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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4
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2answers
850 views

Apparent violation of Newton's 3rd law and the conservation of angular momentum for a pair of charged particles interacting magnetically

Consider a system of the two identical point positive charges situated in the space (isolated from influence of any other external fields) as shown in the figure.Particle1 is at (a,a,0) and Particle2 ...
-2
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0answers
19 views

Max speed of a turning disk for an object to stay at rest

A coin is at rest relative to a disk moving with a angular speed of w: The coin weighs 0.010 kg The distance of the coin to the center of the disk is of 0.20 m The static friction is of 0.45N ...
2
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1answer
40 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
51 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 ...
2
votes
2answers
1k views

How is parity relevant to determining angular momentum?

Question: Particle A, whose spin $\mathbf{J}$ is less than 2, decays into two identical spin-1/2 particles of type B. What are the allowed values of the orbital angular momentum $\mathbf{L}$, ...
3
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1answer
49 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 ...
2
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1answer
84 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 ...
0
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2answers
113 views

How does angular momentum affect the trajectory of a projectile?

I am thinking about a football thrown in a very tight, very fast spinning spiral. If the football is thrown upwards at a high angle, is it possible for the football to not turn over at the top of its ...
0
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1answer
35 views

Angular momentum & Energy using Yukawa's potential

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 ...
0
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0answers
21 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 ...
4
votes
2answers
82 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 ...
1
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0answers
32 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
vote
1answer
33 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 ...
0
votes
1answer
173 views

General definition of vector, spinor, and spin

I am looking for basic and exact definitions of fundamental physical concepts in graduate level. I reach this following definitions. Could you please help to improve these definitions. Spin: ...
4
votes
2answers
82 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 ...
1
vote
1answer
97 views

What are phase conventions in angular momentum and rotation calculations?

I work with complicated angular momentum calculations related to atomic physics; nevertheless, I never need to use anything related to a phase convention (apparently because it's taken care of in a ...
2
votes
2answers
56 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
41 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
49 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 ...
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0answers
23 views

How can I find the equation of motion? [duplicate]

There is a point of mass moving in the xy-plane with harmonic forces acting in x- and y-direction $F_x=-m\omega^2x$ and $F_y=-m\omega^2y$. At the same time there is an additional force acting in the ...
14
votes
3answers
1k 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 ...
0
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0answers
38 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?
3
votes
1answer
270 views

What does Weinberg–Witten theorem want to express?

Weinberg-Witten theorem states that massless particles (either composite or elementary) with spin $j > 1/2$ cannot carry a Lorentz-covariant current, while massless particles with spin $j > 1$ ...
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0answers
27 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
61 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?
7
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3answers
2k views

What made Bohr quantise angular momentum and not some other quantity?

Bohr's second postulate in Bohr model of hydrogen atom deals with quantisation of angular momentum. I was wondering, though: why did he quantise angular momentum instead of some other quantity?
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2answers
63 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 ...
1
vote
2answers
85 views

Where does the angular momentum of the solar system come from? [duplicate]

We inhabit a system with significant angular momentum: http://www.zipcon.net/~swhite/docs/astronomy/Angular_Momentum.html If our solar system formed by gravity gathering its material together to ...
0
votes
1answer
61 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 ...
0
votes
3answers
108 views

Since the gravitational force is only attractive, why does matter not just concentrate into a small sphere?

This doubt has been wandering in my head for a long time. The gravitational force is only attractive force not a repulsive force. Since gravitational force is only attractive force, why not the ...
2
votes
1answer
57 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. ...
1
vote
1answer
42 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 ...
2
votes
1answer
34 views

For Charmonium, why does the spin-spin interaction mostly affect the $L = 0$ states?

For Charmonium, why does the spin-spin interaction mostly affect the $L = 0$ states? My textbook states that this is because "only then is the wave function at the origin non-vanishing". Could anyone ...
1
vote
1answer
109 views

Total magnetic moment in an atom

I have a doubt regarding the calculation of total angular momentum of electron in an atom. Which is the right way to do it? Method 1: Total magnetic moment $$ \begin{align} \vec{\mu_J} &= ...
3
votes
1answer
55 views

3D isotropic oscillator and angular momentum algebra

In our QM class, the prof said: "We are ready to begin constructing the individual states of the 3D isotropic harmonic oscillator system. The key property is that the states must organize ...
0
votes
1answer
125 views

