Questions tagged [angular-momentum]

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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240 views

Why does angular momentum being constant prove Kepler's first law?

So I was watching this video and this video on Kepler's first law in order to understand the proof of Kepler's first law. He started off by saying that for an ellipse, the distance from a focus point ...
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Is there an anticommutator relation for orbital angular momentum?

So I know that there are commutator relations for $L$ such as $[L_x,L_y] = i\hbar L_z$, but is there a relation for the anticommutator? For example, $L_xL_y + L_yL_x$?
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Must the total orbital angular momentum quantum number $L$ be less than the principal quantum number $n$? If so, why?

I am studying LS coupling and term symbols. In my textbook, there is an exercise: Why is it impossible for a $2\ ^{2}\text{D}_{3/2}$ state to exist? The answer says, the total orbital angular ...
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Mechanics: angular momentum of disk

I am studying mechanical engineering and I've got a problem with the angular momentum of objects that have a rotation which is rather complex to describe like the following: The shaft rotates around ...
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Angular momentum and Rotation

Is Rotation a necessary condition for angular momentum? I mean can two bodies under translational motion in particular directions have a total angular momentum that is not zero?
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Still Confused about Linear Momentum in a Circle

A point mass with mass $m$, distance $r$ from circle and constant tangential velocity and constant angular velocity is swung around a circle. ($p$ is linear momentum) Angular momentum is radius x ...
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Understanding the radial distribution function [duplicate]

I am confused why the maximum of the radial distribution function for 2p orbital is closer to the nucleus than that for 2s orbital. Doesnt this mean that there is a higher chance of finding 2p orbital ...
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Conservation of Momentum within Conservation of Angular Momentum

$L=r \times p$ where $L$ is angular momentum, $r$ is radius and $p$ is tangential linear momentum. Using a generic example of a skater spinning on ice with no friction while being stationary, ...
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Angular Momentum of a Rigid body

When defining angular momentum or rather calculating angular momentum what is the difference in the use of the terms "with respect to" , "about a point" or "in the frame of" ? Are the angular ...
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Torques in Euler equation

The Euler equation is given by $$\mathbf I\dot{\boldsymbol \omega}+\boldsymbol\omega\times \mathbf I\boldsymbol\omega= \mathbf M.$$ Also see here. It explains that The expressions for the torque in ...
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Derivation of nuclear spin $I$ for $^{87}$Rb and $^{40}$K

So I know that $^{87}$Rb has $I=3/2$, and has 37 protons and 50 neutrons. I try to make sense of it form the nuclear shell model: taken from here. 50 neutrons: they are a closed shell, so no net ...
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Commutation of $J^2$ and $J_i$ [closed]

For the Hermitian operators $\hat{J_1},\hat{J_2},\hat{J_3}$ that satisfies the commutation relations $$[\hat{J_1},\hat{J_2}]=i\hbar\hat{J_3},$$ $$[\hat{J_2},\hat{J_3}]=i\hbar\hat{J_1},$$ $$[\hat{J_3},\...
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Why is this function an eigenfunction of $\hat{L}_{z}$?

$$\Psi(\varphi)=\frac{1}{\sqrt{2\pi}}(\sin\varphi-\cos\varphi)$$ I am not able to see why the above function is an eigenfunction of $\hat{L}_{z}$ and which is its eigenvalue. I've been trying with ...
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71 views

Can I theoretically completely convert the kinetic energy of a bullet to rotational energy of a disc, when the bullet hits it tangentially?

Will the kinetic energy of bullet be converted to rotational energy of disc(assume the bullet gets stuck to the disc). Let me assume that disc is mounted on a car standing on a frictionless surface. ...
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Stone skipping does spinning help?

I have tried to hurl a stone with some added rotation and it performed slightly better but I have great difficulty replicating this feat for consistency, my question is should I add angular momentum ...
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Is outside force needed to conserve angular momentum?

