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 the angular speed of mass $m$ if we pull the string? [duplicate]

Mass $m$ is rotating on a horizontal friction-less plane around a tiny hole. A massless string is connected to mass $m$ and the other end of it is held by John's hand. John pulls the string to move ...
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What is the angular speed of the mass m if we pull the string? [closed]

Mass m is rotating on a horizontal friction-less plane around a tiny hole. A massless string is connected to mass m and the other end of it is held by John's hand. John pulls the string to move the ...
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Understanding addition of angular momentum for six spin-1/2 nuclei in a molecule

In this paper Matthew Fisher proposes the use of so-called Posner molecules for quantum processing in the brain. I am trying to understand the arguments at the beginning of Section F (Section 6 in the ...
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Can velocity of an object be different as seen from inertial frame and center of mass frame of reference? [closed]

Is it necessary for an object to have same velocity in Center of mass frame and well as inertial frame of reference under the action of a constant force? I was solving one question and I got different ...
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Why is torque measured about the centre of mass?

The original question I was asking was Why does a body not rotate if force is applied on the centre of mass?. The obvious answer is that the torque ${\bf r}\times{\bf F}$ is zero as ${\bf f}$ is zero ...
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Do stellar black hole precess like Earth do?

The precession of Earth caused by the Sun and Moon pull like when you breathe super hard on a spinning top, what about massive blackhole which is a point in space conserving it's angular momentum? I ...
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Effect of Earth's Rotation on Time [closed]

According to Wikipedia: Earth's rotation is slowing slightly with time; thus, a day was shorter in the past. This is due to the tidal effects the Moon has on Earth's rotation. Atomic clocks show that ...
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Why didn't heavier elements settle at the core of the solar system?

As the solar system formed, why didn't all of the heavier elements such as iron, collect where the sun is leaving the lighter elements in the outer solar system?
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How can a spinning body *suddenly* change angular momentum/KE when transitioning its axes (intersecting ellipsoids in the intermediate axis theorem)

This video illustrates the Intermediate Axis Theorem by showing that the system of rotations is confined to the the intersection of the ellipsoid representing angular momentum $$|h|^2 = A\omega_1^2 + ...
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Rod hits rod - angular and linear momentum

I've been analyzing "ball hits a rod in space" type collisions, where speeding ball transfers part of its kinetic energy during elastic collision to the motionless rod, making it gain linear ...
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Do spinning object near a spinning black hole obey the equivalence principle?

According to the equivalence principle the path of an object should not depend on it's composition. But on the other hand a spinning object (e.g. an electron) moving past a rotating Kerr black hole ...
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Does the Stern-Gerlach experiment really suggest superposition?

The Stern-Gerlach experiment is often cited as evidence of quantum superposition and there are some very simple explanations like this one https://www.youtube.com/watch?v=hkmoZ8e5Qn0 in which spin on ...
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Can we solve the general eigenfunction of $L_x$?

Consider the orbital angular momentum in QM, labeled by $L$ ($\mathbf{L}=\mathbf{r}\times\mathbf{p}$). In spherical coordinate, the operator can be expressed as: \begin{equation*} \left\{\begin{...
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Angular momentum and collisions/pure rolling

Consider a general problem of a rigid sphere having only rotational motion placed on a rough surface where it starts rolling after some time. And final velocity is asked. Friction is just enough to ...
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Why is there a factor of $\hbar$ in the physicists' $\mathfrak{su}(2)$ Lie algebra?

The standard (mathematicians') basis for the $\mathfrak{su}(2)$ Lie algebra is: $$X_j = -i\frac{\sigma_j}2$$ where $\sigma_j$ are the Pauli matrices. In physics, observables correspond to real numbers,...
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Why don't the electrons in a paramagnetic material precess around an external field?

When a paramagnetic material is placed in a strong external magnetic field, then you'll find that the magnetic momenta of the electrons in the material will align to the field, causing a net magnetic ...
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Angular momentum and Potential field

In addition to total energy, which components of the angular momentum $(\mathbf{L}_x,\mathbf{L}_y,\mathbf{L}_z)$ are conserved in the presence of an external potential field $V(x,y,z)$? I've learnt ...
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2-body problem, conservative central force, spherical symmetry, conversation of angular momentum, motion in a plane

I am having trouble unpacking the following argument from page 72 of Goldstein's classical mechanics book. We now restrict ourselves to conservative central forces, where the potential is V(r), a ...
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How to construct eigenvectors of angular momentum and directional parity (mirror)?

