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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37 views

Angular momentum $J_z$, how do we get eigenvalue of $m\hbar$?

If we have angular orbital momentum for $z$-direction, we assume that for state $|j,m>$ that eigenvalue is $m\hbar$. Similarly for $J^2$, we assume $j(j+1)\hbar^2$ Can I get reference of ...
7
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3answers
533 views

Questions on the movie Gravity (2013)

To start off, I'm not a physicist but a programmer, and only had a few years of physics education in high school so I'm sorry if I'm asking a stupid question. I just finished watching the movie ...
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1answer
42 views

Dropping objects on a rotating disc: angular momentum?

I'm designing a very simplistic particle simulator. Particles are dropped on a spinning disc and then bounce back (although lose some momentum due to the friction of the disc). I'm working with an ...
1
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4answers
137 views

How is angular momentum conserved

from a classical perspective, what is it about angular momentum fundamentally that means it has to be conserved? Surely if I have a rod about a fixed axis and a moving particle hits the end it will ...
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2answers
51 views

Momentum Equation VS Momentum of Momentum Equation

Newton's second law states that the linear momentum ($P$) rate is equal to the net force: $$F=\frac{d}{dt}P \tag{1} $$ On the other side, there is a same expression for angular momentum ($L$): ...
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1answer
61 views

Do particles also have intrinsic linear momentum (linear analogue of spin)?

We know from quantum mechanics that microscopic particles have spin, which is a kind of intrinsic angular momentum. The particle has angular momentum without physically rotating. In a similar way, do ...
1
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1answer
52 views

Where to hit the pool ball such that it satisfies the given condition? [closed]

The question Where to hit the ball in such a way that after covering a certain distance it rolls back? You are given a pool ball and you have to find where to hit it such that it rolls back after ...
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1answer
51 views

Pauli Matrices & 2D Rotation Operators?

I was doing a strange calculation with my teacher the other day: find the eigenvalues and eigenvectors of the 2D rotation operator. Intuitively, there should be no solution to this problem in ...
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0answers
19 views

what is significance of direction of vector product(torque & angular momentum)?how can one use them practically? [duplicate]

since i came across vector product or cross product i have one doubt that is what direction of torque shows.the direction of product is along axis of rotation(+ve or -ve).is there is any practical use ...
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1answer
55 views

Is it right to write $\varepsilon_{ijk} \delta_{jl}=\varepsilon_{ilk}$? (indices notation)

Consider the $l$ component of vector position $\vec{r}$, $r_l$, and the $i$ component of angular momentum $\vec{L}$, $L_i$. We have that $$L_i=[r\times p]_{i}=\varepsilon_{ijk}r_jp_k$$ ...
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0answers
24 views

What are physical observables that are connected to orbital angular momentum?

We considered a system that is confined to a curved surface. In the quantization process, we have obtained an additional orbital angular momentum that are from the surface geometrical deformation. Now ...
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0answers
62 views

Commutation between angular momentum and Hamiltonian

Consider the following Hamiltonian of a 3-dimensional system: $$H=\frac{p^2}{2m}+V(r)$$ If the components of the angular momentum, $L_i$, commute with $H$, then: $$[H,L_i]=0$$ This condition can ...
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2answers
157 views

Possible inconsistency in Bohr atom model [closed]

It is well known that Bohr model is not totally right. But I recently discovered a very curious inconsistency (if I am right) which I haven't seen explained anywhere. The first postulate of Bohr ...
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0answers
65 views

Conservation of Angular Momentum…or not?

This is my first post on physics stack exchange, but I thought the question was more appropriate than on that of math.stack. I'm currently designing a crude model of the sun-earth orbit (which I have ...
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0answers
59 views

How to measure $\mathbb{L}^2$ and $L_z $ simultaneously

What does an experiment look like, in which both quantities are measured simultanously?
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0answers
16 views

Distance needed to double the moment of inertia of a cylinder

The moment of inertia formula for a solid cylinder is $0.5MR^2$. How would I need to change the radius in order to double the moment of inertia of the solid cylinder?
2
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1answer
50 views

When are energy, mechanical energy, momentum, and angular momentum conserved?

