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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13 views

Time evolution of generalized angular momentum operator

We define this operator : $$M^{\mu\nu} = \int d^3x~(x^{\mu}T^{0\nu} - x^{\nu}T^{0\mu})$$ where $T_{\mu\nu}$ is the energy momentum tensor (see e.g. Energy momentum tensor from Noether's theorem) ...
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2answers
51 views

What should we do If we wanted to increase the angular velocity of a planet? [duplicate]

We could hit it with really fast objects, but could we manipulate the orbit of a large satellite to speed up its rotation? What would be the easiest way?
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3answers
560 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
60 views

Discovery of spin-3 particle at LHCb

I just read a discussion on the CERN website regarding first observation of a heavy flavored spin-3 particle at LHCb. This appears to be a post from last July. Is there anyone knowledgeable enough in ...
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1answer
60 views

What exactly is quantum spin? [duplicate]

What is "spin" as it relates to subatomic particles? I've heard that it's similar to angular momentum but I've also heard that's not completely the case.
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4answers
6k 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 ...
3
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1answer
158 views
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1answer
177 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
52 views

Calculating L^2 operator in spherical coordinates [closed]

I found this development for the calculation of angular momentum L^2 operator in spherical coordinates. The image attached shows the latest step of this. I cannot figure out the algebra between these ...
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1answer
93 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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6answers
2k views

How does a spinning electron produce a magnetic field?

I learned in my undergraduate physics class that atoms have magnetic fields produced by the orbit of electrons and the spin of electrons. I understand how an orbit can induce a magnetic field because ...
0
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1answer
138 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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3answers
227 views

The momentum of a swinging sword

Suppose you are faced with a zombie, and the only way to kill it and save yourself is to chop its head off with your sword. However, you are very weak from illness, and can only afford to strike once. ...
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0answers
15 views

Impulse required to stop a rotating rod at a pivot provided there is no horizontal force at the pivot [closed]

A rod is held horizontally with a pivot at one end and then released. When the rod is vertical it is struck with an impulse that brings the rod to rest (this is in addition to any impulse provided by ...
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1answer
42 views

Total angular momentum operator

How do the eigenfunctions of the total angular momentum operator analytically look like? I mean the operator is given by $J = L+S$ so the eigenfunctions have to be tensor-product states, right? Can ...
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1answer
110 views

Can an atom have angular momentum? At what angle does an atom reflect a single photon?

Groups of atoms, say two of them, can have angular momentum as a group, but only because they individually have linear momentum and are bound together through a force that causes them to pull on each ...
4
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1answer
93 views

In 2-dimensional and 3-dimensional universes, stellar systems and galaxies are flat and disky. But what about in 4-dimensional universes?

I just watched that interesting video: https://www.youtube.com/watch?v=tmNXKqeUtJM In 2 dimensions a cloud of particles rotating in a plane is flat by definition since it's in 2 dimensions. ...
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2answers
488 views

How can a particle with no size have angular momentum?

I was recently reading about Higgs boson and particle spin and I stumbled upon a question that explains what is spin. It explains that electrons have no size yet they have angular momentum. I don't ...
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2answers
44 views

Vector model of addition of angular momenta

I'm trying to understand what Landau and Lifshitz mean in their $\S31$ of "Quantum mechanics. Non-relativistic theory" about vector model of addition of angular momenta: ... This result can be ...
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1answer
42 views

Angular momentum in planetary disk formation

This question is actually more linked to astronomy and astrophysics than to pure physics. I tried posting it on the astronomy page, however it got no answers, so I though this page might help. ...
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5answers
218 views

How is Angular Momentum Conserved when Mass is Released?

I am not a physicist (math/comp-sci) but I understand that Angular Momentum is supposed to be conserved. I find this confusing because there seems to be many simple, common cases where a restrained, ...
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1answer
415 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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2answers
825 views

Probability of getting a particular spin

I'm a beginner in quantum mechanics, and I'm a bit confused about states and the probability to measure certain values. I would like to understand at least the following simplified situation: ...
5
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3answers
58 views

Finding the angular velocity of a rod hit at a distance from its pivot [closed]

A 1m long, 2kg stick is nailed to the wall with a single nail, allowing it to pivot and freely rotate at the end. A 1kg ball, with speed 3m/s makes contact with the stick at some distance x (unknown) ...
3
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3answers
237 views

Why does the electron spin with a particular tilt?

I found this image for the classical description of the electron spin at hyperphysics Can you explain why the axis of rotation makes an angle of 60° with the z-axis and how this particular ...
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0answers
38 views

Do the norms of the total and the orbital angular momentums commute? If yes, why is there a problem with 2p_{1/2}?

Question: For $\vec L$ the orbital angular momentum of an electron, $\bar S$ its spin, and $\vec J:=\vec L+\vec S$ the sum, do $\vec J^2$ and $\vec L^2$ commute? I assume it does: $[\vec J^2,\vec ...
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4answers
571 views

Why is $ \vec{S}^{(A)} \otimes \vec{S}^{(B)} = \frac{\hbar^2}{4}(\sigma_x \otimes \sigma_x + \sigma_y \otimes\sigma_y + \sigma_z \otimes \sigma_z)$?

