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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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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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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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 suitable 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 \...
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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). ...
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Wigner-Eckart theorem: Are expectation values of all vector operators parallel?

The Wigner-Eckart theorem tells us that for any tensor operator, $\mathbf{T}^{(k)}$ that \begin{align} \langle jm|T^{(k)}_q|j'm'\rangle = \langle j'm'kq|jm\rangle \langle j||\mathbf{T}^{(k)}||j'\...
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Query about angular momentum and torque

This question came from studying Rutherford scattering. As you can see in the diagram below, there is an alpha particle moving past a heavy nuclei and being deflected. In the following analysis of ...
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Relation between quantum numbers $j$ and $\ell$

I'm given the following problem: "Consider an atom with orbital angular momentum $l$. What are the possible values of the total angular momentum quantum number $j$? Treat the case of $\ell = 0$ ...
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Question about the angular speed of a rod as it falls to the ground [closed]

I was given a problem yesterday in which a bird flies into a rod and then is stunned. It gives the rod some initial angular speed (found through conservation of momentum). However, my TA then claims ...
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Hamiltonian-commutation, hermiticity and non-hermiticity (QM)

When we have a QM system in an energy eigenstate (say after a measurement of energy) then we can measure any time another quantity that is described by an hermitian operator that commutes with the ...
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Is the $2p\rightarrow2s$ transition possible?

Selection rules in one electron atoms are: $\Delta n=$ any $\Delta l=\pm1$ $\Delta m_l=0,\pm1$ $\Delta s=0$ Parity must change Under strong spin orbit interaction: $\Delta j=0,\pm 1$, but $j=0\...
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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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Does total $\hat{S}^2$ always commute with total $\hat{S}_z$ even for interacting spins?

I was given the following operator $\hat{f}$ describing the interaction of two spin-$\frac12$ particles: $$\hat{f}=a+b{\hat{\bf S}_1}\cdot{\hat{\bf S}_2}.$$ I was told that I can prove that $\hat{f}$...
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Difference in rotation of the atmosphere at different levels

The atmosphere near ground level rotates at the same rate (on average) as the earth's surface because of drag effects beween air and ground, and continues to rotate because of inertia. Correct? My ...
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Lagrangian two body gravitational conserved quantities

I have the Lagrangian for two gravitationally attracting bodies: $$ L ={\frac{1}{2}}M\dot{R}^2 +\frac{1}{2}{\mu}\dot{r}^2 + \frac{Gm_1m_2}{|r|}$$ Where M is the total mass, mu the reduced mass and r ...
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Why is angular momentum always quantized irrespective of the system?

In general, the eigenvalues of the components of position $\vec{r}$ and momentum $\vec{p}$ are not quantized. Certainly, not quantized for a free particle. Is there a physical explanation of how is it ...
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Conservation of Angular Momentum — Earth-Moon System — Earth spin backwards?

I am developing an exhibit for a museum. We want to show how the Earth's spin rate changes as the Moon drifts farther and farther out from the Earth. The visitor has a slider they can move to set ...
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Deriving the equality between the external torque and the rate of change of angular momentum, for a system of particles

I've started working through Analytical Mechanics for Relativity and Quantum Mechanics by Oliver Johns and I'm stuck on deriving a formula. In the section titled "Change of Angular Momentum", Johns ...
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Different global phase shifts of Pauli-$z$ Matrix eigenstates from rotations around $z$-axis

I understand the pauli matrix $\sigma_z = \bigl( \begin{smallmatrix}1 & 0\\ 0 & -1\end{smallmatrix}\bigr)$ rotates a state around $z$-axis by angle $\pi$ in $SO(3)$. We can see it works by ...
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Showing conservation of momentum for arbitrary pendulum trajectories

Consider an isolated system of a pendulum driven by a motor, initially at rest. Conservation of momentum and angular momentum ordains that the center of mass and orientation cannot change in the ...
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Why does magnetic dipole moment $\vec{\mu}=\gamma \vec{L} $?

I have often seen that the relationship between magnetic dipole moment $\vec \mu$ and angular momentum $\vec{L}$ expressed as $$\vec{\mu}=\gamma \vec{L} $$ But consider a current loop of a charged ...