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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68 views

Under what condition is angular momentum conserved in both classical and quantum physics?

Classically, angular momentum is only conserved in a central potential by considering the torque (correct me if I am wrong). In quantum mechanics, it is also true, isn't it? If this is the case, ...
2
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1answer
91 views

Can light be a spinor?

A recent discovery suggests that photons can have half-integer spins. This seems to contradict the well understood notion that photons are vector (1-form) fields What does this mean for the ...
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1k views

Photons with half integer angular momentum - what's happening?

I have just read this article - what is happening? Analysing these beams within the theory of quantum mechanics they predicted that the angular momentum of the photon would be half-integer, and ...
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2answers
65 views

Momentum Conservation

The Problem: There are three masses all of equal mass $m$. One mass breaks of with velocity $v$ at an angle $\theta$ to the rod. I have to find max velocity of $A$ and the time at which this ...
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1answer
34 views

Finding the Mass of a Precessing Top

Consider a symmetric, non-nutating precessing top with one point fixed (the tip if you will). It's symmetry axis is at an angle $\theta$ to the vertical and it steadily precesses at some angular ...
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47 views

Showing classical spin tensor is time independent for free particle

Reading through Weinberg's gravitation book, the following definition is given for the spin tensor (Pauli-Lubanski psuedovector): $$ S_\alpha = \frac{1}{2}\epsilon_{\alpha\beta\gamma\delta} J^{\beta\...
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34 views

Rotation and Momentum

I understand that according to one of Euler's theorems, any solid object's 3D rotational orientation can be represented by a single 3D vector and an amount, i.e. a 4D vector. However, is it correct ...
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1answer
26 views

How high does a slide need to be if the person at the bottom grabs a pole and rotates the pole 72 degrees?

My attempt: $mgh = \frac{1}{2}I \omega^2$ $\omega^2 = 2 \alpha\Delta \theta$, so $mgh = \frac{1}{2}I 2 \alpha \Delta \theta$ $mgh = I \alpha \Delta \theta = \tau \Delta\theta$ $\tau = rF\sin \...
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1answer
60 views

Expressing eigenstates of $\mathbf{L}^2$ and $L_z$ in terms of the Cartesian eigenstates $|n_x\, n_y\, n_z\rangle$

I want to express the degenerate eigenstates of the three-dimensional isotropic harmonic oscillator written as eigenstates of $\mathbf{L}^2$ and $L_z$, in terms of the Cartesian eigenstates $|n_x\, ...
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0answers
81 views

What type of fields are continuous spin representations?

Continuous spin representations (infinite dimensional representations of the Lorentz group) are pretty rarely discussed, and usually not in that much mathematical details. And usually it is done in a ...
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1answer
18 views

Angular momentum energy loss

Suppose a man sits on a freely rotatable light chair holding 2 dumbbells to his chest, he then extends his hands while maintaining the height of each dumbbells (so that gravitational of the system is ...
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92 views

Pendulum question- Angular momentum-impulse

The pendulum of mass m and length l is released from rest at $\theta=0$. Using only the principle of angular impulse and momentum, determine the expression for $\ddot \theta $ in terms of $\theta$, ...
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21 views

Precession or projection?

A spin of 1/2 in a magnetic field is known to rotate around the direction of the field. But then it is also stated that it must be projected spin up or down. Is this simultaneous or happens after ...
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3answers
53 views

Why are pulsar's radiation beams collimated?

Every picture of a pulsar a see shows a very collimated radiation beam. What is the mechanism generating such a collimation? Note: I am not talking about "relativistic jets". I am talking about ...
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0answers
37 views

Heisenberg equation of motion for angular momentum operator

I am working on problem 5, from chapter 3 of Sakurai's Modern Quantum Mechanics. The problem has the following Hamiltonian: $$ H = \frac{1}{2}\left (\frac{K_1^2}{I_1}+\frac{K_2^2}{I_2}+\frac{K_3^2}{...
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48 views

Spinning black hole laser?

Is a laser that uses a rotating black hole's ergosphere as the gain medium possible? The idea is that the coherent light feeds off of the black hole's rotation. Assume that the black hole is ...
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2answers
80 views

What factors will make Earth re-rotate again if it stopped? [closed]

"What will happen if Earth stopped rotating?" have been answered multiple times with a lot of informative and interesting answers. Continuing this hypothetical question, I have another one in mind. ...
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2answers
59 views

What does “transfer” of angular momentum mean?

