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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How to understand zero elements in CG coefficient table?
I understand the standard theory of angular momentum and the reps. of SU(2). I found there are some zero elements in CG coefficient table. I can derive them by using the recurrence relations between ...
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How much should the disk/wheel spin for gyroscopic-precession to take place? Is there a threshold?
Suppose we have a spinning gyroscope whose disk is of mass $m$, spinning at angular velocity $\omega$, and attached to a rod of length $r$.
The precession of the gyroscope around the $z$-axis will be ...
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How? Calculate torque from twisting a gyroscope
Please be patient, I'm not a physics guy.
I'm building a robot that flips itself over using a gyroscope.
The gyroscope spins horizontaly at first, then a servo changes the gyro's rotating axis, ...
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Angular velocity - Gyroscope
I am currently researching the gyroscope on my own and i came across the concept of angular velocity.
The torque ($T$) on a gyroscope is caused by $R\cdot F$, where the force i consider it to be ...
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Rotation of a Spinor
I have a question about an intuitive approach to spinors as certain mathematical
objects which have properties that make them similar to vectors but on the
other hand properties which differ them from ...
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Why should a motorcyclist hit the brakes to make his motorcycle tilt in midair?
Ok, so here's the setup of the problem. A motorcyclist tries to jump over some cars by using a ramp. Right after he leaves the take-off ramp, he notes that his motorcycle is angled slightly upward and ...
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The angular momentum of zero mass limit of Kerr metric
The Kerr metric in Boyer coordinates is
$$
ds^2 = -\left(1 - \frac{2GMr}{r^2+a^2\cos^2(\theta)}\right) dt^2 +
\left(\frac{r^2+a^2\cos^2(\theta)}{r^2-2GMr+a^2}\right) dr^2 +
\left(r^2+a^2\...
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Rod hits rod - angular and linear momentum
I've been analyzing "ball hits a rod in space" type collisions, where speeding ball transfers part of its kinetic energy during elastic collision to the motionless rod, making it gain linear ...
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Dropping a spinning top into a black hole?
Is there a formal treatment for what happens when one drops a spinning top into a black hole? More precisely, if one has a spinning top, of mass $m$ and angular momentum $j$, and lets it drop into a ...
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Generalized electromagnetic angular momentum
Linear momentum has a generalization when electromagnetic vector potential is present:
$$m {\bf v} + q \bf{A} $$
Likewise for energy we have
$$\frac{mv^2} {2} + q \phi $$
I wonder if there is an ...
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Is there angular momentum conservation in models like the Ising model?
In Quantum Mechanics conservation laws are fundamental, I was thinking about spin altering models of interaction such as the Ising Model and realized that it isn't at all clear how angular momentum ...
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Total spin on a two-particle system
How can I know the total spin of a given state quickly? I first encountered this problem when proving the Clebsch-Gordan series.
Consider a two-particle system (to make it easier, let's say identical ...
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What forces are responsible for the circular motion of the center of mass of a gyroscope-like setup in precession?
Suppose we have a disk (of mass $M$) connected to a rod (of mass $m$) attached to a fixed pivot. (Note that initially I thought of the rod hanging off a rope, but I realized it would be better to ...
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Complex conjugate of angular momentum operator
I am trying to derive relation 5.7.5 in " The Quantum Theory Of Fields " by Steven Weinberg :
$$-J^{(j)^*}_{\sigma,\sigma'} = (-1)^{\sigma-\sigma'} J^{(j)}_{-\sigma,-\sigma'}\tag{5.7.5}$$
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How many different axes of rotation can coexist?
I have questions about rotation.
There is a sphere in space. I can apply a force to cause the sphere to rotate around a central axis. An infinite number of possible central axes can be drawn.
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How to write a hamiltonian in minimal basis as a spherical tensor
I am reading this paper where the authors write the atom-blocks of the hamiltonian in a minimal basis set and use some regression technique to fit the hamiltonian to data. This question is about how ...
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How does commutation between the hamiltonian and angular momentum operator (squared) imply conservation of Angular momentum?
