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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Notation - angular momentum for composite systems

In the discussion for the addition of angular momentum for composite systems, my lecturer uses the following notation in his notes when referring to a composite system of two spin-half particles: $ ...
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Conservation of Angular Momentum w.r.t a Reference point

When angular momentum is conserved, does it mean that it does not matter what the reference point is at? Say for example with this image below, the observer stands at two possible points P1 and P2. ...
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What is this angular momentum coupling notation? $\langle \ell 2 m_\ell 0|\ell 2\ell' m'_\ell\rangle \langle \ell 2 0 0|\ell 2\ell' 0\rangle$

I'm reading this unsigned powerpoint presentation of the Nilsson model in nuclear structure physics. On p. 15, they have this: $$\langle \ell'm'_\ell|Y_{20}|\ell m_\ell\rangle = i^{\ell-\ell'}\sqrt{\...
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Angular velocity of rotating rod

Consider the following system: Newton's second law for rotational motion: \begin{equation}\tau=I\alpha \Leftrightarrow rF=\frac{1}{3}mr^{2}\alpha \Leftrightarrow \frac{d\omega}{dt}=\frac{3F}{mr}\end{...
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Representations of the rotation group

(I have already done a similar question, but I did not express myself very well and the question was a bit confusing, so let me try again. If you find the question repetitive, I apologize and you can ...
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Why does zero $x$ angular momentum imply nonzero $z$ angular momentum?

Assume we have a state $\psi =|n, L =1, L_x =0\rangle$. If we compute it's reprentation in $L_z$ basis we get: $$\psi = \frac{1}{\sqrt{2}}|n, L =1, L_z =1\rangle - \frac{1}{\sqrt{2}}|n, L =1, L_z =-1\...
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Would conservation of angular momentum make it difficult to fall sideways in an O'Neill space colony?

It's always bothered me that the O'Neill space wheel puts forth centrifugal force as a suitable replacement for gravity. However, it seems the effects of conservation of angular momentum would induce ...
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Why are the vectors canceled out in this scenario for angular momentum of a particle?

I have a study guide for our next test, and I'm trying to understand the professors answer but I don't understand why i^ * i^ = 0? Here is his work, Why do we know that the P Vector is on direction ...
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There's only time, no space in Quantum Mechanics

In this lecture (44:23) Nathan Seiberg: Topics in 2+1 Dimensional Quantum Field Theories 2. Nathan Seiberg says there's no space in QM and therefore fermions have spin 0. This sounds pretty revolting ...
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$\mathrm{SU}(2)$ as a representation of the rotation group

I have read in a book that the group $\mathrm{SU}(2)$ is one of the irreducible representations of the rotation group. The book begin saying that the rotation group has 3 generators $J_{1}, J_{2}$ and ...
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Rotationally invariant metrics and conservation of angular momentum

This was prompted by an exam question, though the questions are more general: A 2D Riemannian space has the metric: $ds^2=dr^2 + \gamma^2 r^4 d\phi^2$ State what conserved quantity ...
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Rotation of a Point Particle

I wonder if there is a meaning of rotation for a point particle. Does a point particle have angular momentum and does he reply to torque?
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What is the physics behind a pirouette?

Around last week, I watched a ballet production at the Melbourne Arts Centre, and boy was I amazed! These people dressed up in costumes were spinning on their toes in all kinds of ways, and I was ...
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Alternative classical explanation of the Stern-Gerlach Experiment?

Many questions have been asked on this site about the Stern-Gerlach experiment, but as far as I can tell this one hasn't. Does the following classical explanation of the SG experiment work? Model ...
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Angular momentum conservation during collision

If I have a disk which is pure rolling and it strikes with a ladder, so can I conserve angular momentum about point O? I think I can because normal reaction passes through O, so torque due to it will ...
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What is particle spin in terms of waves? [duplicate]

If particles are waves, then what really is spin?
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If angular momentum of an electron in $s$-orbital is zero, then is it true that the electron doesn't move?

If the electron does move, then what is the factor that leads angular momentum of the electron in s-orbital to be zero?
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Precise value of spin in Nms?

