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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Intuition for angular momentum
A single object with mass $m$ is rotating around an origin at a distance $r$ and speed of $v$; so its angular momentum is equal to $mrv$; if we decrease its radius (say shorten the rope) its speed ...
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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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Why are protons/neutrons spin-$\frac{1}{2}$ when they are made up of three valence quarks (also spin-$\frac{1}{2}$)?
If we take the composite angular momentum of the three valence quarks, we should have a proton/neutron spin angular momentum of,
$$S=\{ \frac{1}{2},\frac{3}{2} \}$$
using the general rule for adding ...
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Do quantum measurements violate conservation laws?
When we measure the spin angular momentum of a particle in an axis different to its current spin, we change the direction of its spin, which taken by itself would be a violation of the law of ...
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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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Moment of Inertia, why $r^2$and not $r$?
So my engineering mechanics book includes a brief discussion on area moments of inertia.
Unfortunately, the ensuing chapter is predominately computational in nature. I don't have a thorough grasp of ...
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The momentum of a swinging sword
Suppose you are faced with a zombie, and the only way to kill it and save yourself is to chop its head off with your sword. However, you are very weak from illness, and can only afford to strike once.
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What is the spin rotation operator for spin > 1/2?
For spin $\frac{1}{2}$, the spin rotation operator $R_\alpha(\textbf{n})=\exp(-i\frac{\alpha}{2}\vec{\sigma}\cdot\textbf{n})$ has a simple form:
$$R_\alpha(\textbf{n})=\cos\biggl(\frac{\alpha}{2}\...
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Spin-$n$ particle comes back to itself after $360/n$ degree rotation
On the Wikipedia page for spin, a claim is made that a spin-$n$ particle comes back to itself after a $360/n$ degree rotation.
I quote:
A spin-zero particle can only have a single quantum state, even ...
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Relation between total orbital angular momentum and symmetry of the wavefunction
My question essentially revolves around multi-electron atoms and spectroscopic terms. I understand the idea that the total wavefunction for Fermions should be antisymmetric. Consider as an example, ...
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How do astronomers detect the spin of the black holes?
There are various theoretical models for accretion disks and relativistic jets from black holes that considers the black hole to be either rotating (Kerr geometry) or non-rotating (Schwarzschild ...
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Addition of spin angular momentum for massless particles
How do I add the spin angular momentum of massless particles, like photons, where only the transverse polarizations are allowed?
If all three polarizations were allowed, this would be an easy ...
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Intrinsic angular momentum in classical mechanics
Please note, I am only interested in classical mechanics discussion on this. Please do not involve quantum mechanics.
Inspired by this question: Is Angular Momentum truly fundamental?
My question ...
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Spin conservation in pair production
In QED, when two photons collide, they can turn into an electron and positron pair. We know from $U(1)$ gauge symmetry that the total charge of the initial and final states must be conserved. On the ...
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Why is the specific notation used for term symbols useful?
This has bugged me for a long time.
Term symbols describe electronic states of atoms which have well-defined total electronic angular momentum $J$ as well as total spin and orbital angular momenta $...
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How does electron spin change instantaneously without violating inertia principle?
The inertia in one of the main properties of matter. That is why all process in macro world do not happen instantaneously.
What I do not understand is how we should apply this general idea of inertia ...
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Does the dark matter halo rotate with the galaxy?
If the dark matter halo is stationary related to the arms of the galaxy then tidal effects should slow the galaxy rotation.
If it rotates with the normal matter in the galaxy then shouldn't it ...
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How do point particles transfer angular momentum between each other?
I know that quantum physics says that one can't change the magnitude of spin of a point particle but that still leaves the question of how one changes the direction of spin.
One possible way point ...
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Where does the kinetic energy go?
A uniform cylinder was placed on a frictionless bearing and set to rotate about its vertical axis. After a cylinder has reached a specific state of rotation it is heated without any mechanical support ...
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Will freely rotatable polarizers align?
Will two freely rotatable linear polarizers (placed in sequence and at some angular offset less than, say, 45 degrees) eventually align if you shine (plenty of) unpolarized light at the first one?
If ...
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Direct measurement of $\mathbf S^2$
For concreteness, consider two spin-1/2 particles with spin vectors $\mathbf S_i=(S_i^x,S_i^y, S_i^z)$. The total Hilbertspace is four-dimensional, and as a basis we can take the (simultaneous) ...
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Why do 3d spheres and gravity tend to rotating discs on one plane?
Whether is it our solar system or a whole galaxy, there is usually a massive object (star or black hole) at the centre with gas and objects rotating around it.
The gravitational effect of the star/...
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Is there a specific case for the kinetic energy of a particle to be conserved while angular momentum is not conserved?
This is from a question from one of my country's undergraduate entrance exams, so the usual considerations of not taking extraordinary cases apply.
The question is, in quotes
"A particle moves ...
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Second Kepler's law explanation
What is the explanation for the second Kepler's law? Why is the law valid?
Is it that the total energy of a planet equals to the kinetic energy plus the potential energy?
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"Reversed" Clebsch Gordan coefficients
Consider the sum of angular momenta $J=J_1+J_2$.
When one has a state $|J,M\rangle$ of an eigenbasis of a common eigenspace of $J^2$ and $J_z$, one can write it in terms of the elements $|j_1,m_1;j_2,...
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Huge buildings affect Earth's rotation?
Does constructing huge buildings affect the rotation of the Earth, similar to skater whose angular rotation increases when her arms are closed comparatively than open?
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Where does angular momentum come from when an object gets attracted by a planet?
