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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4
votes
2answers
633 views

Can 3 photons be combined to give a spin-0 projection?

Motivation: The neutral pion decays to 2 photons ($\pi^0\to\gamma\gamma$) most of the time. For the decay of the neutral to 3 photons ($\pi^0\to 3\gamma$) we have an upper limit on the branching ...
0
votes
0answers
34 views

Why can the y and z-components of spin be measured simultaneously? [duplicate]

I have a gut feeling that this is wrong. By the uncertainty principle where $x,y,z$ are the $x,y,z$ components of spin $$ \sigma_{y}\sigma_{z}\geq \frac{\hbar}{2}\langle x \rangle $$ and it can be ...
0
votes
2answers
204 views

Why only 1 component of angular momentum?

Griffiths says that you can have only 1 well defined component of the angular momentum because of the uncertainty principle. From the uncertainty principle, we get that $$ \sigma_{L_x}\sigma_{L_y} \...
0
votes
0answers
33 views

How does this dumbbell rotate?

I am reading the book Spacecraft Attitude Determination and Control by J.R. Wertz, and on page 488 it says: My question is: how does the axis of rotation, $\hat{\omega}$, rotate? How does ...
2
votes
1answer
26 views

Principal moment of inertia for a rotating body

My major is not in physics. I am reading the following paper: (my problem is simple and not related with any optimization) http://arxiv.org/abs/1410.2841 (p.5~p.6) Suppose The ...
-1
votes
0answers
28 views

Angular Momentum of Closed Subshell

Suppose we have a state with $2\ell +1$ fermions all entirely in the subspace of hydrogen eigenfunctions with $n, \ell$ fixed. That is we have a state occupied by $2\ell +1$ fermions involving $\mid \...
-2
votes
0answers
32 views

Flat Disk Rotating Torque [on hold]

I have been trying to work out something. If you had a top like in the following description, how would you calculate the vector torque of the disk? And would it be just due to gravity? If so is the $\...
-3
votes
0answers
36 views

Kinematics of Rigid Body [on hold]

I'm working out in this problem since last week but I'm not able to identify how to calculate the total angular momentum. Can anyone help me? A uniform disk of mass $m$ and radius $r$, mounted on a ...
34
votes
7answers
5k views

Why don't we feel the subtle speed change of Earth's elliptical orbit?

Earth's orbit is a slight ellipse, so to conserve momentum its speed increases when it is closest to the Sun. If the speed changes there is an acceleration. If there is an acceleration there is a ...
3
votes
2answers
52 views

Trying to visualize how a single photon can carry away more than one unit of angular momentum

I have a newbie question that I am trying to wrap my brain around. Single photon gamma emission from a nucleus undergoing a $2^{+}$ to $0^{+}$ transition would involve an emitted photon with angular ...
0
votes
1answer
34 views

Representation of spin operators in a two electrons system

I've studied that the spin space of an electron is a two-dimensions Hilbert space. A possible representation of this space can be constructed defining: $$\chi_+ = \begin{pmatrix}1 \\ 0 \end{pmatrix} \...
1
vote
0answers
32 views

Why are parallel spins energetically favorable for nucleons? [duplicate]

For deuterium, both the proton and neutron preferentially occupy $1s_{1/2}$ orbitals which have orbital angular momentum $l=0$ and spin $s=1/2$. By coupling their orbital and spin angular momenta for ...
3
votes
1answer
21 views

What are possible ways to construct J-matrices (higher order Pauli matrices)?

I'm looking for possible ways to construct $J$-matrices. $J$-matrices are the higher-order version of Pauli matrices. Pauli matrices are suited for spin-1/2 systems, while J-matrices can be for any ...
1
vote
1answer
49 views

torque needed to precess the angle of rotation

If a rigid body with the inertia matrix $I_B$, has the angular velocity $\overrightarrow{\omega_1}$ what torque is needed to rotate it around another axis say $\overrightarrow{\omega_2}$ while keeping ...
0
votes
1answer
46 views

Can free particle (eg. unbound electron or proton) have angular momentum other than spin?

