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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Time dilation and angular momentum

Is angular momentum (let's say the horizontal rotation of a massive disc in the air) sensitive to time dilation or invariant to it? Will its angular momentum, or speed of rotation, increase when ...
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How to calculate the rotation speed of spinning top, which will be enough that it is not falling down or stays within certain angle to vertical axis [duplicate]

I found many articles with the calculation of the precession rotation speed of the spinning top like this or this. They give this equation for Precession rotation speed $\Omega$: $$\Omega=\frac{mgr}{I\...
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Understanding conservation of angular momentum in relation with rotating objects

Conservation of angular momentum says that the angular momentum of a closed system will not change if there is no external torque applied to the system. For example, let's take the example of a ...
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Angular momentum in a rotating frame [closed]

For a rigid body of mass $M$ rotating with an angular velocity $\vec{\omega}$ , the angular momentum is given by- $$\vec{L}_{body/O}=I_{cm} \vec{\omega} + M(\vec{r}\times \vec{v}_{cm/O})$$ where $I_{...
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Physical meaning of the CG coefficient $\langle j_1 m_1 j_2 m_2 |00 \rangle $

This particular CG coefficient has the value $$ \langle j_1 m_1 j_2 m_2 |00 \rangle = \delta_{j_1 j_2 }\delta_{m_1,-m_2} \frac{(-1)^{j_1 - m_1 }}{\sqrt{2j_1 + 1 }}. $$ The interesting point is that ...
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Rotational speed using conservation of angular momentum

I know that angular momentum is conserved, but I don't know how to calculate the new speed of an object after it shrinks. Say you have a spinning object, then it shrinks, then how do you calculate the ...
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Angular velocity of stationary observer

I am studying Kerr metric in Boyer Lindquist coordinates and having trouble in understanding the components of angular velocity of stationary observer with constant r and $\theta$ motion w.r.t ...
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Angular momentum, black holes and up-tunneling events in the vacuum

To give some context on the matter, I found these interesting articles (https://arxiv.org/abs/2007.11428 & https://arxiv.org/abs/2003.04927) where the authors analyzed, among other things, the ...
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What do people mean when they say orbital and spin angular momentum operators act on different spaces?

I was looking for an explanation of why the orbital and spin angular momentum operators commute, and I found many sources saying they act on different vector spaces. I am confused about the use of ...
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Conservation of angular momentum when absorbing a single photon (Jaynes-Cummings model)

Consider a two-level atom of with energy levels $|g\rangle$ and $|e\rangle$, such that dipole transitions are allowed between these two levels. Let $l_{e}=l_{g}+1$ where $l_{e},l_{g}$ are the total ...
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Physical pendulum: axis of rotation

Why is the angular momentum always considered to be parallel to the angular velocity in physical pendulum problems, as if the axis of rotation were a principal axis always? I don't see the ...
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Properties of the Center of Mass

My students are currently going through the rigid rotor and hydrogen atom unit in their quantum physical chemistry course and I found myself at a loss on how to justify what seems a natural way to ...
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Question about upright rod with wheel attached to the bottom that's allowed to fall [closed]

Today, Prof. Rhett Allain posted a question and its solution on his TikTok. You can view it here if you are interested: Question: https://urlebird.com/video/which-stick-will-fall-over-faster-...
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Shape of rotating celestial body in general relativity

It is know from hydrostatic equilibrium and Newton mechanic that rotating celestial bodies have a shape of oblate spheroids and this is confirmed by observations of Sun, Earth, etc. But I wonder what ...
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Atomic Sub-shell question

Which orbital of sub-shells $s$, $p$, $d$ and $f$ have Magnetic Orbital Quantum Number $m_l=0$. Like in p sub-shell, which orbital from $p_x, p_y, p_z$ will have $m_l$ as Zero? Also, how to determine ...
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Understanding the meaning of the directions of $\vec\omega$ and $\vec{L}$

I'm struggling with some basic intuition regarding the angular velocity $\vec\omega$ and angular momentum $\vec{L}$ vectors, for any arbitrary motion. Specifically, I'm trying to figure out what the ...
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Calculating angular momentum using the formula $\vec{v} = \vec\omega \times \vec{r}$

I recently learned that $\vec{v} = \vec\omega \times \vec{r}$. $\vec\omega$ being the angular velocity vector of a particle, $\vec{r}$ being its position vector, and $\vec{v}$ being the linear ...
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Why is angular momentum defined so?

