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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108
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10answers
13k views

Is Angular Momentum truly fundamental?

This may seem like a slightly trite question, but it is one that has long intrigued me. Since I formally learned classical (Newtonian) mechanics, it has often struck me that angular momentum (and ...
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If dark matter only interacts with gravity, why doesn't it all clump together in a single point?

I'm a complete layperson. As I understand, dark matter theoretically only interacts with the gravitational force, and doesn't interact with the other three fundamental forces: weak nuclear force, ...
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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 ...
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Why do fans spin backwards slightly after they (should) stop?

Today, I've decided to observe my PC fan as I shut the computer down. The fan slowly lost angular momentum over time. What I've found really interesting is the fact that the momentum vector change did ...
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Why does everything spin?

The origin of spin is some what a puzzle to me, everything spin from galaxies to planets to weather to electrons. Where has all the angular momentum come from? Why is it so natural? I was also ...
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Do solar systems typically spin in the same direction as their galaxy?

Is the net angular momentum vector of our solar system pointing in roughly the same direction as the Milky Way galaxy's net angular momentum vector? If yes or no, is that common for most stars in the ...
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What if the universe is rotating as a whole?

Suppose in the milliseconds after the big bang the cosmic egg had aquired some large angular momentum. As it expanded, keeping the momentum constant (not external forces) the rate of rotation would ...
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Why the galaxies form 2D planes (or spiral-like) instead of 3D balls (or spherical-like)?

Question: As we know, (1) the macroscopic spatial dimension of our universe is 3 dimension, and (2) gravity attracts massive objects together and the gravitational force is isotropic without ...
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Why are our planets in the solar system all on the same disc/plane/layer? [duplicate]

I always see pictures of the solar system where our sun is in the middle and the planets surround the sun. All these planets move on orbits on the same layer. Why?
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Why don't galaxies orbit each other?

Planets orbit around stars, satellites orbit around planets, even stars orbit each other. So the question is: Why don't galaxies orbit each other in general, as it's rarely observed? Is it considered ...
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Why don't helicopters use reaction wheels to counter the main rotor?

As the main title says. I'm finding myself wondering about helicopters. The tail rotor is a vulnerable and key piece of equipment, especially on military helicopters. I know some helicopters instead ...
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Why aren't there spherical galaxies? [duplicate]

According to the Wikipedia page on Galaxy Types, there are four main kinds of galaxies: Spirals - as the name implies, these look like huge spinning spirals with curved "arms" branching out ...
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If the gravitational force were inversely proportional to distance (rather than distance squared), will celestial bodies fall into each other?

If gravity was inversely proportional to distance, will the dynamics of celestial bodies be much different from our world? Will celestial bodies fall into each other?
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How can the Earth keep spinning with a liquid core?

In regards to the 'conservation of angular momentum' being the explanation of why celestial objects spin... If you fill a ball or any other container with a liquid and try to spin it, you will not ...
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Apparent Violation of Newton's $3^{\text{rd}}$ Law and the Conservation of Momentum (and Angular Momentum) For a Pair of Charged Particles

Consider a system of the two identical positive point charges situated in free space (isolated from the influence of any other external fields) as shown in the attached diagram. Particle $1$ is at $(a,...
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How does a spinning object "know" that it is spinning?

I am constructing a thought experiment about a spinning object that is floating in intergalactic space. I assume that this object is about the size of a planet so that it will have enough gravity so ...
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Why don't we feel the subtle speed change of Earth's elliptical orbit?

Earth's orbit is a slight ellipse, so to conserve momentum its speed increases when it is closest to the Sun. If the speed changes there is an acceleration. If there is an acceleration there is a ...
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Adding 3 electron spins

I've learned how to add two 1/2-spins, which you can do with C-G-coefficients. There are 4 states (one singlet, three triplet states). States are symmetric or antisymmetric and the quantum numbers ...
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Is spin really just "rest angular momentum"? [duplicate]

Spin is the intrinsic angular momentum of a particle. The particle itself is elementary and is not spinning on its axis, and has this momentum even at rest. The absolute magnitude of this momentum ...
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Where are the inaccuracies in the Bohr model of the atom?

The Bohr model of the atom is essentially that the nucleus is a ball and the electrons are balls orbiting the nucleus in a rigid orbit. This allowed for chemists to find a model of chemical bonding ...
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Does spin really have no classical analogue?

It is often stated that the property of spin is purely quantum mechanical and that there is no classical analog. To my mind, I would assume that this means that the classical $\hbar\rightarrow 0$ ...
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Why is there this relationship between quaternions and Pauli matrices?

I've just started studying quantum mechanics, and I've come across this correlation between Pauli matrices ($\sigma_i$) and quaternions which I can't grasp: namely, that $i\sigma_1$, $i\sigma_2$ and $...
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How to define orbital angular momentum in other than three dimensions?

In classical mechanics with 3 space dimensions the orbital angular momentum is defined as $$\mathbf{L} = \mathbf{r} \times \mathbf{p}.$$ In relativistic mechanics we have the 4-vectors $x^{\mu}$ and ...
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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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How Fundamental is Spin-Orbit Coupling to Topological Insulators?

I'm well aware this is a very active area of research so the best answer one can give to this question may be incomplete. Topological states in condensed matter are well-known, even if not always ...
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What causes a rotating object to rotate forever without external force—inertia, or something else?

Someone told me that it is not inertia, but I think it is inertia, because it will rotate forever. In my understanding, inertia is the constant motion of an object without external force. Am I wrong?
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Do black holes have a moment of inertia?