What is the exact value of the spin of a particle with a 'spin' of 'one'? In units of Nms (Newton-meter-second)? And does a boson really have a spin of exactly one, or has that been 'normalized'? ...
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Questions about finding “top rung” and “bottom rung” of angular momentum operator (Proof in Griffiths)

The problem is like this: Let $$L_x = yp_z - zp_y, L_y = zp_x - xp_z, L_z = xp_y- yp_x, \\ L^2 = {L_x}^2 + {L_y}^2 + {L_z}^2 \\ L_\pm \equiv L_x \pm iL_y $$ We wish to find a "top rung" $f_t$ and ...
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Rising/lowering operators and trigonometric functions

I've just started learning about angular momentum and spin theory, and when I came across the definitions of the rising and lowering operators, I noticed the inverse form looks suspiciously like the ...
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How do inspiraling black holes get closer?

In Newtonian mechanics, binaries are stable. We here on earth are very glad that it will not emit its angular momentum and spiral into the sun. What is different about the black holes and neutron ...
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Wigner-Eckart theorem and vectors

Let's consider a system in state $^3$D$_1$: $$\vec{L}^2=L(L+1)=6 $$ $$\vec{S}^2=S(S+1)=2$$ $$\vec{J}^2=J(J+1)=2$$ According to Wigner-Eckart theorem, if this is an irreducible representation, all ...
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Understanding the notion of lose or win of angular momentum in accretion disk

Here is below a slide of one of my lecture in planetology : I understand well the fact that ring A will be slow down by friction with ring B since ring B is rotating slower and the inverse process (...
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Question about Electric Dipole Transition Selection Rules [duplicate]

I learned that the selection rules for electric dipole transition in a hydrogen-like atom is \begin{align} \delta l & = \pm1 \\ \delta j & =0,\pm1 \\ \delta m_j & =0,\pm1 \end{align} I ...
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$z$-polarized laser pulse and conserved $L_z$

I am currently reading a book "Time-Dependent Density Functional Theory: Concepts and Applications". This book says as follows: In its ground state, the valence electrons of $\rm Na_9^+$ form a ...
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Aufbau principle and quantum number $n$ (Bohr) [duplicate]

When we have to check the energy of electron we look for $n+\ell$ as in filling of electrons A/t aufbau? Or is just simply higher then value of $n$ then more the energy of electron? Because when we ...
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Orbital angular momentum for single particle in particle physics

I am taking an introductory course in particle physics and am quite confused about conservation of angular momentum at a vertex. This trouble arose specifically when considering the decay $\pi^0 \...
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What actually is the vector of angular momentum?

If an object spins around a central point, it gets angular momentum which is a vector with an orientation dependent on whether its clockwise rotation or anticlockwise, i get that. But what the vector ...
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Why does the parallel axis theorem apply in this case?

Next, the wheel is flipped over, so the angular momentum of the wheel is now negative. Obviously, the person must start rotating counterclockwise to conserve angular momentum. Since the person is ...
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Is the parallel axis theorem valid for non-rigid bodies?

For some context, consider an idealized situation with a person, rigidly attached to the shaft of a bicycle wheel that can spin. sitting on a chair that can rotate. All bearings are frictionless. ...
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Quantum mechanics angular momentum spherical tensor components

In Sakurai Quantum Mechanics, problem 3.25b we imagine $J_z^2$ as the component of a tensor with components $T_{ij} = J_iJ_j$. $J_z^2 = \frac{1}{3}\pmb{J}^2 + (J_z^2 - \frac{1}{3}\pmb{J}^2) $ The ...
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Reverse Clesbch Gordan coefficients

I'm quite unsatisfied with this answer, so I'm hoping to get an adequate one. I'm trying to understand how to compute the reverse CB coefficents. I'll provide the simplest example. If I have a $l =...
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Can a tilted wheel roll straight?

The common explanation of why a wheel that is falling to one side will turn towards that side to balance itself is gyroscopic precession, i.e. the torque produced by the falling of the wheel plus the ...
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Why does gravitational pull increase when black holes spin?