We know angular momentum is defined as $mvr$. In the context of Lagrangians and Noether's theorem, this definition pops up as the conserved quantity due to rotational symmetry of the system. Is there ...
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How can I calculate action of $\mathfrak{su}(3)$ or other simple algebra ladder operators on "states" from the algebra commutators?

I wanted a way to "derive" Gell-Mann matrices for $\mathfrak{su}(3)$ and generalise this to other semi-simple algebras $\mathfrak{g}$. The way I wanted to approach this is start from the ...
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Very interesting case, where energy is not conserved?

This is not a homework problem. I have a bigger, more conceptual doubt behind it. Applying linear momentum conservation: We get velocity of disc is v (towards right) Now, friction will also apply a ...
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How to calculate torque at the end of a lever arm?

I am messing around with creating small computer simulations to self study. Last time I did physics was in high school. Consider the setup below. An electric motor (black) is spinning a metal disk (...
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Quantum angular momentum of a particle in an homogeneous magnetic field

In non-relativistic quantum mechanics, the canonical momentum of a particle is defined as $$\tag{1} p_i = - i \hbar \: \partial_i. $$ When there's an external magnetic field (suppose for simplicity ...
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How do I know when in rotational dynamics whether or not mechanical energy, translational momentum, and angular momentum are conserved?

In trying to solve this particular problem: I have become confused about the conservation of energy and momentum. Specifically for Case A would angular momentum be conserved because there is net ...
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Getting generalized forces and moments from virtual power method

I have a confusion when applying the Lagrangian method to calculate the equations of motion of a rigid body. I don't understand at what (physical) point the generalized moments should be calculated, ...
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In equation of torque and angular momentum what is the position vector exactly

In terms of vectors: $$ L = r \times p $$ and torque: $$ T = r \times F $$ In both these cases what exactly does the $r$ vector represent? Is it vector from origin of axis or center of mass? How would ...
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How to determine when angular momentum is conserved and when torque is zero?

In physics problems, I struggle to incorporate the ideas of angular conservation and torque. For example, how do I know when torque is zero in a problem like this: can I even apply angular momentum ...
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Proving Kepler's second law of planetary motion using conservation of angular momentum: What about gravity from other planets?

I'm reading An Introduction to Mechanics by Kleppner and Kolenkow. In the chapter on angular momentum, a (beautiful!) example is given by discussing Kepler's second law of planetary motion. The law ...
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Rotational Motion of a rod attached to a hinge

I have been trying to understand the concept behind this for days now and am seemingly puzzled by a variety of methods. The Problem : A rod of mass $M$ and length $L$ is attached to a hinge at one ...
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Azimuthal coordinate operator: Hermition or not? Self-adjoint or not?

I am told that the azimuthal coordinate operator $\hat{\phi}$ is not self-adjoint. I am told this by people who I am sure know much more about this stuff than I do. To my unsophisticated mind, "...
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Maximum value of angular momentum component in quantum mechanics [closed]

Since $[L^2, L_z]=0$, we can say that they share a common eigenbasis, call it $f$, and $L^2f=\lambda f$, $L_z f=\mu f$ The ladder operators for the $z$ component of angular momentum are $$L_\pm=L_x\pm ...
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Angular momentum of the Moon (or any body orbiting another orbiting body)

Let the Moon have angular velocity $\omega$ around the Earth. The Earth itself revolves with velocity $V$ around the Sun. The radius vectors are $r_i$ from Sun to a point on the Moon, $r_i'$ from ...
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Why are missiles rotating in space?

Watching the Starship launch today I noticed it's actually doing some full rotations. Why isn't it controlled? and why does it happen? I have read that it's the same for military missiles too
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Why angular momentum keeps the giroscope standing in "impossible" orientations?

I am trying to understand how gyroscopes can maintain rotation in different "impossible" orientations when spinning. I saw that the behaviour in zero-g is slightly different. On Earth, the ...
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Can a force acting on a single point of a resting, freely movable body cause it to spin without causing translational movement?