The Moon’s gravity produces tidal deformations or “bulges” in the Earth. Because of the Earth’s rotation, the line that goes through the bulges is not aligned with the line between the Earth and the ...
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2answers
55 views

Transformation of $| JM\rangle$ under the group of rotations

I am following the Quantum Mechanics I, Galindo A., Pascual P. and in page 207 explaining the matrix representations of the Rotation Operators in the angular momentum it appears the next (obvious) ...
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1answer
97 views

Transforming to a rotating frame in the $x$-basis

I was reading this paper on analytically Solvable driven time-dependent two level quantum systems. The Hamiltonian considered in the paper is the following: $$H=\sigma_z\cdot J(t)/2)+\sigma_x\cdot h/2$...
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2answers
36 views

Protecting astronauts from G's when taking off/landing

When landing from orbit or launching from the ground to orbit (with chemical rockets or other means of fast acceleration), could one place the astronauts in a centrifuge and spin it to protect them ...
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24 views

Higher $L$ lower energy?

For multi-electron atoms, what is the physical reason behind the fact that a higher total orbital angular momentum, $L$ gives a smaller total energy, $E$?
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91 views

Could 1 force cause a pure moment?

A friend of mine told me if there is only one force, it cannot cause only rotation. I wasn't convinced so I proposed a thought experiment, and now we are both confused. Suppose that we put a rod ( ...
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1answer
66 views

Understanding work with rotational momentum/moment of inertia

Apologies for the basic question but between the vectors and the spinning, I'm getting confused. If I have a wheel with moment of inertia $I$ spinning at some rate $\vec\omega$ around an axis, what ...
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3answers
117 views

Does angular momentum of a system whose moment of inertia is changing remains constant?

An equilateral triangle $ABC$ formed from a uniform wire has two small identical beads initially located at $A$. The triangle is set rotating about the vertical axis $AO$. Then the beads are released ...
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21 views

Clarification: non-relativistic fine structure of a one-electron atom

The fine structure energy shift (in the non-relativistic limit) for a single-electron atom due to spin-orbit coupling is given by $$\Delta E_l\propto\frac{j(j+1)-l(l+1)-s(s+1)}{2l(l+\frac{1}{2})(l+1)}$...
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60 views

Tensor product - Addition of angular momenta

In the book Quantum Mechanics - Cohen-Tannoudji, in chapter X, equation (B-5) says $$ \vec{S^2} = (\vec{S_1} + \vec{S_2})^2 = \vec{S_1^2} + \vec{S_2^2} + 2\vec{S_1}\cdot\vec{S_2} $$ and $$ \vec{S_1}\...
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30 views

Rotation operation on spin-1/2 particles

How does rotation operators work on a particle? What does it do on the particle conceptually? Also does particles spin on its axis?
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29 views

Eddy current damping heat generation

Background According to this source (page 7): https://deepblue.lib.umich.edu/bitstream/handle/2027.42/109373/me450w10project16_report.pdf?sequence=1 the "braking" torque a magnetic field on a ...
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1answer
62 views

Quantum Mechanics: Rotation operators

How do I know what direction of the rotation operator to use on the initial state of a spin-1/2 particle? For example, a spin-1/2 particle initially in the $\lvert y \rangle$ state enters a SGz ...
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2answers
43 views

Momentum of a rack and pinion gear system excited by a time variant force

Background I have a rack and pinion gear system as shown in the image below The pinion gear is attached to a flywheel at the back. The first state of the system, none of the gears or the ...
3
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1answer
56 views

Using symmetry to determine a hydrogen electron's decay route from $|300\rangle$ to $|100\rangle$

Lets say we have an electron in state $|nlm\rangle = |300\rangle$ of the hydrogen atom. By selection rules, we know that it can only decay to ground state in 3 ways, namely through the $|21m\rangle$ ...
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14 views

Counting the possible states for an electron configuration

How do you find the terms and energy levels for the electron configuration $(n_1p)(n_2 p)(n_3 s)$ in the case of LS coupling, where $n_1, n_2$ and $n_3$ are different? How do you find the number of ...
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0answers
56 views

Elegant method to show $[L^2,[L^2,\vec{r}\,]\,] = 2\hbar^2\{L^2, \vec{r}\}.$ [duplicate]

Show that $[L^2,[L^2,\vec{r}\,]\,] = 2\hbar^2\{L^2, \vec{r}\},$ where $\vec{r} = x\, {\hat x} + y\, {\hat y} + z\, {\hat z}.$ "Edit: $\{A,B\} = AB + BA$ is the anti-commutator." I am able to solve ...
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36 views