Franklin Hu has a good experiment here. Franklin uses the correct formula for angular momentum; and he realizes that the Linear or Newtonian velocity must double if angular momentum is to be ...
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Commutation relations

Given that the Hamiltonian for Muonium spin in zero magnetic field is $$\hat{H} = a \vec I \cdot \vec J$$ where $\vec I$ is the spin of a muon, and $\vec J$ is the spin of the electron, what is the ...
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Adding a swirl to poiseuille flow

I came acroos this question and I have no clue how to answer it: If we have poiselle flow in a circular pipe of Length $L$ and pressure gradient $\Delta P$ and introduce a swirl $u_\theta=\omega r$, ...
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1answer
144 views

Computing a matrix element with the Wigner-Eckart-theorem

I learned about the Wigner-Eckart theorem and want to apply it to the following matrix element \begin{equation} \langle j \, m | r_kr_l | j' \, m'\rangle. \end{equation} I know this can be done by ...
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Where does linear momentum go in angular momentum conservation? [closed]

This question is a continuation of another question, found here: Does conservation of angular momentum break conservation of momentum? The first part of this question is exactly the same as the other ...
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Symmetry Properties for Wigner 3j-symbols

I am learning about coupled angular momenta and came across the Wigner 3-j-symbols which are defined by \begin{equation} \left( { \begin{array}{ccc} j_1 & j_2 & j_3 \\ m_1 & m_2 & m_3 \...
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Change of basis from $J_y$'s eigenbasis to $J_z$'s eigenbasis for arbitrary $j$

I have been trying to compute the inner product ($j$ being fixed) $$\langle m_y|a_z\rangle \tag{1}$$ where $J_y|m_y\rangle = m |m_y\rangle$ and $J_z|a_z\rangle = a |a_z\rangle.$ I tried writing $$|m_y\...
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Why does an ice-cube turn faster and faster while melting in water?

Whenever I put an ice-cube into a glass of hot water, so that it melts quickly, and it is initially rotating slowly, I noticed that its rotational speed increases as it melts and 'shrinks'. Why? I ...
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Quadratic formula not working in Quantum Mechanics? [closed]

In quantum mechanics the raising operator of a system with quantum number $s$ and $m$ is such that $$\hat{S}^+|s,m\rangle = \hbar \sqrt{s(s+1)-m(m+1)}|s,m+1\rangle$$ Since there must exists a $m_\...
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If $L_z$ has a $0$ eigenfunction, since $[L_x, L_y] = i\hbar L_z,$, then can $L_x, L_y$ have a simultaneous eigenfunctions?

In the lecture Quantum Mechanics by Dr. Adams in ocw.mit.edu, in the 16th lecture at 7:11, it is stated that since $$[L_x, L_y] = i\hbar L_z,$$ there is no state s.t it is eigenfunction of both $L_x, ...
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Why does $2p$ have highest RDF at $4a_{0}$?

I was reading notes from my first class in Quantum Physics that I received and left confused at the following statement: For each principal quantum number $n$, the orbital set with the highest $\...
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Explanation of the sign of Clebsch-Gordan coefficients

These are the Clebsch-Gordan coefficients when the orbital and spin-angular momenta of a single spin 1/2 particle are added. I'm not able to understand the explanation. What I can understand is that: ...
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Angular momentum in different points

I have a question about angular momentum: Is it possible to have a system where angular momentum is conserved relative to 1 point,but not conserved relative to another?
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Does conservation of angular momentum break conservation of momentum?

Say we have a spinning ring of mass $M$, rotating at $W_0$, at a radius $r$ from some pivot point. This ring has massless spokes extending out to a length of $2r$. From this, we can calculate the ...
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Why are systems joined via a tensor product? [duplicate]

This question comes from seeing that the triangle addition rule for quantum mechanics comes out of groups/representation theory; I thought this was odd as we haven't used any group ideas in QM up to ...
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Confusion about conservation of angular momentum tensor in classical field theory?

In my lectures, we considered the conserved stress energy tensor $T^{\mu \nu}$ and noted that we could always add a conserved tensor to it such that $T^{\mu \nu}$ is symmetric. As a consequence, a ...
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Confusion regarding the possible term symbols/spectroscopic terms for (2p)(3p) configuration

Note: I have read this answer but it still doesn't address my question in terms of the permitted symmetry. I am learning about atomic states, and possible electron configurations. The first example ...
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Why light have angular momentum?