Consider an object effectively travelling in free space, maybe expelled from another solar system a long time ago.
The object enters our solar system and approaches say Jupiter.
Obviously while freely ...
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Spin operators in QM
In a text (Introduction to Quantum Mechanics by Griffiths) I am using it states without motivation that spin angular momentum has the same commutations relations as orbital angular momentum (these ...
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How can a pulsar slow down?
I saw in some astronomy textbooks that pulsars gradually slow down due to the loss of energy by its radiation. I wonder why this is possible?
Although the radiation is now not thermal but in the form ...
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Why is the rotation about COM? [duplicate]
Suppose a ring is given to us with no hinge as such. Now a bullet comes and strikes the ring and gets embedded in the ring.
The ring will now have linear momentum and some rotation going on. Okay, the ...
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How long was a day at the creation of Earth?
Since the earth is slowing its rotation, and as far as I know, each day is 1 second longer every about 1.5 years, how long was an earth day near the formation of earth (4.5 billion years ago)?
I ...
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Why do we think Spin is angular momentum as opposed to some other quantity? [duplicate]
What leads us to the conclusion that spin is angular momentum? Could it not be some other quantity? Sorry if this is a rookie level question.
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Square of the Pauli matrices and the identity matrix
The square of any of the three Pauli Spin matrices is equal to the identity.
Is there any physical meaning to this?
Would you expect it?
Maybe in the context of the $SU(2)$ group?
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How does the source of silver atoms works in Stern-Gerlach experiment?
The Stern-Gerlach experiment used a source of silver atoms. Can you explain what moved the silver atoms from the oven to the screen where their impact was visualised? I am not asking for the deviation ...
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Peskin and Schroeder Equation 3.23
I've been trying (for a while) to prove that $S^{\mu\nu}:=\frac{i}{4}\left[\gamma^\mu,\,\gamma^\nu\right]$ is a representation of the Lorentz Lie algebra, that is, to prove that it satisfies the ...
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In quantum mechanics (QM), can we define a higher-dimensional "spin" angular momentum other than the ordinary 3D one?
Inspired by my previous question Questions about angular momentum and 3-dimensional(3D) space? and another relevant question How to define orbital angular momentum in other than three dimensions? , ...
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How is angular momentum conserved when a spinning top finally stops spinning?
Where does the top's angular momentum get transferred to? Does it very slightly change the angular momentum of the table, and then the angular momentum of the Earth?
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Total orbital and spin angular momentum for a closed shell
I read one Phys.SE question similar to mine, in
Total angular momentum in a full shell
but the question was so confusing and vague. The answer, though, was helpful for me to understand a part of my ...
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What does it really mean that particle has a spin of up/down? And how is spin actually meassured?
I was reading a physics article (related to the recent discovery of a particle that could be the Higgs boson) and the article was discussing electron spin and how spin can only be either up or down. I'...
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Angular Momentum: How do we know that $\hat{J}_z$ have non-degenerate eigenvalues?
We know that the eigenvalues for $\hat{J}^2$ is $2j+1$ - fold degenerate. However, most textbooks I have read, when explaining the ladder operator, shows the action of the ladder operator to be like ...
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Why do things spin?
Let's say I have 2 boxes, one of mass M and one of mass 2M. They are connected by a rigid rod. I drop them from the same height and see that due to the earth's gravity, they accelerate at the same ...
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Is Angular momentum conserved in Impure rolling
In a situation where a disk is rolling WITH slipping on the ground i.e velocity of centre of mass is greater than $r\omega$, is angular momentum conserved about a point on the ground.
What confuses ...
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How to determine whether an eigenstate of total spin is symmetric or antisymmetric?
Here we have two identical paticles with spin $I$, integer or half-integer,
and there are $(2I+1)^2$ states.
Each one of them can be uniquely determined by total spin and its orientation, we can use $...
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Emergence of spin from special relativity
I have pulled up and read as many answered questions as I can find here on why spin emerges as a consequence of making quantum mechanics compatible with special relativity- and still have problems ...
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Difference between spin-orbit coupling and $LS$ coupling (Russell-Saunders)
I'm having some trouble understand what the difference is between these two.
It seems as though there are kind of the same, but that spin-orbit coupling reduces to $LS$ coupling under certain ...
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How is angular momentum measured in experiments/in practice? [duplicate]
Possible Duplicate:
How does one experimentally determine chirality, helicity and spin?
How do you find spin of a particle from experimental data?
We read about and study angular momentum in ...
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The uncertainty in angular momentum
It is known that the different spatial components of the angular momentum don't commute with each other.
$$
[L_x,L_y] \propto L_z \\
[L_y,L_z] \propto L_x \\
[L_z,L_x] \propto L_y
$$
Also it is known ...
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Why water in the sink follow a curved path?
When you fill the sink with water and then allow the water to be drained, the water forms a vortex.. And then it starts to follow a curved path downwards by effects of gravity.
Why this phenomena ...
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Apparent violation of the law of conservation of angular momentum in the torques experienced by two interacting electric dipoles
Question
Consider two dipoles $({p_1}\hat{i}$ and ${-p_2}\hat{j})$ kept in the $x-y$ plane at $(0,0)$ and $(d,0)$ respectively. Calculate the torque about the COM.
Approach 1
Suppose we select the COM ...
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Is it expected that all stellar black holes will be spinning near the maximum allowed $\omega$-velocity?
Using a bit of classical reasoning I'm imagining black hole formation to be much like an ice skater pulling in her arms:
Now, the size difference between a star and its black hole can't even be ...
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