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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83 views

Free rotation of a rigid body

So I am currently reading Fowles and Cassidy and there is something I'm confused about in the section about geometric description of free rotation of a rigid body. I will present the stuff first that ...
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1answer
55 views

Drag in low earth orbit

So I'm looking at the following problem; Arrow type configuration in orbit. Each end of the arrow has a mass and a cross sectional area (we can assume the head and tail are connected by a ...
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2answers
85 views

Generalization of torque and angular momentum

Question: in the simple equations $\tau = r \times f$ and $L = r \times p$, what is the origin of the vector $r$? In many textbook discussions on rotation of a rigid body about a fixed axis, $r$ is ...
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2answers
67 views

Larmor Precession - What does precession actually means?

Larmor Precession - What does precession actually means? Is it change in the orientation of the axis with which electron revolves around the orbit or what. But, shouldn't the radius of the orbit ...
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2answers
99 views

Why is only one quantity of angular momentum i.e. $L_z$ quantized & not $L_x$ & $L_y$?

This is quoted from Arthur Beiser's Concepts of Modern Physics: Why is only one quantity of $\mathbf{L}$ quantized? The answer is related to the fact that $\mathbf{L}$ can never point in any ...
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3answers
53 views

Why can't the angular momentum vector be parallel or anti-parallel to the applied magnetic field?

This is the excerpt from my book, Arthur Beiser's Concepts of Modern Physics: An atom with a certain value of $\displaystyle{m_l}$ will assume the corresponding orientation of its angular ...
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2answers
69 views

Using rotation matrix for spin to write x oriented spin in z-spin basis

$\newcommand{\ket}[1]{\left| #1 \right>}$The problem is to write the ket vector for a particle with spin +1/2 along the x axis, in terms of the standard basis vectors $\ket{+1/2}$ and $\ket{-1/2}$ ...
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25 views

How is angular momentum conserved in this proton+water scenario?

Consider a universe consisting of only one water molecule and one proton. ...
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1answer
45 views

If I start spinning a raw egg slowly why does its angular velocity increase spontaneously?

If I start spinning a raw egg very slowly in place, why does its angular velocity increase spontaneously? This is something I noticed the other day while cooking. It doesn't do the same thing with a ...
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1answer
35 views

Schaum explication of eigenvectors of Lz

In Schaum's Quantum Mechanics, in Chapter 6 Angular Momentum, they say "the eigenvectors of $L^2$ and $L_z$ are functions that depend on the angles $\theta$ and $\phi$ only; hence, we can represent ...
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1answer
24 views

Combining moments of Inertia in gear chain

I've got two objects connected by a rod along it's axis of rotation (e.g. a sphere on top of a flat cylinder rotating around it's symmetric axis). Assuming the effects of the rod are negligible, is ...
1
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1answer
53 views

Operator in Hilbert space of a spin

I'm studying quantum mechanics with Shankar's "Principles of Quantum Mechanics" 2nd edition. I'm afraid that it might be a boring question but I can't understand the following statement (389p): We ...
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0answers
73 views

What is this nested bracket notation?

The following is an excerpt from K. Varga's paper, Precise solution of few-body problems with stochastic variational method on correlated Gaussian basis: ...The function $θ_{LM_L}(\mathbf{x})$ in ...
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1answer
57 views

Negative sign in rotation operator (quantum mechanics, angular momentum)

Schaum's Quantum Mechanics comes up with $$\exp((-i/\hbar)\cdot \theta \cdot{\hat{L}} \cdot {\overrightarrow{n}})$$ as the formula of the rotation operator. Other sources I see don't have the ...
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1answer
66 views

Do particles have spin because there exist spinor representations for the Lorentz group?

I am reading Peskin and Schroeder's An introduction to field theory. They first describe the spinor representation of the Lorentz group, and then they mention the fact that different particles have ...
0
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1answer
73 views

Why do $H$ and $L^2$ commute in spherically symmetric potential?

In this PDF document (a lecture by Shivaly Reddy, page 13), he says that $L^2$ is independent of $r$; therefore it commutes with any function of $r$. This seems related to a problem in ...
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1answer
72 views

What is really the force required to open a door?

I found a few Phys.SE threads in which an impulse is used to exert a torque on a rod, is it possible to get a realistic description of the force required to open a door?: If we have a free 'door' ($l ...
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1answer
48 views

conservation of angular momentum/conservation of energy?

