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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1answer
222 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 ...
0
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1answer
234 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 their ...
1
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0answers
49 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
2k 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 ...
6
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2answers
835 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
762 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
137 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 ...
1
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1answer
2k 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
303 views

General definition of vector, spinor, and spin

I am looking for basic and exact definitions of fundamental physical concepts in graduate level. I reach this following definitions. Could you please help to improve these definitions. Spin: ...
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1answer
5k 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
20 views
2
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0answers
212 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 ...
-1
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2answers
156 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
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1answer
526 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
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1answer
193 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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2answers
206 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
vote
1answer
66 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 ...
2
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1answer
92 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 ...
5
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2answers
434 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
255 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 ...
1
vote
1answer
386 views

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

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 ...
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3answers
2k views

An electron has no known internal structure, does that imply it has an unknown one?

I'm currently reading Alonso and Finn's Electromagnetism book. It explains that the spin contributes to the magnetic moment and is somewhat comparable to a rotation of the particle around its own ...
1
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1answer
73 views

Angular Momentum Conservation Definition [duplicate]

Did I missed something in angular momentum definition? Two identical bodies rotate around mass center. Now I invented anti-gravity and turning gravitational switch off. Those two bodies will move now ...
3
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1answer
232 views

What is the physical importance of the commutation relations of angular momentum?

What is the physical meaning of these commutation relations: $$[L_{z},L_{\pm}]=\pm\hbar L_{\pm}\tag{1}$$ and $$[L_{+},L_{-}]=2\hbar L_{z} ~?\tag{2}$$
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0answers
40 views

Is spin an observable quantity for fundamental particles? [duplicate]

How we know that the spin of fundamental particles? For example spin-0, 1/2, 1,2.. What is the experimental facts about spin?
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1answer
424 views

Angular momentum of the electric field of a point-like electric charge and the magnetic field of a monopole

I am currently reading "Magnetic Monopoles" of Ya. Shnir. My problem is I can not retrieve a result the author provides in the first chapter of the first part. In this chapter, he studies the non-...
1
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2answers
320 views

If a ball spinning on a rod hits another ball, what is conserved linear or angular momentum?

Suppose a 1-kg ball A is fixed to a spoke 0.2 m long, which is attached to an axle so that the ball can rotate (v=10m/s, KE=50J, $\omega$=50 rps, L=2, p=0) Now, there is a second ball B (m=1kg), ...
5
votes
1answer
489 views

How to get rotational speed after disk-disk collision with friction?

Assume two circular disks A and B collide. They have both initial linear momentum and angular momentum. If their surface has no friction, their angular velocity does not change after collision, so I ...
0
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1answer
169 views

Spin-½ and beyond: Measuring spin components other than ± ħ / 2: How to formulate the probability function?

It is my understanding that in quantum mechanics (for 1/2 spin particles) the probability function that describes the direction of a particle's spin state is proportional to the overlap of the ...
2
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0answers
70 views

How do I calculate integer and half integer spin? [closed]

How do I calculate integer and half integer spin, and how do I use the calculations?
6
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3answers
255 views

Why do we look at the representations of $SO(3)$ in QM?

I have a bit of an understanding issue why the representations of $SO(3)$ are so important for Quantum Mechanics. When looking at its Irreps one gets the Spin and Angular Momentum operators and thus ...
2
votes
2answers
77 views

Why do rotations of a multicomponent state function take this form?

I am reading Leslie Ballentine's Quantum Mechanics, section 7.2, which is all about the explicit form of the Angular Momentum operators. I understand how he gets the form for the single component ...
2
votes
1answer
481 views

How does angular momentum transfer between a planet and its moon?

Could you explain how a moon draws angular momentum from a planet? I know that the gravitational force transfers momentum, but I don't understand the mechanics behind it.
2
votes
2answers
184 views

Angular momentum eigenstates

My textbook says that if $L^2$ is the square of the angular momentum and if it's eigenstate is $|\alpha,\beta>$ then its eigenvalue is $\hbar^2\alpha$ i.e. $$L^2|\alpha,\beta>=\hbar^2\alpha|\...
0
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1answer
2k views

Moment of inertia of a cylinder about its base

I've tried to find the moment of inertia of a cylinder rotating about an axis parallel to its base (i.e about the 'End diameter') as one can see here . But when I checked my results with different ...
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2answers
138 views

Why angular momentum about three independent axes?