I am in AP Physics and my only real hangup is knowing when the said quantities are conserved. Please define what is the SYSTEM in your answer. I kind of have the basic idea. For example, if there ...
0
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1answer
81 views

Proof for quantized angular momentum [duplicate]

In Bohr's model, Bohr stated that the angular momentum of the electron is quantized and stated that $$L=\frac{nh}{2\pi}$$ So what is the proof for that equation or, in other words, how did he derive ...
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1answer
49 views

Explaining conservation of angular momentum with a disconnect

A probe is rotating in space and an instrument comes loose and disconnects. I need to explain why the angular velocity $\omega$ of the probe does not change. This equation describes how the angular ...
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1answer
55 views

Comet's distance with and without gravity [closed]

I've got this question that I just can't seem to answer. The question is as follows: A comet approaches the solar system with velocity v and would, if the sun would not attract the comet, pass the ...
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0answers
33 views

Adding angular momenta of 3 spin-(1/2) particles

When adding three spin-$\frac{1}{2}$, $|\frac{3}{2}\frac{3}{2}>$ = $\frac{1}{3} (uud + udu + duu)$ Now, I know that one of the $|\frac{1}{2} \frac{1}{2}>$ states is $|\frac{1}{2} ...
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2answers
47 views

Angular momentum about a moving axis

How can we define angular momentum of a system about an axis that moves parallel to itself? For example Axis passing through CM that is perpendicular to plane of body. When we talk about ...
1
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1answer
146 views

Can space have angular momentum that can be transfered to/from physical objects?

This is related to another question that discusses whether space can have momentum and energy. Apparently gravitational waves or ripples in spacetime is how space stores and transfers energy/momentum. ...
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0answers
53 views

Tensor product of spin states

I just wanted to check that I carried out this problem correctly. I got the correct answer, but I'm not sure if what I did to get it is completely correct. This is from the second part of problem 3.4 ...
38
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2answers
7k views

Why don't galaxies orbit each other?

Planets orbit around stars, satellites orbit around planets, even stars orbit each other. So the question is: Why don't galaxies orbit each other in general, as it's rarely observed? Is it considered ...
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0answers
25 views

How rotational force calculation depends on the distance between the point of force application and the axis of rotation?

I don't understand how the perpendicular distance between the point of force and the axis of rotation gets involved in the calculation of the rotational effect of that force.Is it about rotational ...
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1answer
49 views

Parity operator with other operators

I need to show the following: $$P x P^{-1} = -x, \ P p P^{-1} = -p, \ P L P^{-1} = L$$ where $P$ is the parity operator and $x$, $p$ and $L$ are the position, momentum and angular momentum ...
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1answer
78 views

Angular Momentum of a Photon

Why is it that the angular momentum of a photon is $\hbar$, irrespective of its energy? I encountered such a claim in a text about Raman spectroscopy. Is there an explanation for this using basic ...
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0answers
35 views

Why is this decay process allowed? [duplicate]

I have been given an assignment in which I have been asked to list some quantum numbers for some given allowed processes. One of them is $\Delta^+ \rightarrow p^+ + \pi^0$ I know that $\Delta^+$ ...
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0answers
29 views

Angular momentum in baryon multiplets

In the Murray Gell-mann model particles are brought together as function of their angular momentum. The diagrams can be seen as irreducible representations of $SU(3)$ following multiplication rules ...
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0answers
19 views

Gyroscopic precession force translated 90 degrees? [duplicate]

I was watching a video on propeller gyroscopic effect, please take a look at this 1 minute segment (up to 6:06): https://youtu.be/QGWbjGqmoWo?t=307 Alternatively, here is a summarizing image from ...
0
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1answer
42 views

Angular Momentum and Eigenfunctions in QM

In Griffith's Quantum book, he starts off by finding the commutation relationships between the angular momentum and its components. He then goes on to find the uncertainty relationship ...
2
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0answers
65 views

Precession of angular momentum vector

I'm studying Classical Mechanics on Goldstein's book, so I'm using his terminology and notation. First I'll explain where the question comes from: consider a heavy symmetrical top and consider the ...
2
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0answers
27 views

How fast can an object spin? [duplicate]

Without any forces in space to stop it, assuming an object does not collide with anything or enters any kind of gravitational pull, how fast could the object spin. I mean the earth spins quite fast, ...
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3answers
230 views

Spin and Angular Momentum [duplicate]

What is the difference between spin and angular momentum, are they linked i.e. spin is a form of angular momentum. And is spin what I think it is (the way the electron/particle actually spins)
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3answers
57 views

Is Conservation of Energy maintained when the orbit of a rotating mass increases in diameter?

