# 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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### Balance of a spinning coin

If we place a typical coin on a table, it will almost immediately fall due to gravity. However, with a little push it will roll and not fall anymore until friction eventually slows it down enough to ...
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### How many illusionary axes of rotation can coexist?

Consider the answer to this question: How many different axes of rotation can coexist? Any rigid body, at any time, can only be rotating about one instantaneous axis of rotation. Now, that ...
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### Transformation of the derivative of the scalar field in Ramond's book about QFT

In the book by Pierre Ramond about quantum field theory, he explores in chapter 1.4 (p.13) the behavior of fields under Poincaré transformations. He starts by explaining that infinitesimal ...
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### Quantization of angular momentum of system of particles

Suppose there is a system of particles interacting with each other. Is it the angular momentum of each particles which would be quantized as $\sqrt{n(n+1)} \hbar$ or is the angular momentum of the ...
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### Does asymmetric rigid body experience torque-free precession?

I know that a top (or any axis symmetric body) experience torque-free precession. and I know that asymmetric body, with 3 different dimensions has stable rotation when the angular velocity is near the ...
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### Equivalent definitions of total angular momentum

Consider the equality \begin{equation}\exp\left(-\frac{i}{\hbar}\boldsymbol{\phi J}\right)\left|x\right>=\left|R(\phi)x\right>,\end{equation} where $\left|x\right>$ denotes a position ...
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### Angular momentum of a cylindrical system in general relativity

The definition of energy and enegry flux of a cylindrical symmetric system in general relativity is given by Kip Throne in Phys. Rev. 138, B251 and generalized by Chandrasekhar in Proc. Roy. Soc. Lond....
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### How is angular momentum conserved for the orbiting body if the centripetal force disappears? [duplicate]

When the centripetal force on an orbiting body disappears (e.g. if it the body is a ball and the force was exerted by a string and the string rips, or, more unrealistically, if the body is the earth ...
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### Why is the angular momentum of a 3D kicked rotor non-negative?

We know that for a 2D kicked rotor the angular momentum quantum number can be any integer from minus infinity to infinity. However, for a 3D kicked rotor this is not the case: it can only be positive ...
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### Why conserve angular momentum about COM

In many questions involving collisions between Rigid bodies angular momentum is conserved about center of mass If bodies stick together after collision they estimate com and then conserve about ...
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### Linear momentum of a rotating system