The generic commutation relations for the angular momentum operator are $[J_x, J_y] = i \hbar J_z$, where the $J_i$, $i = x,y,z$ are the components of the angular momentum vector operator, $\mathbf J$....
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3answers
824 views

Why don't we talk about angular momentum at all in fluid mechanics?

People usually talk about similar (or maybe not?) things like vorticity or enstrophy in fluid mechanics, but no one talks about angular momentum, why?
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1answer
111 views

Planar motion in central forces

In a two body problem under central force, corresponding to a potential $V(r)$(assume one body is massive compared to the other so that its motion is negligible), conservation of angular momentum ...
1
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2answers
107 views

Given eigenvalues of $\vec l^2$ and $\vec s^2$, calculate the eigenvalue for $\vec j^2$

There was an exam question that read approximatly: Let $\vec j = \vec l + \vec s$. Given eigenvalues of $\vec l^2$ and $\vec s^2$, calculate the eigenvalue for $\vec j^2$. We came up with $$\vec ...
3
votes
1answer
122 views

What are the proper domains of the position and squared angular momentum operator?

I am looking at the position operator on a compact set $K \subset \mathbb{R}^n$ and the squared angular momentum operator (so essentially the Laplace-Beltrami operator where I just look at the angular ...
5
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4answers
1k views

Where does the electron get its high magnetic moment from?

I have always found the concept of spin a little weird. I had read somewhere that for the charge or size of electrons, their magnetic field is very high. In order to produce such fields, they must be ...
4
votes
2answers
238 views

Weighing head by angular momentum

A popular Phys.S.E question asks how can I measure the weight of my head. One of the answers suggests measuring the moment of inertia. My suggestion was to construct an apparatus that places the ...
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1answer
2k views

Principle Axes of inertia and moments of inertia

Principal axes of inertia is defined as the eigenvectors of the inertia tensor matrices. I understand that a diagonalised tensor can yield these axes, but why are they necessarily form the axes of a ...
2
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0answers
690 views

What is the relationship between Coriolis forces and Angular momentum?

Recently I did an assignment about helicopters, and during the oral exam we talked about Coriolis forces. I know where it comes from, and I've seen the derivation: Example In the case of helicopters, ...
2
votes
1answer
106 views

Formalism and representation in Quantum Mechanics

I am just curious about the formalism of basic Quantum Mechanics. Lets take for instance the system of a spin-$\frac{1}{2}$ particle. The state of the particle is described by a vector in an abstract ...
1
vote
1answer
70 views

Are galaxies “disk” shaped?

When you look a sphere from a fixed observation point, you can easily mistake it for a circle, so I was wondering: are galaxies really "disk" shaped or we just don't have the means to detect the "$z$-...
2
votes
2answers
2k views

Angular momentum for 3D harmonic oscillator in two different bases

I know that the energy eigenstates of the 3D quantum harmonic oscillator can be characterized by three quantum numbers: $$ | n_1,n_2,n_3\rangle$$ or, if solved in the spherical coordinate system: $$|...
38
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6answers
6k views

How can the Earth keep spinning with a liquid core?

In regards to the 'conservation of angular momentum' being the explanation of why celestial objects spin... If you fill a ball or any other container with a liquid and try to spin it, you will not ...
0
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1answer
127 views

Contribution to angular momentum $ L_z$ - due to rotation of probability fluid?

I'm doing a course on QM and this concept is entirely new to me: "The eigenvalue $m\hbar$ of $L_z$ can be understood as the result from the rotational motion of probability fluid around the z-axis. " ...
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0answers
33 views

A question on lowering the total spin

Is there a way to lower the total spin of the state and fixing the $S_z$ rather than lowering the $S_z$ by spin ladder operator? Or in other words, how to connect the $S=1$ state with $S=2$ or $S=0$ ...