I read an example where someone was explaining how the law of conservation of energy does not have to be maintained within a rotating mass even though angular momentum is maintained. The given ...
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2answers
124 views

How to start an artificial gravity?

I understand how artificial gravity in space stations works. It is by normal force the wall exerts on the foot. But I wonder how to start it in the first place. I just learned about centrifugation ...
0
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1answer
99 views

QM angular momentum commutator solution using index notation

there are a few answered questions regarding the commutator of any two 3D angular momentum operator components $[L_i, L_j]$ , however, I am trying to go through fully using index notation so that I ...
0
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1answer
52 views

Conservation of angular momentum poisson brackets vs newtonian mechanics [closed]

So I have the following system. For a mass falling due to gravity the given Hamiltonian is $$ H = \frac{1}{2m}\left( P^{2}_{x} + P^{2}_{y} \right) + mgy $$ In Cartesian coordinates then, $$ x = v_o ...
0
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2answers
120 views

Aren't all spin states (up, down, left, right, in, out) orthogonal?

Hopefully someone can clear up a basic misconception I am having about the nature of spin state vectors. According to the book i am reading, The basis vectors of up/down spin are orthogonal to each ...
51
votes
4answers
6k views

If dark matter only interacts with gravity, why doesn't it all clump together in a single point?

I'm a complete layperson. As I understand, dark matter theoretically only interacts with the gravitational force, and doesn't interact with the other three fundamental forces: weak nuclear force, ...
0
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1answer
34 views

Angular momentum: why must descending and ascending chains terminate?

I'm studying theory of angular momentum, but I haven't understood a step. $M_1, M_2, M_3$ are the components of angular momentum $\vec{M}$. Let's consider ladder operators $M_+=M_1+iM_2$ and ...
1
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0answers
52 views

Angular momentum of rolling disc

Does the angular momentum of a disc in pure rotation depend on the reference point? For example, are $L$ about the center of mass and at a distance equal to half the radius equal or different?
3
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0answers
73 views

Where this relation for general non rigid motion comes from?

In Goldstein's Classical Mechanics book in the chapter about the dynamics of rigid bodies the equation $$\dfrac{dL_i}{dt}+\epsilon_{ijk}\omega_jL_k = N_i$$ is presented. Now, in one exercise, we are ...
2
votes
3answers
125 views

How did planets start to spin and do all of them spin in same direction? [duplicate]

How did planets start to spin in the first place? Some say that gases which condense and form planets start spinning and hence planets acquire a spin. And some say that they start to spin to conserve ...
0
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1answer
126 views

Why is only angular momentum conserved for a planet and not linear momentum?

Suppose a planet is moving in an elliptical orbit with the Sun at one of its focii. I know that the forces in existence will be gravity which provides the necessary centripetal force. Now my book ...
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2answers
56 views

Angular momentum for a given Wavefunction [closed]

Problem: Give a particle in the state $\Psi = e^{\frac{-(x^{2}+y^{2}+z^{2})}{a^{2}}}(\frac{x}{a} + \frac{yz}{a^{2}})$, what are the allowed values for $l_{x}$ (and later for $l_{y}, l_{z}$). Attempt: ...
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2answers
108 views

Are mass and angular momentum related at a quantum level?

Is the mass of an atom related to the amount of angular momentum it contains? It makes sense to me that since the waveform of an electron is much much larger than a particle in the nucleus that its ...
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0answers
78 views

Spin and polarization, QM vs QFT

On page 34 of A. Zee's book QFT in a Nutshell, he states: I expect you to remember the concept of polarization from your course on electromagnetism. A massive spin 1 particle has three degrees of ...
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1answer
66 views

Questions about the velocity of the center of gravity

I have a physics test coming up in a couple of days and I really need to have some things explained to me. It is about something that I think is called in english "the velocity of the center of ...