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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Why is space isotropic in the vector particle's decay?

I come across one proof the Landau-Yang Theorem, which states that a $J^P=1^+$ particle cannot decay into two photons, in this paper (page 4). The basic idea is, the photon's wavefunction should be ...
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2answers
19 views

Angular Momentum conservation in star system

This question is related to what happens to a planetary body(like earth) when the star it is orbiting collapses under its own gravity. Suppose a star is rotating about its axis with some angular ...
3
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1answer
85 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
99 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
20 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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0answers
40 views

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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2answers
78 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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31 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 ...
3
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1answer
89 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
55 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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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
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 ...
2
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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 ...
1
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2answers
40 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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0answers
13 views

Spinning top don't fall and stationary one can't stay upright [duplicate]

Why a spinning top do not fall but a stationary one falls. What kind of law is governing it.
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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 ...
1
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1answer
26 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 ...
0
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1answer
34 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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1answer
51 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?
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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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0answers
30 views

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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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, ...
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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 ...
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 ...
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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 ...
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 ...
9
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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 ...
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 ...
0
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1answer
44 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 ...
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5answers
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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 ...
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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1answer
34 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} ...
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0answers
39 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
10 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
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2answers
123 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
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1answer
157 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 ...
21
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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 ...
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3answers
184 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
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2answers
139 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
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1answer
49 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
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2answers
73 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 ...
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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 ...
2
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0answers
38 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 ...
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4answers
180 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
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4answers
209 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 ...
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3answers
104 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 ...
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0answers
44 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, ...