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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Generalization of torque and angular momentum

Question: in the simple equations $\tau = r \times f$ and $L = r \times p$, what is the origin of the vector $r$? In many textbook discussions on rotation of a rigid body about a fixed axis, $r$ is ...
47
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4answers
7k views

What is spin as it relates to subatomic particles?

I often hear about subatomic particles having a property called "spin" but also that it doesn't actually relate to spinning about an axis like you would think. Which particles have spin? What does ...
13
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1answer
460 views

How to evaluate this sum of coupling coefficients?

I would like to evaluate the following summation of Clebsch-Gordan and Wigner 6-j symbols in closed form: $$\sum_{l,m} C_{l_2,m_2,l_1,m_1}^{l,m} C_{\lambda_2,\mu_2,\lambda_1,\mu_1}^{l,m} \left\{ ...
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140 views

How many km Earth will approach to the Sun if Earth stop spinning (gradually or suddenly)? [closed]

If earth stops spinning around its own orbit, it will loose angular momentum(therefore its rotational kinetic energy) and as i think Earth will go closer to the Sun. The question is how many km ...
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1answer
241 views

How does the Gordon Decomposition of Dirac Current give rise to spin angular momentum?

How does the Gordon Decomposition of Dirac Current give rise to spin angular momentum? I used the Gordon Decomposition to split the Probability Current of the Dirac Field into its orbital current and ...
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66 views

Larmor Precession - What does precession actually means?

Larmor Precession - What does precession actually means? Is it change in the orientation of the axis with which electron revolves around the orbit or what. But, shouldn't the radius of the orbit ...
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1answer
105 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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2answers
68 views

Using rotation matrix for spin to write x oriented spin in z-spin basis

$\newcommand{\ket}[1]{\left| #1 \right>}$The problem is to write the ket vector for a particle with spin +1/2 along the x axis, in terms of the standard basis vectors $\ket{+1/2}$ and $\ket{-1/2}$ ...
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99 views

Why is only one quantity of angular momentum i.e. $L_z$ quantized & not $L_x$ & $L_y$?

This is quoted from Arthur Beiser's Concepts of Modern Physics: Why is only one quantity of $\mathbf{L}$ quantized? The answer is related to the fact that $\mathbf{L}$ can never point in any ...
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3answers
52 views

Why can't the angular momentum vector be parallel or anti-parallel to the applied magnetic field?

This is the excerpt from my book, Arthur Beiser's Concepts of Modern Physics: An atom with a certain value of $\displaystyle{m_l}$ will assume the corresponding orientation of its angular ...
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989 views

Apparent violation of Newton's 3rd law and the conservation of angular momentum for a pair of charged particles interacting magnetically

Consider a system of the two identical point positive charges situated in free space (isolated from influence of any other external fields) as shown in the figure below. Particle 1 is at $(a,a,0)$ and ...
3
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1answer
321 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
500 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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25 views
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1answer
44 views

If I start spinning a raw egg slowly why does its angular velocity increase spontaneously?

If I start spinning a raw egg very slowly in place, why does its angular velocity increase spontaneously? This is something I noticed the other day while cooking. It doesn't do the same thing with a ...
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1answer
214 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
73 views

Why do $H$ and $L^2$ commute in spherically symmetric potential?

In this PDF document (a lecture by Shivaly Reddy, page 13), he says that $L^2$ is independent of $r$; therefore it commutes with any function of $r$. This seems related to a problem in ...
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2answers
110 views

How many hours will be in a day if the radius of Earth increases by 70 m?

I am little confused about the linear momentum and angular momentum, will the linear momentum of earth change due to changing of its radius or it will stay as it was and i know that the moment of ...
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1answer
122 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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1answer
35 views

Schaum explication of eigenvectors of Lz

In Schaum's Quantum Mechanics, in Chapter 6 Angular Momentum, they say "the eigenvectors of $L^2$ and $L_z$ are functions that depend on the angles $\theta$ and $\phi$ only; hence, we can represent ...
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3answers
87 views

How can I find the angular and linear velocity of a 2D body that breaks into two bodies?

Afternoon. This is my first question, so do let me know if I'm doing anything wrong. Looking for help on building a 2D physics game engine with bodies that split in half: I have a two dimensional ...
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1answer
23 views

Combining moments of Inertia in gear chain

I've got two objects connected by a rod along it's axis of rotation (e.g. a sphere on top of a flat cylinder rotating around it's symmetric axis). Assuming the effects of the rod are negligible, is ...
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1answer
238 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 ...
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1answer
147 views

Equivalency of conditions involving angular momentum of a rolling ball hitting a wall

(59th Polish Olympiad in Physics) A ball of mass $m$, radius $r$ and a moment of inertia $I = \frac 25 mr^2$ is rolling on the floor without sliding with the linear velocity $v_0$. It hit the wall ...
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1answer
53 views

Operator in Hilbert space of a spin

I'm studying quantum mechanics with Shankar's "Principles of Quantum Mechanics" 2nd edition. I'm afraid that it might be a boring question but I can't understand the following statement (389p): We ...
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73 views

What is this nested bracket notation?