Perhaps a dumb question to ask, but I was given the following problem to solve: A 10 g bullet traveling at 400 m/s strikes a 10 kg, 1.0-m-wide door at the edge opposite the hinge. The bullet embeds ...
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2answers
127 views

$\hat{L}_{x}$ and $\hat{L}_{y}$ do not commute… or do they?

So $\hat{L}_{x}$ and $\hat{L}_{y}$ do not commute: $ [ \hat{L_{x}}, \hat{L_{y}}] = i\hbar \hat{L_{z}}$ But, what if we perform this operation on a state such that: $\hat{L_{z}} \phi_{l, m_{l}} = ...
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1answer
35 views

Expectation value of total angular momentum $\langle J \rangle$

[I am working with Griffiths Introduction to Quantum Mechanics, 3rd Edition. My problem is general but if you want to look I am reading from ch 4.1 in which the weak-field Zeeman Effect is being ...
0
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1answer
18 views

Angular momentum conservation laws and GHZ article (Greenberger et al 1990)

Can anyone recommend a good book or an online source on angular momentum conservation laws in decay processes? I'm writing a master's thesis concerning Bell inequalities and currently working on GHZ ...
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2answers
50 views

Does momentum change if rotation radius changes?

Angular momentum is defined as $L = r \times p$ where r is the center of rotation and p is the momentum. Since angular momentum is conserved, if r decreases then p must increase. And since p is m*v ...
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1answer
118 views

if the Earth's rotation was slowed down, would it naturally speed back up as it was before? [closed]

Fact: The Earth is rotating on it's own axis every 24 hours. Question: If, for some reason I won't specify the current speed of the Earth and could slow it down(say by 5%). Will it speed up again ...
0
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1answer
36 views

Torque in a non-inertial frame

How can we calculate torque in a non-inertial frame? Take for instance a bar in free fall with two masses, one on either end, $M_1$ and $M_2$. Taking the point of rotation to not be the center of ...
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1answer
58 views

Getting to spins of arbitrary direction

Let me rephrase this question: Let us assume we know that symmetry transformations always look like this: $$U(s)=e^{iKs} $$ with a hermitian Operator K. This tells us that for very small $s$: ...
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0answers
24 views

Expectation value in spin-orbit coupling

So I was just trying a question where it asked to find the Energy shift due to a spin-orbit coupling Hamiltonian to first order using perturbation theory. The Hamiltonian is $$H_{LS} = ...
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0answers
29 views

Addition of 3 angular momenta

I'm struggling to understand how the orbital angular momentum "add" in ground state Nitrogen. As I understand it N has an electron configuration of $1s^22s^22p^3$ and so the 3 outer electrons in the ...
2
votes
2answers
88 views

Deflection Effects on a Spinning Solar Sail

Suppose I have a solar-sail-powered starship flying directly away from a star. The sail is flat and perpendicular to the direction of travel. Now, in order to make the trajectory more stable (we ...
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0answers
74 views

Why Does Moving a Cup of Coffee Up and Down whilst carrying it Make it less Likely to Spill?

Sometimes I have a Very Full Mug of Coffee and I am trying to carry it without it spilling. I noticed that if I moved the Mug up and down when carrying it, it seemed to settle the coffee and make it ...
2
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1answer
58 views

Particle Physics Decay Question - Eta Prime Decay Parity/Angular Momentum Conservation

I was hoping someone could clarify why the following decay does not occur: $ \eta ^{'0} \rightarrow \pi ^{0} + \rho ^{0}$ The quark compositions and spin parity are as followed: $ \eta ^{'0} : ...
0
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1answer
59 views

Shape of galaxies [duplicate]

i want to know why galaxies are spiral in nature.. let us say there is some sort of intense mass (black hole?) at the centre of our milky way galaxy. the intense gravitaional pull is keeping evey ...
4
votes
1answer
63 views

Does Birkhoff's theorem apply to rotating collapsing stars?