I am learning about parity of nucleus and (elementary) particles. For example, proton has a intrinsic parity of $+1$. However, a more general term for parity of proton is $(-1)^l$ where $l$ is orbital ...
0
votes
1answer
51 views

Can light change the shape of a black hole?

If light orbits a black hole without ever getting closer or further from it, and the black hole pulls on the light from all directions nearly simultaneously, does the black hole extend at its equator? ...
0
votes
0answers
20 views

Time derivative of total angular momentum in Dirac equation

I would like to calculate the time derivative of the total angular momentum of a Dirac particle in an electromagnetic field $(\vec A, \phi)$: $$\vec J = \vec r \times (\vec p - \frac{q}{c} \vec A) + \...
0
votes
1answer
282 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 ...
-3
votes
2answers
68 views

In handling two 1/2-spin particles, why is there only one singlet state? [closed]

Why is $\left|\uparrow\uparrow\right\rangle +\left|\downarrow\downarrow\right\rangle$ not discussed, despite having a total spin s = 0?
1
vote
1answer
39 views

π , σ - atomic transitions with respect to a quantization axis

In the absence of a magnetic field, how does one physically (i.e perhaps in a thought expt) access delta_m = 0 or +-1 transitions since (as I understand it) the choice of quantization axis is ...
0
votes
2answers
158 views

Angular momentum about a moving axis

How can we define angular momentum of a system about an axis that moves parallel to itself? For example Axis passing through CM that is perpendicular to plane of body. When we talk about ...
1
vote
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 ...
0
votes
3answers
959 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 ...
2
votes
1answer
109 views

Angular Momentum of the Dirac field

I'm going through the Peskin & Shroeder's discussion on the Dirac field, and I am struggling with a couple of claims they make about angular momentum. First of all, the angular momentum operator ...
0
votes
1answer
120 views

Angular velocity of disc from induced motion

I came across a question regarding linear momentum $L$ and it's conservation, however I tried and got confused. It reads: A $40kg$ girl stands on the very edge of a rotating disc of mass $50kg$ and ...
2
votes
1answer
49 views

Clebsch-Gordan Coefficients - Neutron can't decay into a proton and electron.

I've been reading in Weinberg's Lectures on Quantum Mechanics and in a note under the text it said that I can use the Clebsch-Gordan Coefficients to show that a neutron can't decay into a proton and ...
11
votes
7answers
2k views

Does cutting of trees affect spin angular momentum of earth?

Cutting trees reduces earth's moment of inertia. So the spinning velocity of earth should be reduced day by day. Does it really happen?
1
vote
0answers
64 views

Two impulses on body

Suppose I have a physics simulation with a single body with three degrees of freedom (two axis and rotation). I have two impulses of equal magnitude in opposite directions. When applying these ...
4
votes
2answers
63 views

Half-integer angular momentum

Does half-integer angular momenta mean that the particle will always be found spinning? For example, if a particle is in a $l=\frac{1}{2}$ state, this means $ m=\pm\frac{1}{2}$ and since $L_z=\hbar m ...
5
votes
3answers
150 views

When we say electron spin is 1/2, what exactly does it mean, 1/2 of what?

When we say electron has spin of $\frac{1}{2}$, is that the value of the total spin of electron, or the projection on z axis, or the spin quantum number? When we say "electron has spin of $\frac{1}{2}...
-3
votes
1answer
100 views

How is hydrogen fine structure currently accounted for? [closed]

At a usually reliable site, Hyperphysics, the fine structure of Hydrogen is accounted for by the interaction between the B-field generated by the orbit of the electron, $0.4\:\mathrm{T}$ at $1s$ and $...
3
votes
1answer
40 views

Why objects with magnetic dipole moment sometimes orient towards external B and other times they do precession?