So we are looking at central potentials in QM;
The lecturer poses the question, when is $\textbf{L}$ conserved? He then considers the commutator of $\hat{H}$ and $\hat{L^2}$.
We have;
$$\hat{H}=-\...
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How much force is required to break precession?
Gravity, in this diagram, provides a downward force creating a torque that causes the wheel to precess around the chain. This is cool but counter intuitive, and I am wondering what force is needed to ...
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Dropped sign from Wigner-Eckart Theorem for matrix elements of $x$ in hydrogen atom $n = 2$ shell
Consider the $n=2$ states of the hydrogen atom, which we label by $|n\,l\,m_l\rangle$. I want to calculate whether or not there should be a sign difference in these specific matrix elements of $x$:
$$\...
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Quick question regarding Larmor precession and bar magnets
So I was just reading a bit about magnetic dipole moments, Larmor precession, angular momentum etc., but there was one little thing that was bothering me. As far as I know, any angular momentum will ...
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Factor of 2 error in angular momentum / Coriolis force calculation
The problem
An object is dropped from a helicopter, which is at rest relative to the Earth rotating at $\Omega$ at height $h=500\text{ m}$ above the ground at the equator.
Without using the Coriolis ...
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Hyperfine structure
In Griffiths, the hyperfine structure is described as follows:
So the hyperfine structure is a result of a mechanism called spin-spin coupling, which is the interaction of the spin of the nucleus (...
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Lagrangian of a particle in a gravitational potential and conservation of angular momentum
I'm trying to prove via Noether's Theorem that the angular momentum of a massive particle in a gravitational field is conserved. The attempt follows:
OBS: I'm working in the euclidean space so I'll ...
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Does angular momentum of rotating body depend on its position?
This question might be silly. But angular momentum $\vec{L} = \vec{r} \times \vec{p}$. It always confuses me whether or not angular momentum depends on the origin because the position vector does ...
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How do we argue that there are only integer-spaced $m$ values for angular momentum?
I am following the usual development using ladder operators (in Ballentine Chapter 7) for the angular momentum spectrum (for the joint eigenbasis $|j,m \rangle$ of $J^2$ and $J_z$) and I am satisfied ...
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Simple example for "dynamic mass moment"?
I encountered the concept of "dynamic mass moment" also called "the boost angular momentum" and I am looking for a simple example.
I take as definition (p.18) $$ \vec{N} = (ct)\vec{...
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Lorentz force and conserved quantities
Imagine a permanent magnet at rest in empty space. A proton initially travels along a straight path with a velocity $\vec{v}$ and enters the field of the magnet with $\vec{v}$ perpendicular to $\vec{B}...
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Angular velocity doubt [closed]
Here is a rod of mass $M$ and of length $l$ resting on a smooth frictionless horizontal table. Now a small bullet of mass $m$ comes and collides inelastically with this rod and here I wanted to find ...
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Gyrating proton near magnetic pole of the Earth
Imagine a proton from space which approaches the magnetic pole in the Northern hemisphere of the Earth. The proton spirals around the magnetic field lines. The $\vec{B}$-field is stronger near the ...
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Does a rotating body resist acceleration in a direction that is perpendicular to the direction of the rotation of the body?
I would like to know if a rotating body resists acceleration in a direction that is perpendicular to the direction of the rotation of the body.
Say for example there is a bicycle wheel with a tire on ...
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How come I can spin an object attached to a string as centripetal motion without slanting?
Using a free body diagram, on an object spinning in the air while attached to a string, there would be the force of gravity on the object and the tension force from the string. In centripetal motion, ...
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Probability and the Magnetic Quantum Number
I am currently self-studying quantum mechanics, and I'm working problems on angular momentum. The problem I'm currently working on asks one to consider a particle subjected to a spherically symmetric ...
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Why is the angular momentum needed in theories where the linear momentum is locally conserved?
It is a well-known result that angular momentum conservation is related to the invariance of the Lagrangian respect spatial rotations, here a demonstration of how infinitesimal rotations do not alter ...
