogen Atom

Griffiths in his celebrated book named 'Introduction to Quantum Mechanics' discusses about the total angular momentum of a hydrogen atom on page 187. He writes: If a hydrogen atom is in the ...
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1answer
82 views

How much energy is necessary to set a year to exactly 360 days

How much energy would be necessary to slow down Earth rotation such that a year was 360 days long? In the same spirit: how much energy would be necessary to make the Earth rotate faster around the ...
0
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1answer
42 views

Would days be longer as the polar ice caps melt? [duplicate]

I got question in my mind striking for several days but not able to prove it, suppose polar ice on earth melt, would the days be longer? My friend said it was due to moment of inertia of the earth ...
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1answer
51 views

What formula connects the moment of inertia and angular velocity? [duplicate]

I need to determine angular velocity of a disc when a man with given mass and speed whacks on the edge of it. I calculated the total moment of inertia of disc and body, how do I calculate the ...
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0answers
28 views

Angular momentum and gyro effect on twin wheels

Suppose there are two twin wheels fixed on a vertical rod (z-axis, with a handlebar, like a bike) by an horizontal spinning axle (x-axis) so that the rotation plane is in the y-axis. The wheels are ...
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0answers
88 views

The relationship between angular and linear momentum

Why is orbital angular momentum not 0 when spin and linear momentum are not collinear? Why can it be 0 when spin and linear momentum are parallel? Like in the example of a scalar field at rest ...
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2answers
90 views

The charm of the gyroscope [closed]

I am fascinated by the gyroscope, like everyboy who was so lucky as to get such a toy as a kid. But probably also grown-ups are not immune to its charm. I am not asking for a theoretical explanation. ...
2
votes
1answer
126 views

Angular momentum, what is it, is it conserved, and how do we know?

Firstly, most definitions of angular momentum assume a point about which you define angular momentum. I realize that you can consider the angular momentum about any point, and have many angular ...
2
votes
1answer
84 views

Rotation from Goldstein's Classical Mechanics

I apologize for the ambiguity in my title. It was rather difficult to figure out what is the most appropriate title for my questions. My questions come from chapter 4 and chapter 5 of Goldstein, ...
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1answer
66 views

Angular momentum of light

Can someone explain the classical angular momentum in electromagnetic theory of light? If I shine elliptically polarised em wave on a black disc it rotates. I would like to know how to calculate ...
1
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1answer
57 views

$\dot \omega $ when momentum is conserved

If momentum is conserved when there is no externel force, why is there an acceleration when a momentum parameter is changed (inertia)? How does it accelerate with no external force? For example ...
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0answers
41 views

Angular momentum in an accretion disk

I need to plot the time evolution of the total angular momentum in an accretion disk. This confuses me because I thought this should be constant, since angular momentum has to be conserved? I'm given ...
2
votes
2answers
67 views

How to model energy loss in a rotating body?

I recently asked a question about modeling instability in a rotating rigid body. I now realize that I was mentally confounding two different effects: The "Dzhanibekov effect" in which a rigid ...
2
votes
2answers
139 views

How to explain spin of electron? [duplicate]

How can we explain spin of electron, or the spin of other fundamental particles? If we think the spin of electron is similar to the spin of a ball or planet we make a mistake. We say it is an ...
2
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1answer
59 views

Transfer of angular momentum during oblique impact with(out) adhesion

I am solving a problem of 2 identical spherical particles colliding. The impact is oblique. I consider both normal and tangential contact forces. Tangential force is a combination of elastic force ...