# 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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### Generators of Lorentz transformations

In Chapter 3 of Peskin and Schroeder's Introduction to Quantum Field Theory they write For the rotation group, one can work out the commutation relations by writing the generators as differential ...
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### Physical interpretation of generators of Lorentz boosts

Lorentz transformations can be thought of as pure rotations and pure boosts. The generators of the rotations are proportional to the angular momentum of a physical system. What is the physical ...
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### Conservation of angular momentum using symmetry properties

Goldstein pg 59 It can be shown that if a cyclic coordinate $q_{j}$ is such that $d q_{j}$ corresponds to a rotation of the system of particles around some axis, then the conservation of its ...
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### Change in angular velocity of an initially non-rotating spherical object after a collision

In the theoretical scenario below: Will the object rotate? My first thoughts on this were: The initial angular velocity is $0$. This means it does not have any angular momentum (right...?) and it ...
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### Why do planets have a greater linear velocity closer to the Sun?

I get that the planets need to have a higher velocity to escape the gravitational well which is deeper when closer to the sun. What I don't understand is what causes this higher velocity. Am I missing ...
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### Angular velocity across different reference frames

In classical mechanics: Logically, it appears to me that if I draw a mark on a ball and let it roll, the amount of time that will pass before the mark reaches the same position (in terms of angles: ...
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### A query regarding the definition of Conservation of Angular Momentum

Assuming two hollow cyliders $C_{\text{in}}$ and $C_{\text{out}}$ with radius $r_{\text{in}}$ and $r_{\text{out}}$ such that $r_{\text{in}} < r_{\text{out}}$. Each of the cylinder is uniform and of ...
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### Commutator of spin operators

Suppose we are given $\left[S_X, S_Y\right]$, $\left[S_Y, S_Z\right]$ and $\left[S_Z, S_X\right]$, that is the spin operator commutation relations, can we then determine the matrix representation of ...
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In physics, we often use resolutions of identity $$\sum_n |n\rangle\langle n|=\mathbb{I}$$ to simplify expressions. Sometimes, the "full matrix" (for lack of a better term) \sum_{m,n}|m\... 2answers 44 views ### Composition of angular momentum (quantum): how do we know that finding common eigenspace of J^2 and J_z is enough for degeneracy? I have some basic question on composition of angular momentum (actually spin in my case), I forgot some basis. The fundamental commutation relations between J_x,J_y,J_z (the three components of the ... 2answers 55 views ### Reaction torque of angled nutrunner I have a question regarding the behavior of an right-angled, air/electrical powered nutrunner. More specifically, the reaction torque that the operator is subject to during operation. When the ... 1answer 82 views ### Rotations of spherical harmonics and Wigner D-matrices I seem to be having trouble understanding how Wigner D-matrices rotate spherical harmonics. I asked this question on the Maths Stack Exchange but decided to cast my net a bit wider and ask the ... 3answers 83 views ### Basics about angular momentum in quantum mechanics As usual let |l,m\rangle denote an eigenstate of \vec{L}^2 and L_z. I know that \begin{align} \vec{L}^2 |l,m\rangle &= \hbar^2 l(l+1) |l,m\rangle, \\ L_z |l,m\rangle &= \hbar m |l,m\... 1answer 33 views ### What is the conversion ratio of linear to angular momentum when a ball hits a rod in space? If the ball hits the rod at 90 degrees then the rod will start spinning, while also following the original trajectory of the ball. On what factors does the ratio between the two types of momentum ... 3answers 418 views ### Spin without quantum mechanics? In Emergence of spin from special relativity some answers discuss how spin can arise in non-relativistic quantum mechanics (let's not enter into those details here). However it is also argued that you ... 3answers 602 views ### Emergence of spin from special relativity I have pulled up and read as many answered questions as I can find here on why spin emerges as a consequence of making quantum mechanics compatible with special relativity- and still have problems ... 1answer 41 views ### How to prove Nitrogen atom with total angular momentum L=2 and L=1 are not anti-symmetric? I'm working on Problem 5.13(d) in "Griffiths 《Introduction of Quantum Mechanics》 2nd Edition". It asked to determine the nitrogen electron configuration by Hund's rule. And here is the ... 1answer 68 views ### Why Goldstein's book is claiming that radius and angle doesn't contain time variable even there is \dot{r} and \dot{\theta}?L=\frac{1}{2}m(\dot{r}^2+r^2\dot{\theta}^2)-V(r)p_\theta=\frac{\partial L}{\partial \theta}=mr^2\dot{\theta}\dot{p}_\theta=\frac{d}{dt}(mr^2\dot{\theta})$$Goldstein wrote that \dot{P}_\... 1answer 39 views ### Pulling a mass moving in a circle inwards [closed] In this question, I couldn't derive the right answer if I equate$$\text{tension} = \text{radial acceleration} = \frac{v^2}{r}Why shouldn't I equate that? 1answer 662 views ### Why is the rotation about COM? [duplicate] Suppose a ring is given to us with no hinge as such. Now a bullet comes and strikes the ring and gets embedded in the ring. The ring will now have linear momentum and some rotation going on. Okay, the ... 2answers 60 views ### General solution of a ball elastically colliding with a spinning rod I am working on finding the general solution to a disc colliding with a thin spinning rod in two dimensions floating in free space. The collision is perfectly elastic. The width of the rod is ... 1answer 23 views ### Inequalities of orbital angular momentum eigenvalues (show that is bounded) If we apply the rising/lowering operators for angular momentum to a state |{l,m}\rangle, we get: \begin{align} L_+|{l,m}\rangle = C_+(l,m)|{l,m+1}\rangle \\ L_-|{l,m}\rangle = C_-(l,m)|{l,m-1}\... 0answers 16 views ### Does Initial Angular Velocity Affect Loss of Angular Velocity in Collisions? I derived the following formula for change in angular velocity after a collision using conservation of angular momentum.I_1 ω_i+I_2 ω_2i=I_1 ω_f+I_2 ω_2fI_1 ω_i-I_1 ω_f=I_2 ω_2f-I_2 ω_2i...
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The Schwarzschild interior solution was found not so long after the exterior solution was found. I understand that Kerr solution is significantly more complicated and there are more conditions at the ...
### What is the physical significance of $\langle L_x\rangle=\langle L_y\rangle$ and $\langle L_x^2\rangle = \langle L_y^2\rangle$?
If we find the expectation value $$\langle L_x\rangle = \langle L_y\rangle = 0$$ and $$\langle L_x^2\rangle = \langle L_y^2\rangle,$$ what is the physical significance that their values are equal?