I haven't been taught tensor product in class but they have taught us addition of spin. I looked up online in this link->http://homepage.univie.ac.at/reinhold.bertlmann/pdfs/T2_Skript_Ch_7.pdf#page=10 ...
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4answers
556 views

Why are the magnetic moment and the angular moment related?

Why are the magnetic moment and the angular moment related? I've always read everywhere that they are related but found nowhere a satisfactory explanation of the cause
5
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3answers
503 views

The Asymmetry between Real and Imaginary in the three Pauli Spin Matrices

The Pauli spin matrices $$ \sigma_1 ~=~ (\begin{smallmatrix} 0 & 1 \\ 1 & 0 \end{smallmatrix}), \qquad\qquad \sigma_2 ~=~ (\begin{smallmatrix} 0 & -i \\ i & 0 ...
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7answers
7k views

Why don't spinning tops fall over?

One topic which was covered in university, but which I never understood, is how a spinning top "magically" resists the force of gravity. The conservation of energy explanations make sense, but I don't ...
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2answers
204 views

Why are the spin operators defined as they are?

$$\begin{align*}S_z &= \frac{\hbar}{2} \left(\left|+\right>\left<+\right| - \left|-\right>\left<-\right|\right)\\ S_y &= i\frac{\hbar}{2} \left(\left|-\right>\left<+\right| - ...
2
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0answers
20 views

For Charmonium, why does the spin-spin interaction mostly affect the $L = 0$ states?

For Charmonium, why does the spin-spin interaction mostly affect the $L = 0$ states? My textbook states that this is because "only then is the wave function at the origin non-vanishing". Could anyone ...
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2answers
31 views

Need help with relationship between angular momentum, linear and angular velocity

I am in an introduction to engineering physics course and just trying to see if my understanding of angular motion is correct or if I have the wrong idea. So as I understand it, angular velocity is ...
3
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1answer
218 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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2answers
29 views

How did the planets (in the Solar System) start to revolve around the sun if they were attracted towards the Sun via the gravitational force? [duplicate]

The planets in the Solar System revolve around the Sun in almost circular paths called orbits. The Sun pulls the planets with the gravitational force,but the planets do not get drawn to the Sun but ...
0
votes
1answer
97 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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1answer
83 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
295 views

Conservation of Angular Momentum and linear velocity

I have a problem where a cylinder is moving on a horizontal surface, starting with velocity $v_0$. It is given that its radius is $10\text{cm}$, its mass is $200\text g$ and the coefficient of ...
0
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1answer
27 views

Fine Structure Correction

The fine structure correction is composed of the relativistic correction and spin-orbit coupling. The lowest-order relativistic correction to the Hamiltonian is $$ H_r' = -\frac{p^4}{8m^3c^2}$$ ...
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1answer
47 views

Pipe in space outputs gas - what is its angular momentum at $t$ and $t+dt$? [closed]

Given a pipe in space (neglect gravitational force): The speed of the gas is $v_0$ (in relative to the edge of the pipe) The length of the pipe is $l$ The pipe rests (not moving) at $t=0$ The gas ...
-1
votes
1answer
31 views

Calculating values related to angular momentum and then their uncertainties [closed]

Here is the problem: And here is my work (sorry it is handwritten, it would take a while to type this out) My problem is that I'm not sure if it's right or if it makes sense to keep getting 0 ...
5
votes
1answer
177 views

How to get rotational speed after disk-disk collision with friction?

Assume two circular disks A and B collide. They have both initial linear momentum and angular momentum. If their surface has no friction, their angular velocity does not change after collision, so I ...
0
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1answer
53 views

Question about angular momentum operator

To show that the eigenvalue to $L^2$ is proportional to $\hbar^2$ is shown from $L_z=xP_y-yP_x$ $p_y=-i\hbar\frac{\partial}{\partial y}$ $p_x=-i\hbar\frac{\partial}{\partial x}$ ...
0
votes
1answer
66 views

How does the Earth rotate, given that the torque acting on it while revolving is zero?

I've come to understand that the torque acting on the Earth while revolving the Earth is zero. Torque is the force responsible for rotation of a body. So how does the Earth rotate?
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2answers
115 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 ...
0
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1answer
64 views

How does frequency change with centripetal force?

Using the equation $$F_c = {{mv^2}\over{r}}$$ I can see that mass and velocity are directly proportional to centripetal force. I can also see that the radius length is inversely proportional to ...
4
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2answers
150 views

How can mean value of a quantity $be$ an operator?

In Laundau & Lifshitz Quantum Mechanics. Non-relativistic theory in $\S29$ a problem is given: PROBLEM Average the tensor $n_in_k-\frac13\delta_{ik}$ (where $\mathbf{n}$ is a unit vector along ...
2
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3answers
152 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 $| ...
10
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6answers
2k views

Why does a curling rock curl?

In the game of curling, players "curl" a granite "rock" (of precise size and roughly a flattened cylinder) down a "sheet" of ice towards a target; the "rock" will curve in its path in the direction of ...