So say we have a thin rod resting horizontally on a flat frictionless surface. The rod is pinned at its center, and a small mass collides perfectly inelastically with one end of the rod after moving ...
Let $\Bbb R^3$ be our configuration space. Consider the Lagrangian $L\colon T\Bbb R^3 \cong \Bbb R^6 \to \Bbb R$ given by$$L(x,y,z,\dot{x},\dot{y},\dot{z}) = \frac{m}{2}(\dot{x}^2+\dot{y}^2+\dot{z}^3) ... 1answer 49 views ### Angular momentum operator in different bases The Eigenvectors of L_3 (for spin 1) are \left| m \right> with m=1,0,-1. One can compute the matrix D_i=\begin{pmatrix}\left< 1 \middle| L_i \middle| 1 \right> & \left< 1 \... 1answer 63 views ### What would be the direction of force exerted on two stationary posts by pivoting levers which are spring loaded? [closed] I am having a difficult time with visualizing/determining what would be the direction of force exerted on two stationary metal rods by two pivoting levers which are spring-loaded. To help explain ... 2answers 81 views ### Quantized value of spin angular momentum and underlying mysteries I think the quantized value of the spin angular momentum is \hbar/2  rather than \hbar  is the basic reason for the 4\pi rotation of a wave function to retain its initial state again? Is it true?... 1answer 33 views ### Uranus: The Spin In his prog. , on the outer planets, Brian Cox stated that Uranus spins on its side because it once endured an interplanetary collision. Such a cataclysm would normally be devastating for both ... 0answers 30 views ### Particle interactions simulator I'm an A-Level student trying to write a program that will take in two particles (like a proton and electron) and output the new particles. I'm planning to implement the conservation laws so that the ... 1answer 38 views ### Radius vs speed for flywheel energy storage If I understand the formula correctly, the equation for kinetic energy of a flywheel is mw^2r^2 whereas the formula for "centrifugal force" is mw^2r. So how come so much focus is on the speed of ... 1answer 1k views ### Why don't all electrons contribute to total orbital angular momentum of an atom? There are 47 electrons in a Silver atom, but talking about its orbital angular momentum we only take the outermost valence electron which occupies the 5s orbital. Why don't the remaining inner 46 ... 3answers 50 views ### Angular momentum and angular velocity The angular velocity \vec{\omega} lies along the axis of rotation. And the angular momentum \vec{J} is the cross product of \vec{r} \times \vec{p}. Which according to me should also lie along ... 1answer 63 views ### Conservation of Angular Momentum in Spherically symmetric potential In Goldstein Book it is given that: Since the problem is spherically symmetric, the total angular momentum vector$$\boldsymbol{L}=\boldsymbol{r}\times \boldsymbol{p}$$is conserved. What does the ... 2answers 36 views ### Confusion in conservation of angular momentum Problem statment: A rod hinged at one end is released from the horizontal position. When it becomes vertical its lower half separates without exerting any reaction at the breaking point. Then find the ... 2answers 35 views ### Angular momentum and Gyroscopic precession of a top [closed] A top is spinning in the counterclockwise direction as seen from above. Its axis of rotation makes an angle of 15º with the vertical. If frictional forces can be neglected, which of the following is ... 3answers 32 views ### Is the velocity of the spinning rod constant after it's hit? Say we've got a rod floating around in space, with two masses of m_0, one attached at each end. Let's say the rod has a length of l. There's another mass, m_1, moving at some velocity v ... 0answers 50 views ### Spacial Wavefunction Symmetries and Identical particles I was reading this and it mentions in the 3-electron section, that for a spacial wave function to be symmetric under fermion swapping, it must be a function of even parity. Similarly for anti-symmetry ... 0answers 74 views ### Ground state of an odd, deformed nucleus: intuition for what happens to the j_x and j_y of the odd particle This is something that relates closely to my long-ago PhD research, and it's a point that I never satisfied myself thoroughly on. I have a copy of a standard text that covers this general topic, de ... 1answer 55 views ### How can a non-rotating black hole or singularity be created? Every star or other massive body in the universe rotates, if only a little. If such a body collapses, its spin, any spin at all, and thus, angular momentum approach infinity as r approaches 0. Angular ... 0answers 49 views ### If there are eigenstates of L_z in a degenerate subspace, are there also eigenstates of L^2? The question arises from an exercise but tackles deeper understanding of angular momentum operators. Suppose we have a 2D harmonic oscillator and an infinite square well in the third dimension: \... 7answers 3k views ### If the mass of the Earth is decreasing by sending debris in space, does its angular momentum also decrease? [duplicate] We are sending huge amount of debris into space from earth, and also very heavy satellites and rockets, then the mass of earth must be decreasing over time. If the mass will decrease, then ... 1answer 46 views ### What is the significance of having two formulas for area moment of inertia? What is the significance of calculating area moment of inertia twice? I mean calculating area moment of inertia w.r.t axis and calculating same area moment of inertia w.r.t centroidal axis? Why not ... 