My question is in the title: Do black holes have a moment of inertia? I would say that it is: $$I ~\propto~ M R_S^2,$$ where $R_S$ is the Schwarzschild radius, but I cannot find anything in the ...
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Physical meaning of the angular momentum

Still reading Classical Mechanics by Goldstein, I'm struggling on a very basic notion: angular momentum. I physically understand it as the momentum of an object rotating around something given a ...
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Classical proof of the gyromagnetic ratio $g=2$

I was reading Representing Electrons: A Biographical Approach to Theoretical Entities, by Theodore Arabatzis. At a certain point, where he is explaining the history of the magnetic moment of the ...
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Is the angular momentum of the ceiling fan quantized?

According to quantum mechanics, any quantum angular momentum is quantized in units of $\hbar$. Does it mean that the angular momentum of the ceiling fan (due to its rotation) is quantized? If yes, ...
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Why didn't the debris collapse back into the Earth at the time of Moon's formation?

The most accurate theory for the formation of our moon is the Giant impact hypothesis, which says that a Mars sized body collided with our early Earth and after this collision all the debris got ...
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Why Silver atoms were used in Stern-Gerlach experiment?

For the Stern-Gerlach experiment done in 1922: Why were silver atoms used? Silver atoms contain many electrons in different shells (with different angular momemtum quantum numbers. Why are those not ...
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What is the prevailing opinion in scientific community about Hans C. Ohanian's description of spin?

In the paper What is spin?, Am. J. Phys. 54 (1986) 500, by Hans C. Ohanian, spin is described as a circulating flow of energy in the wave-field of a particle. Is this the generally agreed upon ...
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What do the Pauli matrices mean?

All the introductions I've found to Pauli matrices so far simply state them and then start using them. Accompanying descriptions of their meaning seem frustratingly incomplete; I, at least, can't ...
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Rotation angle of a giant water lily when a child crawls on its rim

Below is a picture of Giant Water Lily. Scientific Name: Victoria Amazonica. Leaves of some of these could be as big as 3 m diameter and carry a weight of 45kg spread evenly and can support a child. ...
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Due to relativity, does the surface of a pulsar have less area than the layer beneath it?

A pulsar or spinning neutron star can reach relativistic angular velocities. Special relativity asserts that objects traveling near the speed of light contract in length. Therefore, it seems ...
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Why doesn't the uncertainty principle contradict the existence of definite-angular momentum states?

We know that for a position variable $x$ and momentum $p$, the uncertainties of the two quantities are bounded by $$\Delta x \Delta p \gtrsim \hbar$$ Now, this is usually first explained with $x$ ...
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Origin of Ladder Operator methods

Ladder operators are found in various contexts (such as calculating the spectra of the harmonic oscillator and angular momentum) in almost all introductory Quantum Mechanics textbooks. And every book ...
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Half-integer eigenvalues of orbital angular momentum

Why do we exclude half-integer values of the orbital angular momentum? It's clear for me that an angular momentum operator can only have integer values or half-integer values. However, it's not clear ...
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Can a non-rotating ball have angular momentum?

Suppose a ball is going straight along a fixed line without rotating. Now you consider a point which is not along the trajectory of the ball. If I want to consider the angular momentum about that ...
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Quantization of a particle on a spherical surface

Suppose we have a particle of mass $m$ confined to the surface of a sphere of radius $R$. The classical Lagrangian of the system is $$L = \frac{1}{2}mR^2 \dot{\theta}^2 + \frac{1}{2}m R^2 \sin^2 \...
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Why does a Yo-Yo sleep, and then awaken?

What are the mathematics / mechanics principles behind a sleeping Yo-Yo, and in particular, what changes with a wrist-snap flick that causes it to "awaken" and return to your hand?     &...
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Elementary argument for conservation laws from symmetries *without* using the Lagrangian formalism

It is well known from Noether's Theorem how from continuous symmetries in the Lagrangian one gets a conserved charge which corresponds to linear momentum, angular momentum for translational and ...
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Integral of the product of three spherical harmonics

Does anyone know how to derive the following identity for the integral of the product of three spherical harmonics?: \begin{align}\int_0^{2\pi}\int_0^\pi Y_{l_1}^{m_1}(\theta,\phi)Y_{l_2}^{m_2}(\...
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2answers
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How does one experimentally determine chirality, helicity, spin and angular momentum of a fundamental particle?

If I've got an instance of a fundamental particle, how can I separate out the measurements of these four quantities? (I think) I understand the theory behind them, and why the particles in the ...
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Why does a spinning top get back upright when knocked?

I have observed that, a spinning top, when toppled by knocking it with finger, becomes almost upright again (with negligible precessional motion), instead of undergoing precession while being heavily ...
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Why is angular momentum a vector?

I have read a bit about this and am still wondering why we actually care about the direction of angular momentum, because that the vector representing angular momentum is perpendicular to the momentum ...
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How should we think about Spherical Harmonics?

Studying Quantum Mechanics I only thought about Spherical Harmonics $Y_{l,m}(\theta , \phi)$: $$Y_{l,m}(\theta , \phi)=N_{l,m}P_{l,m}(\theta)e^{im\phi}$$ as the simultaneous eigenfunctions of $L_z$ ...
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Can the direction of angular momentum and angular velocity differ?

While studying rotational mechanics, I came across a section where it mentioned that angular momentum may not necessarily be parallel to angular velocity. My thoughts were as follows: Angular ...
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1answer
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Explaining The Unbelievable Pendulum Catch

What would be a theoretical explanation of an "ideal" 14:1 mass ratio in this experiment, also demonstrated in this video? The experiment ties one nut to one end of the string and 14 nuts to the ...

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