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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 does gravitational pull increase when black holes spin?

I was reading "the science behind interstellar", and found that Kip Thorne purposefully used a SMBH in his simulation which had its maximum attainable spin around its own axis. He argued that this was ...
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Why can an inner product of an eigenvector also be used as an eigenvector?

In quote box below, there is an inner product of an angular momentum eigenvector. Why can you use this inner product as a new eigenvector for the next part of the work? And why do they "of course" ...
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Why does the Earth not fall towards the Sun? [duplicate]

According to http://wtamu.edu/~cbaird/sq/mobile/2013/07/01/why-doesnt-the-earth-fall-down/ , the earth does not fall down because of the gravitational force of the sun. At the same time , earth's ...
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Can I feed enough spin up electrons to a black hole to affect its angular momentum?

I was reading classical spin vs quantum field spin. I know spin in quantum mechanics is just a quantum number. But what happens if I try to intentionally feed many electrons all in the same spin state ...
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Basis function of $\Gamma_2$ irrep of point group $T_d$?

From Properties of the Thirty-Two Point Groups (Koster, et. al.), the basis function of the $\Gamma_2$ irrep of the point group $T_d$ is $l_xl_yl_z$, where $l$ is the angular momentum operator. ...
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Impulse on a Gyroscope

I've been studying gyroscopes, and I understand why a fast spinning gyroscope doesn't fall. However, I don't understand why a slow spinning gyroscope does fall, or why a large enough impulse to a fast ...
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Linear and angular momentum

If I push on an object not through the center of mass, we say that the translational effect on the entire object is the same. In other words, we can turn that off-center force into a force through the ...
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Well-definedness of Holstein-Primakoff transformation

In many-body physics, Holstein-Primakoff transformation is defined as follows: \begin{align} S_i^+ &= \sqrt{2S}(1-a_i^\dagger a_i/2S)^{1/2}a_i, \\ S_i^- &=\sqrt{2S}(1-a_i^\dagger a_i/2S)^{1/2}...
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Does moment of inertia only work for special cases?

I was looking into the moment of inertia expression for angular momentum. The angular momentum of a group of particles can be expressed as a linear transformation of the angular velocity vector. This ...
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Rotational Motion (angular momentum)

I don't understand why the angular momentum remains constant even after the distance of the particle (from the origin) keeps on increasing. Maybe I'm not reading the graph the way it is but I don't ...
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Symmetry of the spin function and T0 and S states

$|T_0\rangle = \frac{1}{\sqrt{2}}(|\uparrow \downarrow\rangle + | \downarrow\uparrow\rangle )$ is a triplet state, whose spin function has to be symmetric. $|S \rangle = \frac{1}{\sqrt{2}}(|\...
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Velocity of a spool of string being pulled [on hold]

The question given is In working this, I assumed that it was in pure rolling motion and as such friction was negligible. Working through, I found $ ΔKE = \frac{1}{2}Iω^2 = \frac{1}{2}I\frac{v^2}{R^2}...
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Ladder Operators - Quantum Mechanics [closed]

In my lectures notes, we define the raising operator as $$L_+ \Phi_{l,m_l} = \hbar \sqrt{l(l+1) - m_l (m_l + 1)} \hspace{1mm} \Phi_{l, m_l + 1}$$ Then we later look at spin-orbit coupling using ...
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Matrix representation of spin-1/2 operators in Sakurai

Hello and thanks for reading. I'm an undergrad working through the first chapter of Sakurai's text and was going through the principles of the spin-1/2 system. The author demonstrates closure and ...
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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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Orbital angular momentum quantum numbers - subtracted?