The following is an excerpt from K. Varga's paper, Precise solution of few-body problems with stochastic variational method on correlated Gaussian basis: ...The function $θ_{LM_L}(\mathbf{x})$ in ...
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1answer
57 views

Negative sign in rotation operator (quantum mechanics, angular momentum)

Schaum's Quantum Mechanics comes up with $$\exp((-i/\hbar)\cdot \theta \cdot{\hat{L}} \cdot {\overrightarrow{n}})$$ as the formula of the rotation operator. Other sources I see don't have the ...
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3answers
185 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
72 views

What is really the force required to open a door?

I found a few Phys.SE threads in which an impulse is used to exert a torque on a rod, is it possible to get a realistic description of the force required to open a door?: If we have a free 'door' ($l ...
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2answers
88 views

Deflection Effects on a Spinning Solar Sail

Suppose I have a solar-sail-powered starship flying directly away from a star. The sail is flat and perpendicular to the direction of travel. Now, in order to make the trajectory more stable (we ...
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1answer
66 views

Do particles have spin because there exist spinor representations for the Lorentz group?

I am reading Peskin and Schroeder's An introduction to field theory. They first describe the spinor representation of the Lorentz group, and then they mention the fact that different particles have ...
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2answers
106 views

$\hat{L}_{x}$ and $\hat{L}_{y}$ do not commute… or do they?

So $\hat{L}_{x}$ and $\hat{L}_{y}$ do not commute: $ [ \hat{L_{x}}, \hat{L_{y}}] = i\hbar \hat{L_{z}}$ But, what if we perform this operation on a state such that: $\hat{L_{z}} \phi_{l, m_{l}} = ...
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48 views

conservation of angular momentum/conservation of energy?

Perhaps a dumb question to ask, but I was given the following problem to solve: A 10 g bullet traveling at 400 m/s strikes a 10 kg, 1.0-m-wide door at the edge opposite the hinge. The bullet embeds ...
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1answer
116 views

if the Earth's rotation was slowed down, would it naturally speed back up as it was before? [closed]

Fact: The Earth is rotating on it's own axis every 24 hours. Question: If, for some reason I won't specify the current speed of the Earth and could slow it down(say by 5%). Will it speed up again ...
0
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1answer
35 views

Expectation value of total angular momentum $\langle J \rangle$

[I am working with Griffiths Introduction to Quantum Mechanics, 3rd Edition. My problem is general but if you want to look I am reading from ch 4.1 in which the weak-field Zeeman Effect is being ...
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3answers
674 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 ...
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2answers
450 views

Ten-ping bowling: Can a ping pong ball knock over a bowling pin?

In this video we see a rather unorthodox bowling technique on display. The gentleman appears to knock over all of the pins using only a ping pong ball. It's a fake, of course: you could never knock ...
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1answer
18 views

Angular momentum conservation laws and GHZ article (Greenberger et al 1990)

Can anyone recommend a good book or an online source on angular momentum conservation laws in decay processes? I'm writing a master's thesis concerning Bell inequalities and currently working on GHZ ...
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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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Does momentum change if rotation radius changes?

Angular momentum is defined as $L = r \times p$ where r is the center of rotation and p is the momentum. Since angular momentum is conserved, if r decreases then p must increase. And since p is m*v ...
2
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1answer
146 views

Problem on Einstein - de Haas experiment

I am a Physics student (4th year) and I'm trying to study the Einstein - de Haas effect in laboratory. That is what I got: a suspended Iron cylinder with about 5 cm height and a radius of 0.8 cm is ...
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2answers
452 views

How to write Schrodinger equation when a particle with some spin quantity and orbital angular momentum

Quantum mechanics: Suppose that there is a particle with orbital angular momentum $|L|$. But the particle also has spin quantity $|S|$. The question is, how do I reflect this into Schrodinger ...
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3answers
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Adding 3 electron spins

I've learned how to add two 1/2-spins, which you can do with C-G-coefficients. There are 4 states (one singlet, three triplet states). States are symmetric or antisymmetric and the quantum numbers ...
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1answer
58 views

Getting to spins of arbitrary direction

Let me rephrase this question: Let us assume we know that symmetry transformations always look like this: $$U(s)=e^{iKs} $$ with a hermitian Operator K. This tells us that for very small $s$: ...
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1answer
34 views

Torque in a non-inertial frame

How can we calculate torque in a non-inertial frame? Take for instance a bar in free fall with two masses, one on either end, $M_1$ and $M_2$. Taking the point of rotation to not be the center of ...
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24 views

Expectation value in spin-orbit coupling

So I was just trying a question where it asked to find the Energy shift due to a spin-orbit coupling Hamiltonian to first order using perturbation theory. The Hamiltonian is $$H_{LS} = ...
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29 views

Addition of 3 angular momenta

I'm struggling to understand how the orbital angular momentum "add" in ground state Nitrogen. As I understand it N has an electron configuration of $1s^22s^22p^3$ and so the 3 outer electrons in the ...
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Why Does Moving a Cup of Coffee Up and Down whilst carrying it Make it less Likely to Spill?

Sometimes I have a Very Full Mug of Coffee and I am trying to carry it without it spilling. I noticed that if I moved the Mug up and down when carrying it, it seemed to settle the coffee and make it ...
2
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1answer
57 views

Particle Physics Decay Question - Eta Prime Decay Parity/Angular Momentum Conservation

I was hoping someone could clarify why the following decay does not occur: $ \eta ^{'0} \rightarrow \pi ^{0} + \rho ^{0}$ The quark compositions and spin parity are as followed: $ \eta ^{'0} : ...