In his answer to another post user Albertus Magnus describes the situation of a bullet hitting a rod in free space on its tip in a "purely tangential" way causing the rod to spin in a purely ...
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Usage in the Clebsch-Gordan (CG) coefficients' recursive relation

In Sakurai's Modern Quantum Mechanics, its 3.8.39 is \begin{aligned}\sqrt{(j\mp m)(j\pm m+1)}\langle j_1j_2;m_1m_2|j_1j_2;j,m\pm1 \rangle \\=\sqrt{(j_1\mp m_1+1)(j_1\pm m_1)}\langle j_1j_2;m_1\mp1,...
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How we can deduce from symmetry of $ θ^{μν} $ that total energy-momentum due to field spin is zero?

I am self-studying the book “James H. Luscombe, Core Principles of Special and General Relativity”. In “CHAPTER 9 : Energy-momentum of fields” of the book, it starts by introducing Noether’s theorem ...
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Why are the angular momentum raising and lowering operator coefficients real?

I had a homework problem where I had to find the coefficients for the angular momentum raising and lowering operators. I know the answer is supposed to be $\sqrt{l(l+1)-m(m\pm1)}$. I have figured out ...
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How a tire send a car flying? [closed]

https://abc7news.com/118-freeway-crash-caught-on-video-los-angeles/13027476/ The incident happened on Thursday, March 23, in Chatsworth, Los Angeles. In which a vehicle went flying into the air after ...
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Bike leaning angle computed in stationary frame

In the problem of computing leaning angle ($\theta$) of a turning bike, the traditional approach is to move to the accelerating reference frame and compute the balanced torques with respect to the ...
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Is it possible that black holes spin in discreet spin quanta?

Roy Kerr recently wrote a paper critical of the Penrose singularity theorem. One interpretation of his paper is that the singularity problem might be an artifact of the Schwarzchild metric and that a ...
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Angular Momentum Operators generates rotation transformations - Stern-Gerlach device explanation?

In a lecture we were taught how the angular momentum operator $\vec{L}$ acts as the generator of rotations in quantum mechanics, which are defined using the following equation: $R_u(\alpha)=\hat{1}-(i/...
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Wigner-Eckart theorem for exponentiated vector operator?

Consider the Hamiltonian of two spinning particles in a magnetic field with $$H = \vec{B}\cdot\vec{\mu}$$ where $$\vec{\mu} = \alpha \vec{L}_1+\beta\vec{L}_2$$ Now I wish to compute its partition ...
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$6j$-symbol example in Quantum Mechanics

Can anyone provide me a simple context in quantum mechanics where the $6j$-symbol plays a role? I wish to understand the physical meaning of the $6j$-symbol so such a context will be helpful.
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Momentum conservation laws and explanation

I understand that momentum can be conserved along a certain axis while not along another. If there are forces that are affecting our system in the axis we are interested in that means the momentum ...
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Wigner-Eckart theorem: Completeness relation

Consider the Wigner-Eckart theorem given by $$\langle \alpha' j m'|A^q|\alpha j m\rangle = \frac{\langle \alpha' j m'|\mathbf{J}\cdot\mathbf{A}|\alpha j m\rangle}{j(j+1)}\langle j m'| J^q|j, m\rangle$$...
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Which Potentials lead to Kepler's second Law?

Which type of potentials lead to Kepler's second law "same area in same time"? $$dA=\frac{1}{2} \vec{r} \times \vec{dr}.$$ $$\frac{dA}{dt}=c=\vec{r} \times \frac{\vec{dr}}{dt}=\vec{r} \...
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What creates the vertical component of the angular momentum of the whole spinning wheel and axle?

I have been watching this Veritasium YouTube about Gyroscope Precession and I understand why the spinning wheel will rotate about the string. But now that the whole spinning wheel and axle is rotating ...
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Addition of angular momenta with relative coefficients

Suppose I wish to add angular momenta with some relative coefficients $$\vec{J} = \alpha \vec{J}_1 + \beta \vec{J}_2$$ Can any one explain how this would be done? And how different would it be from ...
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Projector onto Adjoint and Singlet Representations for $SU(N)$

For $SU(2)$, we can contract two spin-1/2 indices and they break apart into two irreducible representation as (math notation) - $$ 2\otimes2 = 3\oplus 1 $$ that is the triplet and the singlet sector. ...
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Angular momentum completeness relation

Can anyone tell me if the angular momentum completeness relation is given by $$ \sum_{l=0}^{\infty} \sum_{m=-l}^{l} (2l + 1) |l,m\rangle\langle l,m| = I $$ or $$ \sum_{l=0}^{\infty} \sum_{m=-l}^{l} |l,...
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