Light carries momentum which is an intrinsic property or ability to move something at least how I interpret it, I got no issue on how it is able to conserve momentum when it is absorbed by another ...
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Racah's Clebsch Gordan J dependence in Theory of Complex spectra ii

I have a question concerning Giulio Racah's derivation of the closed algebraic form of the Clebsch-Gordan coefficients in his Theory of complex spectra ii paper (Phys. Rev. v 62, pp 438 1942). I have ...
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What does vector operator for angular momentum measure?

Consider the vector operator for angular momentum $\hat L=\hat L_x \vec i +\hat L_y \vec j + \hat L_z \vec k$. Does this mean that if we want to measure the angular momentum of a particle in state $\...
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Why is the relative angular momentum of quark+antiquark in a pion equal to zero?

In a set of lecture notes provided by my lecturer, it says that a pion consists of a quark ($q$) and an antiquark ($\bar{q_2}$) with relative $L=0$. The negative parity and the fact that $S=0$ makes ...
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Commutator of $\hat {L}_x$ and $\hat{V}(\hat{r})$ [duplicate]

Consider the angular momentum operator $\hat{L_x}=\hat y\hat{p}_z-\hat{z}\hat{p}_y$ and the potential operator $\hat{V}$ where the potential $\hat{V}=\hat{V}(\hat{r})$ is spherically symmetric. It ...
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How come everything in the universe except the universe itself are spinning? [duplicate]

The planets and stars are spinning, galaxies and clusters are spinning so shouldnt the universe also spin? I think objects spin is to preserve angular momentum but it must also implied that in the ...
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How to generate a rotating electric field? [closed]

Does it involve the use of any magnets? And if so is there a geometric centre where the resultant field is zero.
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Probability to get an Eigenvalue of Angular Momentum Operator on an Arbitrary Ket

Hello physics SE community, I am currently working on Principles of Quantum Mechanics by Shankar and i get stuck in page 336 (its not even an exercise). It basically said that "we may expand any $\...
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2$\pi$ Rotation on integer vs half-integer spin states

I want to know how to get the following result: $$ e^{-i2\pi J_y / \hbar}|j, m\rangle = (-1)^{2j}|j, m\rangle $$ for an arbitrary spin state $|j, m \rangle$. What I've tried is to expand the ...
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Sci-fi ships falling on planets

I hope the question is suitable for this forum.... Watching Star Trek: The Next Generation, I have found at least a couple cases where a navigation malfunction on a shuttle makes it fall towards the ...
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Is spin 1 described by $SO(3)$ or $SU(2)$ [duplicate]

What spin is described by which rotation group? I always only find information about spin-1/2
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How does physics know something is spinning or rotating? [duplicate]

From a purely mathematical point of view, as far as I'm aware, there is no difference between rotating a singular point by a phase phi, using its own location as the centre, or rotating all but the ...
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Gyroscopic precession on a friction-less surface

I am having trouble understanding the total energy for a heavy spinning symmetric top (Gyroscope) on a friction-less surface. I am trying to understand it via the Lagrangian of the gyroscope. My ...
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Imagining zero orbital angular momentum for s-orbitals

Orbital Angular momentum of a s-orbital is always zero. One can easily imagine why this is so: QM says $\hat{p}=-i\hbar \nabla_{r}$, and since the s-wave functions are radially symmetric, the momentum ...
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Operational definition of rotation of particle

The question in brief: what does it mean, operationally, to rotate an electron? Elaboration/background: I am trying to understand how representation theory applies to quantum mechanics. A stumbling ...
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Rotating object on table: from sliding to rolling

A object which is rotating around a horizontal axis is placed on a surface, and starts sliding (with kinetic friction). After some time, it starts rolling without sliding through the table. The goal ...
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Conservation of Momentum vs. Energy [closed]

If a mass $m$ travelling at velocity $v$ collides ideally with a massless shaft mounted on a massless bearing with an identical mass on the other end of the shaft: Conservation of momentum requires ...
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Which way does a cylinder on a slab roll after the slab is removed?

An article by Tokieda[1] begins: I lay a cylinder on a sheet of paper. I pull the sheet from under the cylinder, briskly or gently. When the sheet is pulled out, which way will the cylinder roll?...