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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25 views

Simplification of matrix-element given the Wigner-Eckardt theorem and Clebsch-Gordon coefficients of a 1,1/2 system

How can I simplify the following matrix-elements $$\left\langle 1,1/2;m_1,m_2\left| S \right| 1,1/2;m_1^{'},m_2^{'} \right\rangle$$ given the Wigner-Eckard theorem $$\left\langle j,m|S|j^{'},m^{'} ...
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1answer
120 views

Why do particles have spins such as $1/2$, $3/2$, $5/2$? [duplicate]

What does it mean to have 'half' spin? I have looked on Wikipedia and a few youtube videos on spin but they don't explain what it means to have $1/2$ spin. I am 18 and only starting to learning about ...
2
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0answers
63 views

How to get from momentum to force

Situation: I have a solid object (black) attached to a rod (blue) as shown below: The rod is fixed at the top. The solid object is a cylinder as shown, with a rate of rotation ...
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1answer
37 views

Azimuthal angle in bloch sphere

I was wondering if there is any direct physical meaning behind the Bloch sphere parametrization in the sense that if I choose the angle $\phi =0$, then what does this mean for my spin state? Does ...
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2answers
130 views

Proving that conservation of momentum doesn't apply to electron in H-atom

To prove that the conservation of linear momentum doesn't apply to electron in H-atom, is it sufficient to show that angular momentum operator ($\hat L$) and momentum operator ($\hat p$) do not ...
2
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1answer
82 views

Question about surface term in QFT problem

I am trying to follow the solution of the following problem (Srednicki 39.2): To show that: $$J_z b_s^\dagger(p\hat z)|0\rangle=\frac{1}{2}\ s\ b_s^\dagger(p\hat z)\ |0\rangle, $$ where $J_z$ ...
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1answer
62 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 ...
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3answers
143 views

How can you conclude that the angular momentum of a particle moving in a central field of force will be constant?

When determining the magnitude of the angular momentum vector $|\vec L |$, for a particle in a central field, my textbook concludes the following: $L=|\vec{r}\times m\vec{v}| = mr^2\dot{\theta}$ = ...
4
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1answer
122 views

How to interpret spin observables constructed by non-standard phase choices?

If we try to find matrix elements of ladder operators ( $J_{\pm}$) for spin when they act on eigenstates of $J^2$ and $J_z$ ( $\newcommand{ket}[1]{\left|#1\right\rangle} ...
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0answers
57 views

Relative velocity between a ball hitting a rod [closed]

A ball of mass $m$ travelling with a velocity $v_0$ collides elastically, and perpendicularly with a rod at a distance $d$ from the center of the rod. The rod has a mass $M$ and lies on a frictionless ...
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1answer
206 views

Conservation of angular momentum in a free rod

When a collision is elastic and no external torque acts on a system, angular momentum is conserved I found this example and checked the results: A ball (m = 1 Kg , v = p =+22 m/s, Lm = +11, Ke = 242 ...
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2answers
70 views

How's equilibrium possible here?

Here's the question.......Two point masses $m$ and $2m$ are attached at each end of a light rod. The rod is pivoted at the center and is free to move in a vertical plane. Then find the angle $A$ when ...
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1answer
46 views

Is the distance involved in calculating angular momentum to an axis or a point?

I'm a high school student.I still don't really understand angular momentum and moment of inertia. I know the moment of inertia of a point mass is defined as $mr^2$. For any other shape, we integrate ...
2
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1answer
38 views

Angular momentum effect on quantum energy

I'm doing some computational research into quarkonium states and I've written a code that determines energy levels by finding a solution to the Schrodinger equation for a given angular momentum. I.e. ...
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1answer
153 views

Find angular velocity of motor

I'm quite bad at this, but I'm trying to change that and I need some assistance. Please bare with me while I attempt to explain what I'm trying to figure out and correct me where I'm wrong. Basically ...
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2answers
114 views

Dumbbell rotation

What if apply impulse to dumbbell consisting of two masses and massless rod? It is clear for me that left dumbbell will move straight line. But it is not clear for me what kind of motion will have ...
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2answers
49 views

Do comets spin? Why do satellites/space station not spin?

Do comets spin? Why don't satellites or space-station spin? If spin is fundamental thing, then it should be found in all (moving) objects.
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3answers
153 views

$F=ma$ contest problem on angular momentum [closed]

Problem #25 from the 2009 $F=ma$ contest: Two discs are mounted on thin, lightweight rods oriented through their centers and normal to the discs. These axles are constrained to be vertical at all ...
3
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1answer
156 views

Paradox: electric current in a coil on a disc - will this disc spin if the circuit is opened?