0answers 31 views ### What's the relation between the Lorenztz group and spin of particles? I know that particles are defined in terms of irreducible representations of the Poincaré group, and that the state of a massive particle is defined by its mass and spin, which are the eigenvalues of ... 1answer 73 views ### An ice cube orbiting the Earth Recently I am stuck with a question about an ice cube that is orbiting the earth from a certain radius and it starts to melt down by the sun. Which of the followings are wrong? The cube will start ... 1answer 35 views ### Wicks contractions of stress-energy tensor and plane partitions I am working out the number of wick contraction of a number n of stress-energy tensor in 4D CFT. The strategy is as follows: For 1 stress energy tensor T_{\alpha\beta}, you have only one ... 1answer 23 views ### Conservation of Angular momentum or Work = 0 , which is valid? In the figure, the block on the smooth table is set into motion in a circular orbit of radius "r" around the Center hole. The hanging mass is identical to the mass on the table and remains in ... 1answer 51 views ### Some Clebsch-Gordan coefficients for j_{1}=1 and j_{2}=1 I've successfully derived every coefficient, but not the one that has j=0. Starting from |J=2,M=2⟩ and applying J_{-} we derive |2,1⟩ and |2,0⟩ and using orthonormality (and the Condon-... 1answer 72 views ### Show that when angular momentum L_x and L_y commute with operator G, then L_z also commutes with G I want to prove that if Angular momentum L_x and L_y commute with an operator G, angular momentum L_z also commutes with G. if [L_x , G] = [L_y, G] = 0 then [L_z , G] = 0 I know that ... 3answers 129 views ### Strange bra-ket notation I encountered a question, where I need to find the constant. But the state is given like this:$$|\psi\rangle = A(|1,1\rangle -i|1,-1\rangle+2|1,0\rangle)$$So normally eg. when the state is given ... 2answers 43 views ### Angular velocity of thrown object? I was reading this and came across the statement After releasing the knife, it will fly forward and continue to rotate around its center of gravity with the same angular velocity it had during ... 1answer 39 views ### Reaction wheel: angular momentum conservation or action-reaction? Reaction wheel are commonly used in spacecraft to change its attitude: an onboard inertia wheel is accelerated or decelerated along an axis to make the spacecraft rotate around the same axis. While ... 1answer 74 views ### Spin of elementary particles Going by the explanation given by Stephen Hawking (as given in Brief History of Time) , the spin of a particle is no. of rotation you give to that particle so that it looks the same. Like you give ... 0answers 34 views ### Angular momentum and external torque In John Taylor - Classical mechanics it was mentioned that the equation L' = \Gamma^{ext} is true even with respect to the center of mass. Here we are working with a system of particles, L = \sum ... 1answer 91 views ### **Mathematical Derivation** of the fact that all planets will orbit on the same plane There is some discussion about this Here. If an isolated system of particles under gravitational force is allowed to decrease its energy by means such as inelastic collision, then eventually all ... 1answer 50 views ### Symmetries of Wigner 3j-symbols by exchange I know that Wigner 3j-symbols have certain symmetry factors arising by exchange of two columns within one symbol. But what happens if you have two 3j symbols and do an exchange like this:  \left(\... 2answers 48 views ### How are these two versions of the conservation of angular momentum different? Here are two versions of the conservation of angular momentum. The total angular momentum is constant if there is no external moment on the system The total angular momentum of a particle is constant ... 1answer 45 views ### Why is L_z operator more important the L_x or L_y operators? When we talk about orbital angular momentum, we always use L_z but never talk about L_x or L-y. Why is that? 0answers 28 views ### Symmetry relation of Wigner-Eckart I saw a symmetry relation following from the the Wigner-Eckart Theorem looking like this$$(\xi j|| T_L || \xi'j') = (-1)^{j-j'} (\xi' j'|| T_L || \xi j)^*$$I know that it must come somehow under ... 0answers 29 views ### Noether current Lorentz rotation massive vector field I'm considering a massive vector field in classical field theory. With the Lagrangian density$$\mathscr{L}=-\frac{1}{4}V^{\mu\nu}V_{\mu\nu}+\frac{1}{2}m^2V^{\mu}V_{\mu}.$$I want to prove from the ... 1answer 90 views ### Why does electron-positron annihilation conserve parity? I think I'm missing something quite basic here but consider the process:$$ e^- + e^+ \rightarrow 2\gamma$$Fermions have opposite parity to antifermions so the parity quantum number before the ... 0answers 30 views ### Matrix representation in angular momentum basis I'm trying to find a way to verify that the following expansion is valid for any potential, including noncentral ones,$$ \langle \textbf{k}' |V|\textbf{k}\rangle = \frac2\pi\sum_{lm} V_l (k', k) Y_{...
General arguments about introduction of angular momentum to QM is that under a transformation of coordinates the x and y position operators mix (as it is usually written) \hat{x}' = \cos(\theta) \...