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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Why are composite particles grouped with force carrying particles?
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Huge confusion with Fermions and Bosons and how they relate to total spin of atom
says a hydrogen atom is a boson.
I'm confused. I thought bosons were force carrying - e.g. a photon, gluon, etc?
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Commutators between momentum and total angular momentum [closed]
Do $p^2$ and $r^2$ commute with $J^2$? Where $p$ is the momentum, $r$ is position coordinate and $J=L+S$ is the total angular momentum. I think the answer is yes due to the fact that the angular ...
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Separability of an Hamiltonian with spin
I'd like to know if this Hamiltonian $\hat{H}=\frac{p^2}{2m}+\frac{1}{2}m\omega^2r^2+\frac{A}{\hbar^2}(J^2-L^2-S^2)$ is separable into two parts $H_1=\frac{p^2}{2m}+\frac{1}{2}m\omega^2r^2$ and $H_2=\...
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Angular Momentum about a Point
I am confused by two different definitions of the angular momentum of a particle P about a moving point Q, with point O as the origin of the inertial frame. I learned the first definition from my ...
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Will a spacecraft with angular momentum have to course correct if it thrusts along the same axis as its rotation?
For the sake of illustration, let's say you have a cylindrical spacecraft, sitting "at rest" in space, relatively speaking. It has a thruster on one end. If it fires the thruster, it goes ...
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Deriving a recursion relation for Clebsch-Gordan coefficients
I refer to Sakurai's Modern Quantum Mechanics. Using the lower signs for equation $3.369$ on page $212$,
$$\sqrt{(j+m)(j-m+1)}\langle j_{1}j_{2};m_{1}m_{2} | j_{1}j_{2};j,m-1\rangle = \sqrt{(j_{1}+m_{...
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Confusion about the Wigner-Eckart theorem
Background
This will be a lengthy thread, but I made sure that all 3 questions are related to each other and related to the same topic.
I currently encountered the W.E-theorem and while I do ...
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Equation to tell if precession will happen?
So I have an seen the equation to calculate precession but it breaks down at when there is not sufficient angular momentum, for example if an object is not spinning we divide by zero and the ...
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Angular Momentum of asymmetric physical pendulum (Rigid Body)
The angular momentum of a rigid body respect to a pole $O$ located on its axis of rotation $z$ is uniquely determined if we know its angular velocity:
$\vec{L}_O = I_z\vec{\omega} - \omega\iiint_V ...
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Will a radioactive ball conserve its angular velocity?
Consider a uniform spinning sphere in vacuum. In principle it should spin forever, because of angular momentum conservation. However, assume that the sphere is made of radioactive material: since it ...
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Force of brake pads on a wheel
I have a hollow-cylinder wheel model, braked with brake pads located at a distance d of the wheel's center axis. The brake pads have a contact area S. They are also forced towards the wheel with a ...
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Angular Momentum and Coefficient of Restitution
If there was a situation where you had two rods pinned in the center and the left rod having an initial angular velocity $\omega_1$, and the right rod was at rest. I am wondering what the final ...
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Why is angular momentum equal to mass times radius times velocity?
When momentum is mass times velocity, why is angular momentum mass times radius times velocity?
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Null conserved angular momentum
If the angular momentum of a particle is conserved and it is also 0, then is it true that the particle moves along a line? If so, how can we derive the equation for the trajectory from both the above ...
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Angular momentum of an extended mass for fixed origin imply the same result for nonfixed origin?
Consider an extended mass (say a collection of n particles where the internal force between them is central). For any fixed origin/inertial reference frame, the angular momentum satisfies
$$\begin{...
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Is there a limit to how close faraway objects can get due to the conservation of angular momentum?
Say a 1kg object is going 1 meter/sec tangentially to a point 600,000,000 meters away, its angular momentum is $$1kg*1m/s*600,000,000 meters$$ If it were to decrease its radius to the point similar to ...