In the context of diatomic molecules I have seen it has come up that an eigenvalue $M_L\hbar$ of $L_z$ is doubly degenerate with respect to reflection about a plane containing the $z$ axis, whose ...
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Find angular momentum using center of mass frame

Suppose I have a square-shaped plate getting hit by a ball as shown in the picture below (notice how the force vector applied by the ball is not parallel to the $r$ vector). Let's set the origin to be ...
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Angular velocity, Angular Momentum and Torque considered vectors to explain gyroscope precession and related phenomena? [closed]

Are angular velocity, angular momentum and torque "real" vectors in the sense that acceleration and force are? Or are they only considered vectors to explain phenomena like gyroscope ...
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Trajectory of an object when asymmetrical forces are acting on it [closed]

I'm trying to code a game that uses physics...but I don't how to figure something out: If I have a 2x2 square (in any unit), with two thrusters/jets whatever you want to call it, on the back, each 1x1 ...
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Expectation value of $\sum_{a=1}^2\left(\frac{3r_a^ir_a^j}{r_a^5}-\frac{\delta^{ij}}{r_a^3}\right)$ for the helium ground state

My question is somewhat related to this one: Expectation value for spherically symmetric states In the case of the hydrogen atom, we have that in the ground state the following expectation value ...
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Computing matrix elements using Wigner-Eckart Theorem

I am trying to compute the matrix elements \begin{equation} \langle j \, m | a_{1}^{+} | j' \, m'\rangle \end{equation} \begin{equation} \langle j \, m | a_{2}^{+} | j' \, m'\rangle \end{equation} ...
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Quick question regarding Larmor precession and bar magnets

So I was just reading a bit about magnetic dipole moments, Larmor precession, angular momentum etc., but there was one little thing that was bothering me. As far as I know, any angular momentum will ...
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Physical interpretation of the definition of angular momentum in classical mechanics

To what I understand, the following is a valid way to introduce the angular momentum $\mathbf L$ in the Lagrangian system of a rigid body. We can consider the extended configuration space to be $M\...
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Why doesn't dark matter collapse into a black hole? [duplicate]

Dark matter supposed to be affected only by gravity and no other force. At the same time, however, dark matter forms halos around galaxies, that become visible examining how galaxies and clusters bend ...
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Expected Gaussian distribution on screen in Stern-Gerlach Experiment

In the Stern-Gerlach experiment, they used a beam of silver atoms travelling in z direction (which has valence electron in the 5s shell), so the electrons carry zero angular momentum. Now since they ...
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Getting incorrect result for Angular Momentum Density

I am finding the answer $\dfrac{-\mu_0 Q.m}{16\pi^2 \cdot r^5}\sin(\theta)$ direction to $\theta$ but the answer is $ r^4$. Where does the $r$ come from?
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Angular momentum and Schrodinger equation

I'm studying stationary states and their orbital angular momentum in 3D Schrodinger equation. I have tried to understand by myself the situation but I get lost. I think it might be useful to know ...
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Why Spin angular momentum effect (quantization) is observed only under varying magnetic field?

Is there some reason behind the appearance of spin effects only under the application of variable magnetic field. I know that we need variable magnetic field to act force on charge particle with some ...
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Symmetry of Wigner's 3j symbol

I'm trying to understand the symmetry of Wigner's 3$j$ symbols. $3!=6$ permutations, as well as flipping the sign of all magnetic quantum numbers yields 12 operations, which are sometimes called the &...
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Is conservation of angular momentum responsible for rotating a rigid body when it slows down an internal wheel?

Suppose that there is a rigid body, such as a satellite, which contains inside it a wheel that is spinning at a constant rate. This means that the satellite has a certain, constant, angular momentum ...
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What is the evidence (experimental observation) that elementary particles have spin angular momentum?