I was reading "the science behind interstellar", and found that Kip Thorne purposefully used a SMBH in his simulation which had its maximum attainable spin around its own axis. He argued that this was ...
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Why can an inner product of an eigenvector also be used as an eigenvector?

In quote box below, there is an inner product of an angular momentum eigenvector. Why can you use this inner product as a new eigenvector for the next part of the work? And why do they "of course" ...
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Why does the Earth not fall towards the Sun? [duplicate]

According to http://wtamu.edu/~cbaird/sq/mobile/2013/07/01/why-doesnt-the-earth-fall-down/ , the earth does not fall down because of the gravitational force of the sun. At the same time , earth's ...
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Can I feed enough spin up electrons to a black hole to affect its angular momentum?

I was reading classical spin vs quantum field spin. I know spin in quantum mechanics is just a quantum number. But what happens if I try to intentionally feed many electrons all in the same spin state ...
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Basis function of $\Gamma_2$ irrep of point group $T_d$?

From Properties of the Thirty-Two Point Groups (Koster, et. al.), the basis function of the $\Gamma_2$ irrep of the point group $T_d$ is $l_xl_yl_z$, where $l$ is the angular momentum operator. ...
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Impulse on a Gyroscope

I've been studying gyroscopes, and I understand why a fast spinning gyroscope doesn't fall. However, I don't understand why a slow spinning gyroscope does fall, or why a large enough impulse to a fast ...
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Linear and angular momentum

If I push on an object not through the center of mass, we say that the translational effect on the entire object is the same. In other words, we can turn that off-center force into a force through the ...
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Well-definedness of Holstein-Primakoff transformation

In many-body physics, Holstein-Primakoff transformation is defined as follows: \begin{align} S_i^+ &= \sqrt{2S}(1-a_i^\dagger a_i/2S)^{1/2}a_i, \\ S_i^- &=\sqrt{2S}(1-a_i^\dagger a_i/2S)^{1/2}...
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Does moment of inertia only work for special cases?

I was looking into the moment of inertia expression for angular momentum. The angular momentum of a group of particles can be expressed as a linear transformation of the angular velocity vector. This ...
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Rotational Motion (angular momentum)

I don't understand why the angular momentum remains constant even after the distance of the particle (from the origin) keeps on increasing. Maybe I'm not reading the graph the way it is but I don't ...
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Symmetry of the spin function and T0 and S states

$|T_0\rangle = \frac{1}{\sqrt{2}}(|\uparrow \downarrow\rangle + | \downarrow\uparrow\rangle )$ is a triplet state, whose spin function has to be symmetric. $|S \rangle = \frac{1}{\sqrt{2}}(|\...
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Matrix representation of spin-1/2 operators in Sakurai

Hello and thanks for reading. I'm an undergrad working through the first chapter of Sakurai's text and was going through the principles of the spin-1/2 system. The author demonstrates closure and ...
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Angular momentum w/ changing moment of inertia

A man of mass m1 is standing on a disk with radius R and mass M at a distance r The man starts walking around the disk with constant angular speed w1 and as a result the disk begins to rotate in the ...
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Orbital angular momentum quantum numbers - subtracted?

Reading Griffiths' Quantum Mechanics. We have the electronic confirmation of Carbon as $$(1s)^2 (2s)^2 (2p)^2$$ in the ground state. He says There are two electrons with orbital angular ...
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How does orbiting work exactly? [duplicate]

First of all I'm not a physicist or anything and I don't know much about physics, so I'm sorry if this doesn't make sense at all :) And if possible please try to explain it with words instead of ...
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Can conservation of angular momentum be derived from energy consideration? [closed]

About the context of this question: A dramatic illustration of back and forth conversion of kinetic energy and gravitational potential energy is when a celestial body has an highly eccentric orbit. ...
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Angular momentum of a body about a point rotating about its own axes

I want to calculate angular momentum of a sphere about point O. The sphere is rotating about its two axes with angular velocities $w_1$ and $w_2$. I know that angular momentum = $m\vec{r}\times\vec{v}...