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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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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What determines the direction of precession of a gyroscope?
I understand how torque mathematically causes a change to the direction of angular momentum, thus precessing the gyroscope.
However, the direction, either clockwise or counterclockwise, of this ...
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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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Total spin of two spin-$1/2$ particles
On my book I read:
$S_{z-tot}\chi_+(1)\chi_+(2)=[S_{1z}+S_{2z}]\chi_+(1)\chi_+(2)=[S_{1z}\chi_+(1)]\chi_+(2)+[S_2\chi_+(2)]\chi_+(1)=...$
Now, I have two questions:
What's $\chi_+(1)\chi_+(2)$ ? I ...
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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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Do mankind and manmade activities/constructions have any effect on the rotation of the Earth?
We walk or ride on our vehicles to our destinations daily. Does our movement have any effect on the rotation of the earth according to Newton's law? What will be the effect if we move all the peoples ...
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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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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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Why do all the planets of the solar system orbit in roughly the same 2D plane?
Most images you see of the solar system are 2D and all planets orbit in the same plane. In a 3D view, are really all planets orbiting in similar planes? Is there a reason for this? I'd expect that the ...
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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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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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How do the Planets and Sun get their initial spin?
How do the Planets and Sun get their initial rotation?
Why do Venus and Mercury rotate so slowly compared to other planets?
Why does Venus rotate in a different direction to Mercury, Earth and Mars?
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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 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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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 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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Lie bracket for Lie algebra of $SO(n,m)$
How does one show that the bracket of elements in the Lie algebra of $SO(n,m)$ is given by
$$[J_{ab},J_{cd}]
~=~ i(\eta_{ad} J_{bc} + \eta_{bc} J_{ad} - \eta_{ac} J_{bd} - \eta_{bd}J_{ac}),$$
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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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Why does spin have a discrete spectrum?
Why is it that unlike other quantum properties such as momentum and velocity, which usually are given through (probabilistic) continuous values, spin has a (probabilistic) discrete spectrum?
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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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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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How can a singularity in a black hole rotate if it's just a point?
I guess nobody really knows the true nature of black holes, however, based on everything I know about black holes, there is a "singularity" at their center, which has finite mass but is infinitely ...
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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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How does Newtonian mechanics explain why orbiting objects do not fall to the object they are orbiting?
The force of gravity is constantly being applied to an orbiting object. And therefore the object is constantly accelerating. Why doesn't gravity eventually "win" over the object's momentum, like a ...
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In a universe with four spatial dimensions would there be elementary particles with intrinsic isoclinic spin?
Elementary particles have an intrinsic property called spin which is different from classical spin as it does not involve actual rotation and the magnitude of spin cannot be changed but particles with ...
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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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Ice skater increase of energy
This may be a very basic question but I am not seeing how it works.
Consider the standard example of an ice skate rotating about his/her center of mass and pulling in his/her arms. The torque is zero ...
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Why is orbital angular momentum quantized according to $I= \hbar \sqrt{\ell(\ell+1)}$?
I simply have no idea how this result is found $$I=\hbar \sqrt{\ell(\ell+1)}.$$ The result seems to just be dumped in textbooks rather than explained. I can get the result that $I_z=\hbar m_j$. ...
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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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The Planck constant $\hbar$, the angular momentum, and the action
Is there anything interesting to say about the fact that the Planck constant $\hbar$, the angular momentum, and the action have the same units or is it a pure coincidence?
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Why doesn't the deuterium nucleus have spin $0$?
A deuterium nucleus is composed of a proton and a neutron. Both have spin $\tfrac12$ so I would expect the deuterium to have two possible spins: $1$ for the triplet and $0$ for the singlet. But ...
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Why does Venus spin in the opposite direction?
Given: Law of Conservation of Angular Momentum.
Reverse spinning with dense atmosphere (92 times > Earth & CO2 dominant sulphur based).
Surface same degree of aging all over.
Hypothetical large ...
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Why does a ballerina speed up when she pulls in her arms?
My friend thinks it's because she has less air resistance but I'm not sure.
Steve Marrero
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What causes matter to initially rotate/spin/orbit?
What causes matter to initially rotate/spin/orbit? All I can find is the statement that in space particles of dust/gas/matter contract into a spinning disk due to gravity (to form stars, solar systems,...
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Spin - where does it come from?
I study physics and am attending a course on quantum field theory. It is hard for me to draw connections from there to the old conventional theories.
In quantum field theory spin originates from the ...
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Why are the higher angular momentum states of a hydrogen atom closer to the nucleus?
I was looking at a plot of hydrogen radial wave functions $r^2|R_{nl}(r)|^2$, and I noticed that for fixed $n$, the states with smaller $l$ were "further out" from the nucleus. This conflicted with ...
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Effect of the tail of the cat in the falling cat problem
To explain why a falling cat can turn by 180 degree without external torque and without violation of the conservation of angular momentum, one usually models the cat as two cylinders as in
http://en....
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Why is the value of spin $\pm 1/2$?
I understand how spin is defined in analogy with orbital angular momentum. But why must electron spin have magnetic quantum numbers $m_s=\pm \frac{1}{2}$? Sure, it has to have two values in accordance ...
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Is all angular momentum quantized?
Angular momentum is definitely quantized in elementary particles and electrons in atoms. Molecules also have characteristic rotation spectra.
Is it true that all angular momentum is quantized, ...
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Need help understanding an equation of motion for a pendulum [closed]
I solved the Lagrangian of a simple pendulum (with help from online examples as this concept is new to me) and ended with the following:
$$\ddot{\theta}+\omega^2\theta=0$$
But in the example I was ...
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What are some useful ways to imagine the concept of spin as it relates to subatomic particles?
The answers in this question: What is spin as it relates to subatomic particles?
do not address some particular questions regarding the concept of spin:
How are some useful ways to imagine a ...
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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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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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What is the orbital angular momentum (OAM) of individual photons?
Update @ 21.01.2018
People investigate and talk about orbital angular momentum (OAM) of photons. For example, see this well-cited paper here and the PRL here. The latter starts with the remark
It ...
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How do you explain spinning tops to a nine year old?
Why don't spinning tops fall over? (The young scientist version)
My nine year old son asked me this very question when playing with his "Battle Strikers" set. Having studied Physics myself, I am very ...
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Physical interpretation of 2-forms dual to pseudovectors
Mathematically for every 3D pseudovector $x^i$ there is a 2-form $F_{ij}=\epsilon_{ijk}x^k$ such that the 2-form transforms properly under all orthogonal transformations. Therefore I would expect it ...
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force applied not on the center of mass
When applying a force outside of the center of mass of the body, the body will get both linear and angular momentum. Right?
Does the linear velocity from this force equal to the linear velocity from ...
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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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What is the initial angular momentum of a rigid body given an offset impulsed force?
What is the imparted angular momentum to a rigid body if the impulse force is offset by a distance $h$ from the center of mass and the imparted momentum from the center of mass is $mv$?
For a ...
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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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