Birkhoff's theorem states that every spherically symmetric vacuum solution to $R_{\alpha\beta} = 0$ is static, which greatly assists in the solution to the Schwarzschild solution by eliminating time ...
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1answer
40 views

Angular momentum & Energy using Yukawa's potential [closed]

I was doing my Gravitation problems and I found this one that I'm unable to solve. Yukawa's theory for nuclear forces states that the potential energy corresponding to the attraction force ...
2
votes
1answer
93 views

Angular momentum - proof for integer eigenvalues

I am confused about a proof my Quantum Mechanics textbook has left "as an exercise for the reader". So, we've got the angular momentum operator $\hat{L}$. We've also got the generalized angular ...
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0answers
25 views

Need clarification for Relation between angular momentum and centripetal force

I've recently started studying angular momentum, so, as far as I understand, angular momentum is conserved as long as any form of centripetal force can be maintained in the new system or otherwise it ...
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0answers
39 views

how to rotate scaled-vector (orientation) by scaled-vector (rotation)

Recently I seem to have gotten the physics-engine portion of my 3D simulation/game engine [apparently] working correctly. The most convenient way to store and compute position and orientation are in ...
1
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1answer
80 views

Why does a diver changes his body positions before and after diving?

Before a diver dives in a pool, he changes his body positions several times. When he is about to jump from board he extends his arms and legs but sometime after jumping he closes his body in a ...
3
votes
2answers
103 views

How does the kinetic energy of a ballerina increase? [duplicate]

When a ballerina pulls her arms in, her rotational kinetic energy increases because angular momentum is conserved. That means that work must have been done on her. I saw somewhere that there is work ...
4
votes
2answers
105 views

Spin, orbital angular momentum and total angular momentum

If I understand correctly, spin is an intrinsic property of particles, which follows the algebra of angular momentum, but has nothing to do with an "orbital angular momentum" in that the particle is ...
2
votes
2answers
80 views

Relation between magnetic moment and angular momentum — classic theory

How do I prove the relation between the vectors of magnetic moment $\vec\mu$ and angular momentum $\vec L$, $$\vec\mu=\gamma\vec L$$ ? Many text books and lecture notes about the principles of ...
1
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2answers
56 views

Conservation of angular momentum about combined center of mass

If a ball collides with and sticks to an unhinged uniform rod on a smooth table (the path of the ball does not necessarily pass through the center of the uniform rod), is angular momentum conserved ...
1
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1answer
95 views

Spin commutation relations

For orbital angular momentum defined as $L= r \times p $ we can prove, in quantum mechanics, the commutation relations. Also, we could prove these relationships through the study of rotations ...
14
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3answers
2k views

Does holding weights allow you to run faster?

I'm not talking about training with weights so that when you run without them your muscles are used to pushing more weight so with less weight it'll be easier, I'm talking about while actually holding ...
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0answers
41 views

Star vs Blackhole - Accretion Disk

Simple question: can we prove that what we call today a "star" is not a accretion disk of a "tiny" black hole that happens to rotate in all the 3 axis?
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0answers
33 views

commutation relation of angular momentum operator in non cartesian coordinates

The angular momentum operator $J$ in quantum mechanics with the commutation relation \begin{equation*} [J_i,J_j]=i\hbar\epsilon_{ijk}J_k \end{equation*} has the structure of a Lie-algebra. It is ...
3
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1answer
75 views

Angular momentum conservation at quantum level

how angular momentum of system is conserved when electron jumps higher energy state to lower energy state and photon is emitted(circularly polarized)? i read somewhere that it is NOT conserved .Why?
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66 views

Calculations with angular momentum

Is the following correct, when adding 3 angular momenta/spins: \begin{align} 1\otimes 1\otimes \frac{1}{2}&=\left(1\otimes 1\right)\otimes \frac{1}{2} \\ &=\left(2\oplus 1\oplus ...
3
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1answer
107 views

How to use Clebsch-Gordan coefficients for 3 particles?

I have a Hamiltonian for 3 particles of spin 1 that I boiled down to: \begin{equation} k(\textbf{S}^2+\cdots), \end{equation} where: \begin{equation} \textbf{S}=\textbf{S}_1+\textbf{S}_2+\textbf{S}_3. ...
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1answer
55 views

After a glancing collision, why do air hockey pucks spins around in circle?

For a lab testing the conservation of momentum, I had to hit an air hockey puck so that it would hit another stationary puck in a glancing collision. After the pucks collided, they travel their ...
0
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1answer
73 views

Free-falling from rest into a Kerr black hole

Is it impossible for a particle (with zero angular momentum) to free-fall from rest at infinity into the ergosphere of a Kerr black hole? It seems like it is very easy to show this is the case, but ...