Reading Griffiths' Quantum Mechanics. We have the electronic confirmation of Carbon as $$(1s)^2 (2s)^2 (2p)^2$$ in the ground state. He says There are two electrons with orbital angular ...
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How does orbiting work exactly? [duplicate]

First of all I'm not a physicist or anything and I don't know much about physics, so I'm sorry if this doesn't make sense at all :) And if possible please try to explain it with words instead of ...
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Can conservation of angular momentum be derived from energy consideration? [closed]

About the context of this question: A dramatic illustration of back and forth conversion of kinetic energy and gravitational potential energy is when a celestial body has an highly eccentric orbit. ...
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Angular momentum of a body about a point rotating about its own axes

I want to calculate angular momentum of a sphere about point O. The sphere is rotating about its two axes with angular velocities $w_1$ and $w_2$. I know that angular momentum = $m\vec{r}\times\vec{v}...
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How does changing radius (constant mass) affect rotational kinetic energy?

I'm trying to understand how rotational energy would change if radius shrinks but mass stays the same. The initial question was posed as follows: "The radius of a disk of matter forming around a ...
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Again on Spin Operator in Dirac Field Theory (Peskin & Schroeder)

Good morning, I've already seen that this topic has been discussed so long, but my doubts remain unchanged. At page 61 of Peskin & Schroeder, An Introduction to QFT, there is the demonstration ...
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Measurement of spin asymmetries in semi-inclusive deeply inelastic scattering (SIDIS)

I have been reading several papers regarding the spin asymmetries for SIDIS. One thing I was trying to understand is the method of extraction of symmetries. When I read the single spin asymmetries, ...
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Spin Orbit Coupling term

I was seeing this enlightening video of DrPhysics on Spin Orbit Coupling: https://www.youtube.com/watch?v=aftOY3OkAgA&list=PLF15670EECA944A13&index=9 And I think there is a mistake. Around ...
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Doubts about interpretation of the curves of effective potential energy

The image shows a graph of the effective potential energy. Where,$K=-Gm_{1}m_{2}$ and $L$ is the angular momentum. The graph of the effective potential energy that can be seen in this publication was ...
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Rotational potential energy on a system of two masses

On a homework assignment, we were given the following problem: This system is held at equilibrium according to the configuration in the image; initially the body B is at rest, and the body A is ...
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A body is projected from ground with some angle to the horizontal, how the angular momentum about the initial position of the motion increases?

A body is projected from ground with some angle to the horizontal, how the angular momentum about the initial position of the motion increases? I have tried to solve this problem using parallel axis ...
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Is it possible to form a toroidal star?

Perhaps a fast spinning star (not spherical) where a black hole forms in the center, but the event horizon is smaller than the equatorial radius but larger than the polar radius?
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Transformation to canonically conjugate coordinates in Special Relativity

Just like we can Fourier transform a field from $$x^\mu = (ct, x,y,z) \rightarrow p^\mu = (E/c, p_x, p_y, p_z)$$ via a Fourier transform, for spherical coordinates can we Fourier transform in the same ...
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Difference between angular momentum $L$ and $J$ in quantum mechanics

what is the difference between angular momentum L and generalized angular momentum J and their components?
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Quantum energy levels of a point mass rotating about a fixed point

The question is: A particle of mass m is attached to a fixed point in space by a massless rigid rod of length a and can freely rotate about this point. Find the quantum energy levels of the system. ...
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Understanding spin & spatial components of wave-functions

I would like to understand the following statement: The $S$ and $P$ states can be expressed as products of the spin wavefunctions, $|+\rangle$ and $|-\rangle$, and the spatial wavefunctions, $|...
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Why does not dark matter gather and form celestial bodies? [duplicate]

since the only thing we know about dark matter that it "attracts" and affect our Baryonic matter's momentum and speed, which means that it does have mass of a sort. so why didn't we witness a ...
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Numerical method to find the roots of the expected value of a spin 2j state

Currently I am working with finding the solutions for the following problem: I have a unit sphere in which I have n points defined by their polar and azimuthal angles: $\theta_n , \phi_n$. I then do ...
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Relaxation/thermalization of High spin nuclei

Is it practical to keep nuclei excited to high spin for long(ish) times? What mechanisms drive the relaxation of nuclear spin? Which texts would treat this subject with detail?
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What happens energy-wise if you put a gyroscope at the north pole?