Given the magnetic dipole moment in external uniform magnetic field $\vec{B}$, I am trying to understand why sometimes $\vec{\mu}$ simply aligns with the $\vec{B}$ and stays that way, while other ...
2
votes
3answers
113 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 think)...
4
votes
1answer
150 views

Protoplanetary disks, angular momentum and prograde orbits

So you've got a protoplanetary disk and you're going to gravitate yourself some planets together. The disk is made up of the usual planetary system stuff, dust and gas and whatnot, orbiting a common ...
0
votes
1answer
75 views

Applying angular momentum operator [closed]

How are the algebraic steps to applied the angular momentum operator defined as: $$\hat{L}=-i\hbar[r\times\nabla]$$ to $$\Psi=a~ \psi_{431}$$ where the $\psi_{nlm}$ are the eigenfunctions of the time ...
0
votes
0answers
11 views

Specific microstate(s) corresponding to total angular momentum quantum number

Given a certain number of electrons in a certain electronic configuration (say, d$^2$ or (n$_1$p)(n$_2$d)), all combinations of the quantum numbers $m_l$ and $m_s$ can be constructed. Each of these ...
2
votes
1answer
167 views

Para and ortho hydrogen angular momentum values

In Wikipedia, it is said that: Orthohydrogen, with symmetric nuclear spin functions, can only have rotational wavefunctions that are antisymmetric with respect to permutation of the two protons. ...
6
votes
1answer
519 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 ${T^\mu}_\nu=\frac{\partial\mathcal{L}}{\partial(\partial_\mu\phi)}\partial_\nu\phi-{\delta^\mu}_\...
5
votes
3answers
1k views

Has a body angular momentum and torque only in a circular path?

In different contexts, my book(Principles of Physics by Resnick, Halliday ,Walker) , they wrote For torque, the path need no longer be a circle and we must write the torque as a vector $\vec{\tau}...
2
votes
1answer
49 views

Maximum Angular Momentum for an orbit in GR

[The reference for this question is the book Gravitation by Misner,Thorne, & Wheeler.] The trajectories of massive particles around a spherically symmetric body is governed by the effective ...
3
votes
1answer
149 views

Sequential Stern-Gerlach devices - realizable experiment or teaching aid?

At least one textbook [1] uses sequential Stern-Gerlach devices to introduce to students that the components of angular momentum are incompatible observables. Viz., the $z$-up beam from a SG device ...
0
votes
1answer
107 views

Boomerang angular momentum

So I'm building a boomerang to fly 200 feet in order to do that I was told to increase the moment of inertia to increase the resistance from change in state, and I was told that it would increase the ...
59
votes
5answers
7k views

If dark matter only interacts with gravity, why doesn't it all clump together in a single point?

I'm a complete layperson. As I understand, dark matter theoretically only interacts with the gravitational force, and doesn't interact with the other three fundamental forces: weak nuclear force, ...
1
vote
2answers
628 views

Too big to revolve like an atom? [closed]

At what point do objects naturally start revolving as a disk? From an atom, with which the electron revolves as a sphere, to a galaxy, that revolves in the same direction? I herd about rigid ...
40
votes
3answers
7k views

Why don't galaxies orbit each other?

Planets orbit around stars, satellites orbit around planets, even stars orbit each other. So the question is: Why don't galaxies orbit each other in general, as it's rarely observed? Is it considered ...
0
votes
1answer
47 views

How to calculate the linear momentum on a dumbbell? [closed]

In this picture there is a dumbbell and a mass in motion that hits one of the masses of the dumbbell. Now the problem is I have to find the velocity of the CM and the rotational speed around the CM. ...
3
votes
1answer
125 views

How can black holes have electric charge and spin? [duplicate]

If the star's mass supposedly collapses into a single point, and it ends up having "said" zero volume, then how can people say that the hole has a specific spin or that it can have an angular momentum?...
2
votes
1answer
31 views

Does the size of a black hole change depending on its charge or spin?

I was talking to this friend of mine who said that the size of a black hole could vary depending on its "charge" and spin. He said the size of a black hole would reduce if it had a spin or charge. The ...
17
votes
2answers
2k views

What is black hole spin?

First of, congrats to the people at LIGO. In this article, the BBC notes that the latest LIGO results show that a new black hole was formed with a spin of $0.2$ (dimensionless number). What exactly ...