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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Find the eigen state of angular momentum for a trial wave function [closed]

If I have a simple trial wave function like this, $$\psi(r_x,r_y,r_z)=\exp(-v_1(r_x^2+r_y^2)-v_2r_z^2)$$ Can you tell me the detials for how to get the eigen state for $J=0$ for this wave function ...
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1answer
73 views

Angular momentum of a rigid body about any points

Is angular momentum about all points same if the body is rigid and is rotating/translating/rolling with a constant velocity? Why? No external force is acting on the body.
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1answer
21 views

Changing angular momentum with no forces to do torque

Suppose a particle of mass $m$ moves in a straight line at velocity $v$ some distance away from an axis, as shown here at times t1 and t2 (where the axis of rotation is located at the origin of the ...
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1answer
49 views

Torque and Angular Momentum

An ice skater is spinning in a circle with an angular velocity, $\omega$, and rotational inertia $I$. Let's say that the skater then pulls his arms directly inwards at a constant rate over a time of ...
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0answers
45 views

What kind of torques cause an object to precess?

In studying precession, my textbook (Taylor's Classical Mechanics) makes the assumption that a top spinning about its symmetric axis, but tipped at an angle $\theta$, will precess nicely so long as ...
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4answers
2k views

What would happen if the Earth was in a polar orbit around the sun?

This is a question that has been bugging me for a while now, I was wondering about the effects on the Earth if it was in different orbital situations to what it is now, and one of those was what would ...
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1answer
105 views

How are these marbles being accelerated?

This question refers to an effect visible starting at around 5m45s in this video1. (The question will make little sense if one has not first watched the clip.) The observation At around 5m45s we ...
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24 views

How can I calculate the torque of draw force which affect on spinning ball flying in the air?

I am studying the Magnus effect on a flying ball i have calculate the magnus force but i trying calculate the angular acceleration, because the angular velocity of the ball is not constant. I have ...
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1answer
267 views

Angular momentum paradox with 2 identical gears

Consider two identical gears touching each other. The system is friction less. One has a handle that you use to apply a torque on the entire system. If you turn the handle, there will be a non-zero ...
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1answer
107 views

How many eigenstates for four (non-identical) spin 1/2 particles? [closed]

Question Consider a system of four non-identical spin 1/2 particles. Find the possible values for the total spin and state the number of eigenstates for each of these. Attempt So I coupled S1 and ...
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1answer
51 views

Operators and addition of angular momenta

Consider a two particle system with one particle having spin 1/2 and the other spin 1. One state of the system is $||\frac{3}{2},\frac{3}{2}\rangle\rangle$ where a double ket means this is in the ...
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42 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 ...
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3answers
559 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
85 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 ...
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4answers
185 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
60 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
68 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 ...
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1answer
55 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
69 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
23 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
62 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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26 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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68 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
172 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
68 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
61 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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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?
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1answer
82 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 ...
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1answer
111 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
51 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
62 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
38 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
102 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 ...
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1answer
152 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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63 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 ...
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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
31 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
63 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
97 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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1answer
66 views

Angular momentum in baryon multiplets

In the Murray Gell-Mann model, particles are brought together as a function of their angular momentum. The classification diagrams can be seen as irreducible representations of $SU(3)$, following ...
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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 ...
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1answer
44 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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70 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
28 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, ...
2
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3answers
493 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
89 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
136 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 ...
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1answer
146 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 ...
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1answer
55 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 ...