I had an idea for energy generation: put a gyroscope at the north or south pole connected to a dynamo or similar. The idea was that when the gyroscope resists the Earth's rotation, it would drive the ...
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How did Goudsmit and Uhlenbeck figure out the electron has spin $\frac{\hbar}{2}$?

Most stuff I read online says that to explain the Anomalous Zeeman Effect they had to assume the electron's gyromagnetic ratio is $\frac{-e}{m}$ instead of the classical $\frac{-e}{2m}$. But, since ...
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Schwinger oscillator model

How do we reach the equation 3.8 .10 I didnt understand how its second last step changes into equation 3.8.10
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Angular Momentum vs Kinetic Energy [closed]

Suppose we have a spinning top, with angular velocity $\omega$, its speed is null and there is no force applied to it. Let $J$ be its moment of inertia. We can say $E_k = \frac{1}{2}J\omega^2$ and $L ...
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Angular Momentum and assymetric axis

The question I came across , If a semicircular disc rotates uniformly (const. angular velocity) about an axis passing through its Centre of mass , and prependicular to its plane , do we need an ...
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Angular momentum and Zeeman effect

Supposing an Alkali atom positioned in magnetic field in $z$-axis. I understand linearly polarized laser propagating in $z$-axis can induce $\sigma$ transmission. But I could not figure out how laser ...
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Angular Momentum Coupling and 3jm Symbols

I have a question regarding j coupling. At the moment, I try to learn the diagrammatic approach which is written down in Varshalovich, Chapter 11. But there I have now a question regarding the ...
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Angular Impulse equations for rotational dynamics

Consider a 3d rigid body at rest initially, assuming no net external forces acting on it. It is set in perpetual rotation along one of its principal axis. Now an angular impulse (which is a vector) ...
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Is any given triplet spin state an eigenstate of some $j^z$ in the correct basis?

Imagine you have a triplet spin state, which in general can be written as $$|\psi \rangle = \alpha | \uparrow \uparrow \rangle + \beta ( | \downarrow \uparrow \rangle+ | \uparrow \downarrow \rangle) ...
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Why is the angular momentum of blackhole measured by orbital motion of falling objects around it?

When massive star collapsed under it's own weight, it can becomes a blackhole and I have to believe angular momentum is conserved. Since we cannot directly measure the rotation of blackhole, I read ...
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Why does the gyroscope not move upwards?

I have been watching a lot of videos on gyroscopes. Everything I see says there are two steps in gyro precession: Gravity pulls down imparting a torque The gyroscope moves forward It seems to me ...
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Semi-classical Hydrogen Atom Angular Momentum under Magnetic Field

Suppose we have a semiclassical hydrogen atom in its ground state at the x-y plane with the proton being at the origin. Let there be a magnetic field $\vec{B}=B\hat{z}$. By deriving the orbital ...
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Conservation of Linear Momentum w/ Rotating Body

I am a high school physics student and I have a question on part (a) regarding the conservation of linear momentum. It says to use the conservation of linear momentum to solve for the velocity of the ...
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Matrix representation of spin-2 system? [closed]

I am surprised no one has asked this before, but what is the matrix representation of a spin-2 system? Also, what are the equivalent of the Pauli matrices for the system?
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Can I express the Hamiltonian in terms of $L_z$ operator only, not $L_x$ and $L_y$? Is it generally true, that $-\omega L_z = H$?

I encountered the relation in the Solution of Problem 5.1 in the book by Kyriakos Tamvakis titled "Problems and solutions in quantum mechanics": $$\frac{i}{h}[H,\textbf{L}]=-\frac{i \omega}{h}[L_z, \...
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Total angular momentum operator on $|m\rangle$ and $|m-1\rangle$ results in different eigenvalue [duplicate]

In the lectures by Prof. Leonard Susskind, he mentioned that the total angular momentum squared operator can be represented by $$ L^2 = L_z^2 + L_z + L_- L_+ $$ ($L_+, L_-$ being ladder operators). ...