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The nuclear spins of alkali metals
Looking at the different isotopes of alkali metals and their nuclear spins, I notice that nearly all of their bosonic isotopes have nuclear spin of 3/2. Surely there must be an explanation in nuclear ...
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Symmetry of spin wave function
I know that for orbital angular momentum, the symmetry under interchange of two particles of the orbital wave function is $(-1)^{L}$. Also, for a two spin-$1/2$ system, if the total spin couples into ...
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Relativistic angular momentum confusing definition
After reading Wikipedia, I'm confused by the relativistic angular momentum definition. OK for the 4-angular momentum tensor. But does it mean that the following more intuitive "angular momentum&...
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Precise definitions for higher spin operators
I am trying to understand the matrices and vectors presented in this section
https://en.wikipedia.org/wiki/Spin_(physics)#Spin_projection_quantum_number_and_multiplicity
I am looking for a reference ...
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In relation to the correspondence principle, what happens when the orbital magnetic quantum number $m_\ell$ is very large?
If for each value of the orbital quantum number $\ell$ there are $2\ell+1$ possible associated magnetic quantum numbers $m_\ell$, and they are interpreted as the only allowed orientations that the $...
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Is angular momentum conservation Galilean invariant?
Suppose I have a system of particles with constant total angular momentum $\mathbf{L} = \sum_a m_a \mathbf{r_a \times v_a}$ in frame K. If frame K' moves with velocity $V$ with respect to K and their ...
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Angular Momentum Conservation and Conservation of Energy
A heavy solid sphere is thrown on a horizontal rough surface with initial velocity $u$ without rolling. What will be its speed, when it starts pure rolling motion?
So using conservation of energy, I ...
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Is the constancy of earth rotation speed the only reason why don't feel the rotation of earth? [duplicate]
i searched the reason of why we don't feel the rotation of earth about its axis but i found the reason is the constancy of its rotation speed ( the rate of rotation velocity is zero )but i find a ...
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Motion and momentum of spinning mass
Two college friends get together 50+ years after their physics class and begin to discuss forces, momentum, spinning bodies, and space propulsion. It developed that
they had widely differing opinions ...
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A dilemma regarding torque when a body moves in circular motion
Consider a mass 'm' tied to a rope and I am rotating it in a circular path with constant angular speed.One component of the tension balances the weight and the other component provides centripetal ...
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Why is isoclinic rotation preferred in spaces of $d \gt 3$ dimensions?
This question, for example, takes it for granted that double rotations of objects in four-space will naturally tend to decay into isoclinic rotations.
But, why? How does that transfer occur? It seems ...
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How do the inertia tensor varies when a rigid body rotates in space?
The inertia tensor is clearly constant the in a frame moving with the rigid body. But what is the simplest way to see why its columns can be considered rotating vectors in space with the angular ...
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If a boy tries to walk on a circular disc , the disc rotates but the boy remains stationary. Why it violets the law of cons. of angular momentum?
Suppose a boy tries to walk on a circular disc of mass = m, radius = r, with a velocity = v. As it is an isolated system, the center of mass of the system will not change, that means boy will not have ...
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The mathematics of different particle rotations
So, in general (if I understand this correctly):
Force particles behave differently than matter particles under rotation
The matter particles need a 720° rotation to put them back into their initial ...
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Does an irregular rigid body can only rotate in three directions?
Suppose that at a certain instant the angular momentum with respect to the center of mass is not parallel to the angular velocity. Does this necessarily imply that the angular momentum is rotating ...
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(Why) Is orbital angular momentum conserved for point masses?
The introduction of the angular momentum as $\vec l = \vec r \times \vec p$ is also true for point particles. So $\vec l$ must refer to the orbital angular momentum (and not the "spin") in ...
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Two final velocities for a mass launched from Earth
i'm trying to find the final velocity of a mass that is launched vertically from the earth, only considering the gravitational force.
My first attempt was with angular momentum:
$r$ is the distance ...
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Is It true that If the angular momentum is zero with respect to any point then the system is at rest?