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Decay of a $\rho$ particle
Would someone please explain the following found on P. 125 of these notes?
On the other hand, two $π^0$’s cannot be in an $l = 1$ state. The reason for this is that pions are bosons and so the ...
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Why is the decay of a neutral $\rho$ meson into two neutral pions forbidden?
Why is the decay of a neutral $\rho$ meson into two neutral pions forbidden? (Other modes of decay are possible though.)
Is it something with conservation of isospin symmetry or something else? Please ...
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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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Angular distribution of two-body decay with orbital angular momentum
I'm currently studying the two-body decay where a particle (Be) with spin-1 decays into a pion (spin-0) and spin-1 particle $X$. The system is prepared so that the Be is polarized with a spin ...
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What causes the rotating ball on a string to rotate upwards?
See image below:
Say I have a mass 'm' on a string or a very thin rod being twirled around on some pivot point by a motorised axle. Originally its twirling around in equilibrium in a horizontal plane ...
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How does Kepler's Second Law show that a planet further from the sun will move slower?
This is probably a very stupid question. We are told that due to Kepler's Second Law, which according to this very straightforward explanation:
"Kepler's second law of planetary motion describes ...
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Hydrogen spectrum for transitions of $\ell$, $m_{\ell}$
In this question, there is a spectrum exhibiting transitions corresponding to the azimuthal quantum number $\ell$ of a system corresponding to a spinning $\rm{Cs_2}$ molecule.
Regarding hydrogen-like ...
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Explanation about the rotation spectrum from cold $\rm Cs_2$ molecules
In the book Mécanique quantique (Jean Dalibard), there is an example to illustrate the quantification of the $L^2$ squared angular momentum.
This example is extracted from A. Fioretti et al, Eur. Phys....
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Bohr hydrogen atom model and quantum mechanics on quantisation of angular momentum
Bohr's model says that angular momentum is quantised to integral multiples of reduced Planck's constant, $$L = nh/2\pi$$
but in quantum mechanics, angular momentum operator has non-integer eigenvalues,...
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Does rigid body rotation contradict Newton's first law?
Per Newton’s law, an object will move along a straight line with a constant speed if no force is acting upon it.
No portion of a rotating ball is moving in a straight line (except those on the axis ...
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Angular Momentum of a rigid, extended object: When we see a rotating object, is the state of rotation totally relative?
Angular momentum of an object is a physical quantity that depends on the chosen point about which to calculate the angular momentum.
It is often said that an object that has been thrown up in the air ...
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Confused about the direction of the Magnus effect force
From what I've read, the cause for the force acting as the result of the Magnus effect is the formation of a bended wake behind the moving sphere.
Take a look at that picture:
(source: jschetz at www....
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What does the notation $\frac{1}{2} \otimes \frac{1}{2} = 1 \oplus 0$ mean exactly?
My question is very similar to the question here, however I want to ask about some specifics. I am having trouble keeping track of exactly how we are "tensor-producting" or "direct-...
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Find the angular momentum of a pulley system after the mass $M$ has descended through a height $h$ [closed]
Two masses $M$ and $m$ are connected by a light spring going over a pulley of radius $r$. The pulley is free to rotate about its axis which is kept horizontal. The moment of inertia of the pulley ...
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Nuclear state notation $J^\pi$
I have learned from nuclear physics literature that a nuclear state can be denoted as $J^\pi$, where $J$ is the spin and $\pi$ is the parity, such as $0^+, 1^+$. But when I read some papers on nuclear ...
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Vorticity and angular momentum
In Taylor-Couette flow, the interior fluid becomes fully turbulent if the relative angular velocity of the cylinders is high enough. The turbulent fluid has a vorticity distribution, and each of the (...
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Dependence of the Eigenvalues of the Angular Momentum Operator on the Mass, Energy and the Reference point wrt which the Angular Momentum is Measured
In classical mechanics, the angular momentum $\textbf{L}$ of a particle is
$$
\mathbf{L = r\times p}
$$
where the $\mathbf r$ is the position of the particle measured from some origin. That means that ...
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