From what I have read here, the concept of spin is attributed to a calculation based on a mathematical model using quantum mechanics. For example, How can a particle with no size have angular momentum?...
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Feynman 20-4: Question regarding centrifugal force and rotation in three dimensions

For full reference, refer to https://www.feynmanlectures.caltech.edu/I_20.html#Ch20-SUM Here's the quote that I think is relevant to the question: 'Consider a wheel that is fastened onto a shaft in a ...
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Difference between Linear Forces and Forces Applied along a rotation axis

I am confused between How forces work when applied in singular linear direction vs Force Applied to a continuous mass along an axis(example to rotate it). Example 1: Consider an object of Mass $m$ ...
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König Theorem with revolving center of mass frame

I have the following doubt: suppose the center of mass frame itself of a system of particles is revolving around a given axis in a fixed reference frame with origin $O$ (let the origins of the two ...
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Isospin and Clebsch Gordan coefficients [closed]

If I have to combine 2 spin $\frac{1}{2}$ particles I do with Clebsch Gordan coefficients so that for example $|{\frac{1}{2},\frac{1}{2}}\rangle|{\frac{1}{2},\frac{-1}{2}}\rangle=\frac{1}{\sqrt{2}}(|{...
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Dirac's Principles of Quantum Mechanics, Electron Spin

In Section 37 (The spin of the electron), Dirac writes, "The eigenvalues of $m_z$ are $\hbar/2$ and $-\hbar/2$, so the eigenvalues of $\sigma_z$ are 1 and -1, and $\sigma_z^2$ has just the one ...
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Problem with formula for cylindrical chandelier problem

The problem says: A cylindrical chandelier is hung on a wire and when it rotates around its siege an angle $\theta$ the twisting moment acting on it is $\tau$ = $−\theta$. The moment of inertia is ...
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Can a magnetic field have a orbital angular momentum

Is it possible to 'twist' a magnetic field? I am not referring to the electrical field but the actual magnetic field. In OAM (orbital angular momentum) we can twist light waves and sound waves however ...
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Why should angular momentum be conserved in this case?

Consider two disks (not friction-less) with some moment of inertia ($I_1$ and $I_2$). Both of them are given angular velocities ($\omega_1$ and $\omega_2$) both in same sense. Now if we bring both ...
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Wigner's $9$-$j$ symbol - four electrons orbital angular momentum coupling

In constructing the total angular momentum operator, that is the sum of 4 independent angular momentum operators: $$J=J_1+J_2+J_3+J_4 $$ one has the following set of commuting operators and ...
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Invariance of angular momentum states to 180 degree rotations

Can it be shown that an angular momentum eigenstate $ | j, 0 \rangle $ with even $j$ is invariant to 180 degree rotations about the y axis (or any axis $\bot$ z)? I was able to do this using ...
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Hilbert space of two particles of spins $j_1$ and $j_2$, noninteracting versus interacting

For a system of two noninteracting particles of spins $j_1$ and $j_2$, the joint Hilbert space $\mathcal{V}$ is the tensor product of the individual Hilbert spaces $\mathcal{V}_1$ and $\mathcal{V}_2$. ...
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Conservation laws in Newtonian mechanics

Newton's third law is equivalent to conservation of momentum. Assuming conservative systems, we get conservation of (mechanical) energy. Assuming central forces, we get conservation of angular ...
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Why does $[L_i,\textbf{L}^2]=0$ and $[L_i,H]=0$ imply that $[\textbf{L}^2,H]=0$?

For a particle in a central potential, the orbital angular momentum magnitude operator $\textbf{L}^2$ commutes with the Hamiltonian operator $H$, i.e. $$[\textbf{L}^2,H]=0.$$ I read that one way to ...
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Why do unfixed objects always rotate about their centre of mass?

Statement: I understand similar questions have been asked; however, none of them really helps me. The detailed version of my question is as follows: Why do unconstrained and unfixed objects always ...
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Can a non-rotating black hole start rotating?

Can a non rotating black hole start rotating? Intuitively it is not possible, but intuition often leads to wrong conclusions. I have only basic physic knowledge, however I like to wonder about ...
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How can black hole rotate? [duplicate]

I was reading about black holes and I've found part saying that black hole is a point and anther saying that black hole can rotate. However the points are dimensionless, so they can't rotate - How can ...

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