If the angular momentum is zero with respect to any point, surely the system is at rest. It is intuitive that this is the case but I would like to prove it. I guess supposing the opposite leads to ...
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Can conservation of angular momentum be proven?
It's been a while I was thinking about conservation of angular momentum. The fact which makes me uncomfortable is why does uniform angular velocity implies,
$$\vec{\tau}^{\text{EXT}}=0.$$
I was trying ...
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How does gravity make us rotate about the rotation axis of earth?
A body at the surface of earth experiences at least two obvious forces - gravity and its weight (normal of the surface). Both of these forces act on the radial axis that goes through the center of ...
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Rotation and Killing vectors in Minkowski spacetime
There are $3$ Killing vectors in the Minkowski spacetime related to the conservation of angular momentum. Sometimes it is mentioned that it is related to the rotational symmetry of the spacetime. But ...
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Angular velocity of a ball if force is applied above its center
I am wondering what the angular velocity would be if you apply a force over time to a ball above its center (but not tangential). For instance, if a ball of was lying on a flat surface and you apply a ...
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Is change of angular momentum of two rotating disks colliding w.r.t. time $L(t) = \omega_0 I(1-e^{-t/C})$?
If you have two rotating disks with a different angular velocity $\omega_0$ and $\omega_1$, different area and material, how can you describe the angular momentum w.r.t. time which seems to be a ...
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A squared quantum operator is the same as using the same operator twice? So can't we find $L^2$ operator by using the $\mathbf L$ operator twice?
I understand that we can use the ladder formula and dervie the $L^2$ operator but is it wrong to use the L operator formula directly and apply it twice to observe the $L^2$ instead?
\begin{align}
L^2 &...
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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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Deriving an identity with rotation generators [closed]
I am trying to justify the following identity on page 68 of Osborn's notes on group theory:
$$e^{-i\pi J_{3}}J_{2}e^{i\pi J_{3}} = -J_{2}.$$ Here, the $J_{i}$ are the typical angular momentum ...
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What is the angular momentum of a particle rotating around an axis in 3D?
What would be the angular momentum of the particle at position $r_i$ in the diagram above?
The vector from the axis of rotation is $R_i$ and the tangential velocity is $v_i$ so the magnitude of ...
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"Precession" of a free electron
I'd like to gain as deep of an understanding as possible of the following diagram from Introductory Quantum Mechanics, 4th ed., by Richard Liboff:
I'm not looking for help with solving the easy ...
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What does it mean by spin 1/2 or spin 2 field?
I see in common discussions people simply use the terminology spin 1/2 field or spin 2 fields as if it is some common term like hamiltonian. How to think about these fields and understand what it ...
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Does the angular momentum of a Black Hole give insight into a potential solution for the singularity?
Alright so, i want to make one thing clear. I am a bit of a dumbass who watches a lot of PBS Spacetime and read a paper or to on visualising Black Holes. Example image (10k):
I asked a very similar ...
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Why can't spherical nuclei rotate?
When studying nuclei it is said that spherical nuclei do not rotate, instead rotations are considered for deformed nuclei only. I do not understand why is that. If one can write the hamiltonian of ...
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Why does angular velocity changes as i strech my hands?
Suppose I am sitting on a turnable chair. I have given that turnable chair some angular velocity $\omega$ and it starts rotating around me as axis of rotation.
Now at that instant suppose I expand out ...
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Probability of possible results of measurement - hydrogen atom
I know that hydrogen atom's eigenfuction is :
$\psi(\vec r)= \sqrt{ 1 \over 24 a_B^5} r e^{-r \over2a_B} Y_1^0 |+>$,
where $Y_1^0 =\sqrt{3 \over 4 \pi} cos\theta$.
So, since I have just one ...
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Three particle composite angular momentum states
I'm working on this problem to determine the ground state angular momenta ($S,L,J$) for nitrogen using Hund's rules, and I want to see if the total orbital angular momentum $L=2$ is possible (the ...
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