Uncertainty in orientation of angular momentum

To calculate the uncertainty it looks like I'm going to find an expression for the root mean square of either $J_x$ or $J_y$, or the $J$ in the x/y plane? But I'm not sure if that's what it means by "...
0
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1answer
53 views

Angular momentum definition? [closed]

The definition of linear momentum is this: Momentum is a vector quantity defined as the product of an object's mass, $m$, and its velocity, $\vec v$. So According to that definition,The definition ...
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1answer
63 views

What is the speed of the skaters in this case? [closed]

You're choreographing your school's annual ice show. You call for eight 60kg skaters to join hands and skate side by side in a line extending 12m. The skater at one end is to stop abruptly, so the ...
3
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1answer
46 views

Which force transfers angular momentum in tidal locking?

The moon is in tidal lock with the earth, but a long time ago it was not. As the moon became tidally locked with the earth, its angular momentum changed and the delta went into it's orbit and possibly ...
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0answers
45 views

Addition of $N$ spin halves

If I have two spin-halves, then \begin{align} \frac{1}{2} \otimes \frac{1}{2} = 0 \oplus 1. \end{align} If I have three spin-halves, then \begin{align} \frac{1}{2} \otimes \frac{1}{2} \otimes \frac{...
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0answers
46 views

Help finding CG coefficient in Wigner-Eckart Theorem

Here is a Wigner-Eckart problem from class that I am having trouble understanding. $$\langle 310|T_{10}|300\rangle =\langle 31||T_1||30\rangle\langle 10;00|10\rangle $$ where $\langle 10;00 | 10\...
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1answer
43 views

Conservation of Angular Momentum for an Object Not Rotating

I have a point mass connected to a string with negligible mass. The point mass has mass $m$ and is moving at a velocity $V$. The string is of length $r$, and it is keeping the point mass tied to a ...
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2answers
81 views

Angular momentum of rolling sphere [closed]

A sphere of uniform density $\rho$ and radius $r$ is rolling without slipping on a perfectly flat surface. It is moving in a perfectly straight line and its axis of rotation is parallel to the plane ...
4
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2answers
70 views

Is the conservation of angular momentum violated in electron jumps from one orbital to another?

I don't really know any quantum mechanics. But in our class, we were introduced to Bohr's model of the atom with his postulate that the angular momentum of an electron in the $n$-th orbit is $\frac{nh}...
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1answer
25 views

What is the minimal G-force curve in 2-dimensional space?

Given two parallel roads, which need to be connected, what shape of curve would produce the minimum overall horizontal G-force(s) on travelers? Is it a $sin$ or $cos$ wave? Is it a basic cubic ...
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1answer
38 views

Vector interpretation of Kepler's 2nd law ( r X a = 0 )

I just read the vector interpretation of Kepler's second law and the conclusion put me in a confusion. The interpretation concludes by demonstrating that r X a = 0, where boldfaced r and a are ...
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1answer
32 views

Isn't there any analog between angular momenta in Classical/Quantum Mechanics, especially for the ground state?

By the ground state, I mean something like the state of the hydrogen atom with the lowest its total energy, where the quantum number $l$ is 0, which means we can't get any orbital angular momentum at ...
1
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1answer
56 views

Physical reason behind $\langle +,x | \hat S_z |+,x \rangle=0$? [closed]

For a spin half particle we have the following relation: $$\langle +,x | \hat S_z |+,x \rangle=0$$ I have seen this to derive the Pauli matrices and therefore am wondering without knowing anything ...
0
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1answer
40 views

Coriolis object deflection and conservation of angular momenutum

I'm trying to understan kinematic inertial explanation of the apparent deviation of objects due to fictitious forces in rotating Earth. Take an object moving from the equator northwards, or ...
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1answer
39 views

If a rotating ball gets disintegrated to dust or energy what happens to its angular momentum?

Say a rotating ball or neutron star gets completely annhilated to energy by meeting its anti-matter counterpart (also rotating in the same direction), what happens to the angular momentum? It cannot ...
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1answer
37 views

Can angular momentum not be conserved in a straight line motion?

Consider a particle moving an a straight line, with constant velocity $v$. The angular momentum (pivot point $O$) can be calculated as $$L=mr v_{\theta}$$Where $v_{\theta}$ is the velocity ...