I encountered this problem in a book, but there were no solution written there. The setup: there is a plastic (insulator) circular disc, that is suspended in a way, that can very easily rotate (so ...
1
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1answer
58 views

What is the ultimate “goal” of two particles in a gravitational field? [closed]

What is the ultimate "goal" of two particles in a gravitational field? Will the particles eventually occupy the same point at the same time if nothing stops them? What stops them from achieving the ...
2
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0answers
69 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 ...
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1answer
68 views

Scalar field gives spin $0$ particles

Related to this question. What needs to be shown is that the total angular momentum (derived from the Klein-Gordon lagrangian) acting on a ket with $0$ momentum, gives 0. This would mean that a ...
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2answers
207 views

Boomerang physics and aerodynamics

I posted a question before on this website asking how to build a boomerang for a project which can fly at least 200 feet, so how would I increase the flight path. A user responded with: slow down the ...
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1answer
82 views

Total angular momentum in QFT

Can anyone show explicitly how the QFT total angular momentum operator $$\hat{\vec{J}} = - i \int \frac{d^3p}{(2 \pi)^3} \hat{a}^{\dagger}_{\vec{p}} ( \vec{p} \times \nabla_{\vec{p}}) ...
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129 views

Calculating the square of angular momentum operator in cylindrical coordinates

I want to evaluate the square of angular momentum, $L^2$, in cylindrical coordinates. I found components of $L$ in cylindrical coordinate. How can I find eigenvalue and eigenfunction of $L_z$?
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114 views

Spin, parity, etc. conservation in decays/reactions

I have a long list of short physics questions I'm reviewing, and there are several that ask about whether certain decays or reactions are allowed. Clearly these questions are testing my knowledge of ...
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1answer
122 views

How does a rotation operator change the angular momentum of a quantum system?

I think I'm having some problems understanding the role of rotation operator $$\mathscr {R} = e^{-i/\hbar \hat{L_z} \theta}.$$ Suppose we have a quantum system in the state $\vert \psi_0 \rangle$ ...
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1answer
158 views

Boomerang torque and angular momentum

I'm building a boomerang for a project, but I've made it a goal for myself to have a boomerang which can fly at lest 200 feet, so how would I increase the flight path. Angular momentum increases in ...
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2answers
87 views

What is the initial angular momentum of a rigid body given an offset impulsed force?

What is the imparted angular momentum to a rigid body if the impulse force is offset by a distance $h$ from the center of mass and the imparted momentum from the center of mass is $mv$? For a ...
0
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1answer
58 views

Why $2j+1$ number of states?

In this statement from Modern Quantum Mechanics by J.J. Sakurai: If $j$ is an integer, all $m$ values are integers; if $j$ is a half-integer, all $m$ values are half-integers. The allowed ...
2
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1answer
76 views

Why is the Earth self-rotating? [duplicate]

What drives this happen? Would it be the internal energy or by an external force? I did try to Google the answer, but could not find a good one.
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2answers
88 views

Magnetic quantum numbers - axes correspondence

We know that the magnetic quantum number describes the space orientation of an orbital within an atom. For the $p$-orbital, the magnetic quantum numbers can be -1,0,1 (one for every axis). We have ...
0
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1answer
53 views

How to determine whether an eigenstate of total spin is symmetric or antisymmetric?

Here we have two identical paticles with spin $I$, integer or half-integer, and there are $(2I+1)^2$ states. Each one of them can be uniquely determined by total spin and its orientation, we can use ...
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0answers
27 views

What are some most advanced theories explaining why same charge repel, opposite charge attract? [duplicate]

It is the holidays with a lot to think about. One of the thing that I couldn't get out of my mind was something I read in Stephen Hawking's "Brief History of Time". In it, he described the repelling ...
2
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1answer
259 views

The subtle differences between angular momentum and centrifugal force?

I am a mathematician wanting to understand the differences between the concepts of angular momentum and centrifugal force. The following two ideas are clear to me from a physical point of view, but ...
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0answers
63 views

Determining Parity of Decaying Quantum System

Show that a particle of spin $1$ cannot decay into two identical particles of spin $0$. The $\rho$-meson has spin $1$ and can decay into two spinless (spin-$0$) $\pi$-mesons, or pions, with ...
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1answer
60 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 ...
4
votes
2answers
510 views

Why is the Milky Way flat? [duplicate]

I read recently that the galactic "flatness" of the Milky Way is due to the rotation of the galaxy combined with a vast stretch of time. Yet, I also read where 1) the Milky Way rotates once every 225 ...
2
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0answers
95 views

Lorentz transformation - Bjorken & Drell

I'm trying to derive (14.25) in Bjorken & Drell (B&D) QFT. This is $$\tag{14.25}U(\epsilon)A^\mu(x)U^{-1}(\epsilon) = A^\mu(x') - \epsilon^{\mu\nu}A_\nu(x') + \frac{\partial ...
2
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2answers
87 views

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
56 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
votes
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 $j > 1$ ...
2
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1answer
137 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 the newest version.). Despite the title, the author claims it in a quite general ...
0
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1answer
33 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
69 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
171 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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6answers
396 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
81 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
42 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 ...
0
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2answers
45 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 ...