Equivalency of conditions involving angular momentum of a rolling ball hitting a wall

(59th Polish Olympiad in Physics) A ball of mass $m$, radius $r$ and a moment of inertia $I = \frac 25 mr^2$ is rolling on the floor without sliding with the linear velocity $v_0$. It hit the wall ...
2
votes
2answers
49 views

Correct vector space of eigenkets of angular momentum

When we say an particle is in the state: \begin{equation} |l,m\rangle, \end{equation} what is the underlying state space, as a vector space? Is it a tensor product vector space, of dimension: ...
1
vote
1answer
24 views

Force responsible for increasing a spiraling object's tangential velocity

Suppose we have a small mass attached to a string that has been fed through a hole in the friction-less table on which the mass is rotating. Pulling the string downwards thus decreases the radius of ...
0
votes
3answers
641 views

Conservation of Angular Momentum, as related to a flywheel

Trying to work out some pesky flywheel dynamics for a project I'm working on, would love some for your assistance to better understand the underlying concepts. For a given flywheel (thin-walled ...
0
votes
1answer
147 views

Difference between expectation values of $L^2$, $L_z$ and measuring $L^2$, $L_z$

I was given with this hydrogen radial wavefunction $$ R_{21} =\left(\sqrt{\frac{1}{3}}Y^0_1 + \sqrt{\frac{2}{3}}Y^1_1\right) $$ and was asked to find a) What are the expectation values of the ...
2
votes
1answer
38 views

Notation of angular momentum operators vs numbers

I'm reading about finding the mass of quarks in mesons. In the lecture notes, it says We need to find $\langle\boldsymbol{s}_q\cdot\boldsymbol{s}_\bar{q}\rangle$. Since $L=0$, then ...
0
votes
2answers
79 views

Meaning of the Angular Momentum in Quantum Mechanics

There was a discussion about the angular momentum in QM in an online course that I am attending now. The discussion and the answers did not satisfy me so I wanted to ask it on Physics SE. In the ...
2
votes
3answers
161 views

Deriving cross product from angular momentum algebra

Is it possible to derive: \begin{equation} \hat{L}=\hat{r}\times \hat{p} \end{equation} from the angular momentum algebra: \begin{equation} [\hat{L}_i,\hat{L}_j]=i\ \hbar\ \epsilon_{ijk}\hat{L}_k\ ? ...
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2answers
100 views

In the time of the dinosaurs the Earth rotated once in 17 hours rather than about 24 hours, where did the rotational energy and angular momentum go?

where did the rotational energy and angular momentum go? Some claim that the angular momentum went to the Moon. Astronauts put a corner reflecting mirror on the moon and reflected a Laser and timed ...
2
votes
0answers
162 views

Collision of Discs and Snooker Kicks

I woke up this morning thinking about spinning discs. Could someone verify whether my reasoning below is correct? Problem 1 Suppose have two identical uniform discs constrained to move in a plane. ...
1
vote
1answer
46 views

Movement and Rotation of a Inverted-Pendulum-like Object with External Forces

I'm struggling to model the movement of a complex object based on an external force. Let's start with a simple example of what I'm looking for. We have a block $b$ of mass $M_b$, moving ...
2
votes
3answers
173 views

Physical interpretation of applying a unitary operator to a state

When we apply one of the Pauli matrices $\sigma_y$ on one of its eigen-vectors $| \odot \rangle$, what does the eigen-value tell us about $| \odot \rangle$? Is this considered a measurement of $| ...
5
votes
1answer
592 views

What does it mean for a particle to have spin of 2? [duplicate]

When I first started to study quantum mechanics, my physics text book told that particles have spin of either 1/2 or -1/2. Then I recently read an article saying that gravitons are expected to be ...
2
votes
2answers
40 views

Why does the raising operator, when acting on a ket with a maximum second quantum number, yield zero?

I'm studying the general formalism of angular momentum in quantum mechanics from Zettili's "Quantum Mechanics: Concepts and Applications", and came across the following equation (labeled 5.37) on page ...
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0answers
28 views

How to calculate angular momentum in this scenario? [closed]

The answer to part a) is 1080. However, for part b) I don't understand why the equation wouldn't simply be $I_i\omega_i = I_f\omega_f$. Why do we have to subtract $m_bv cos \phi$ from ...