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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7
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5answers
6k views

Why are some galaxies flat?

What is the explanation for the flatness of some galaxies? (If it's due to their rotation then why they are rotating, why some other galaxies are not flat etc., I would like to hear a nice and ...
5
votes
2answers
569 views

Half wave plate and angular momentum

Given: A half wave plate freely floating in space. Circularly polarized light, falling perpendicularly to it. The plate changes polarisation of the beam to the opposite one. Therefore it ...
4
votes
2answers
223 views

Accretion disk physics - Stellar formation

I was going through the Wikipedia page for Accretion disks, and I couldn't comprehend what the meaning of this is: "If matter is to fall inwards it must lose not only gravitational energy but also ...
3
votes
1answer
123 views

Matrix representation angular momentum

We are supposed to give a matrix representation of $L\cdot S$ for an electron with $l=1$ and $s=\frac{1}{2}$. I read $L\cdot S$ as $L \otimes S$. Is this correct? Then we would have e.g. for ...
3
votes
2answers
332 views

Why can't I just think the spin as rotating?

I'm going mad about the problem. I really don't understand why do electron have 1/2 spin number, why they are not actually spinning. I can accept that the electrons have their own magnetic field, ...
3
votes
0answers
164 views

Right-angle lever paradox in special relativity

I remember to have read somewhere an interesting special relativity "paradox" considering two perpendicular rods $A$ and $B$ of equal proper length $L$ fixed at point $O$. In the "rest" frame equal ...
2
votes
1answer
113 views

How does $SU(2)$ group enters quantum mechanics?

What is the reason that $SU(2)$ group enters quantum mechanics in the context of rotation but not $SO(3)$? What really rotates and which space it rotates? It cannot be the physical electron that ...
2
votes
2answers
2k views

What causes precession or nutation in a spinning object?

What causes precession in a spinning object? What causes nutation in a spinning object? What causes a top, gyroscope, and the earth to wobble? Just because it's a simple question, I'm not ...
2
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1answer
882 views

Converting angular velocity to linear velocity through friction

A very basic question here; it's related to this one, but not quite the same. If a rotating rigid body (a sphere for the sake of discussion) with mass $m$, radius $r$ and inertial tensor $I$ has ...
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1answer
173 views

Finding the Basis vectors of a Killing field vector space

I have solved the Killing vector equations for a 2-sphere and got the following answer. $A,B,C$ are three integration constants as expected. $$\xi_{\theta}=A \sin{\phi}+B\cos{\phi}$$ ...
0
votes
1answer
75 views

Purely mechanical description of how gravity causes a gyroscope to precess

I know the vector equation that relates torque to moment of inertia and angular momentum. What I want to know is what physical mechanisms actually occur to keep the gyroscope from falling. Where is ...
8
votes
4answers
2k views

What causes a soccer ball to follow a curved path?

Soccer players kick the ball in a linear kick, though you find it to turn sideways, not even in one direction. Just mid air it changes that curve's direction. Any physical explanation? Maybe this ...
5
votes
1answer
132 views

Orbital angular momentum of photon

People talk about orbital angular momentum (OAM) of photons. Is there some physical example that cannot be explained without assuming that photons have non-zero OAM? Does different photons have ...
5
votes
1answer
523 views

Angular momentum and EM wave

Is there any sense in saying that circularly polarized EM waves have angular momentum?
4
votes
1answer
324 views

Questions about angular momentum and 3-dimensional(3D) space?

Q1: As we know, in classical mechanics(CM), according to Noether's theorem, there is always one conserved quantity corresponding to one particular symmetry. Now consider a classical system in a $n$ ...
3
votes
4answers
286 views

What causes matter to initially rotate/spin/orbit?

What causes matter to initially rotate/spin/orbit? All I can find is the statement that in space particles of dust/gas/matter contract into a spinning disk due to gravity (to form stars, solar ...
3
votes
1answer
132 views

Angular momentum of a rotating black hole

Is there an upper limit to the angular momentum of a rotating (Kerr) black hole?
3
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2answers
1k views

What does it really mean that particle has a spin of up/down? And how is spin actually meassured?

I been reading some physics articles (related to the recent discovery of the particle that could be a Higgs boson) posted online and it was talking about electron spin and how it can only have values ...
2
votes
1answer
365 views

Angular momentum components as independent integrals of motion

I was told that in order to solve the Kepler problem (6 degrees of freedom in total) you have to proceed, step by step, to reduce those degrees of freedom using the integrals of motion. You do so ...
2
votes
1answer
282 views

Measuring the mass using angular velocities

I have 2 objects which are intially connected together, $O_1$ and $O_2$. When they are connected together, they have a rotation rate about their center of mass of $w_1$. $O_2$ is cleanly released from ...
2
votes
3answers
545 views

How long for a frictionless top to fall over?

We've previously discussed why it is that spinning tops do not fall over, see: Why don't spinning tops fall over? However, as the highest rated answer notes, the angular momentum of the spinning top ...
1
vote
2answers
105 views

Possible spin states?

Given a system of two particles with spin up and down, I have troubles to understand the possible states of this system. I would have normally thought, that the possible states are the tensor ...
1
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2answers
91 views

Does turning sharply on a bicycle conserve more energy than a wide turn?

I use a bike to commute, so I spend a lot of time thinking about how to get the most bang out of my momentum. Aside from the extra distance traveled in a wide turn, does making a sharp turn save you ...
1
vote
2answers
270 views

Angular momentum conservation in pion decay?

I have seen the charged pion decay $$\pi^{-}~\to~ \bar{\nu}_{\ell} +\ell^{-}$$ represented with diagrams containing a $W^-$ in the $s$-channel. The $\pi^-$ and $W^-$ have angular momentum $0$ and $1$ ...
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0answers
175 views

Angular Momentum Conservation in Gravitational Interaction

thanks for any help. I'm trying to show that in a 2body problem, angular momentum is conserved given that $\dfrac{dp}{dt}=\dfrac{-GMm(rv)}{r³}$, where p is momentum, t time, G gravitational constant, ...
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vote
2answers
349 views

Will a spinning object come to rest?

Will a sphere spinning on its own axis come to rest given enough time, provided no other forces act upon it? I know that if you have two spinning spheres in the depths of space and orbiting each ...
1
vote
2answers
226 views

Spin of a particle and spin quantum number [duplicate]

what actually does the spin quantum number of a particle describe about? What it means when we say photon has spin 1, Higgs boson has spin 0, etc..?? What actually does that numerical value explain? I ...
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1answer
126 views

What do the $j$ and $m$ stand for in $|j,m\rangle$ for angular momentum in quantum mechanics?

I'm assuming it is a jth state with m value as total angular momentum?
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3answers
239 views

Displacement with zero velocity

I know that we can rotate a deformable object using internal forces only in space. Thus we can cause an angular displacement without the use of any external forces. The following youtube video shows ...
0
votes
2answers
511 views

Doesn't Conservation of angular momentum contradict the need for a centripetal force?

If an object is rotating in space, then there has to be a centripetal force acting upon it to constantly change its direction. I thought if an object begins to rotate in space, it would slow down ...
0
votes
1answer
111 views

Quantization of Electron Spin

Why is electron spin quantized? I've seen the derivation for the Hydrogen atom's energy levels, but my professor jumped to electrons having spin 1/2 or -1/2 as experimental. Why do electrons obey the ...
0
votes
0answers
37 views

Spin angular momentum AND spin magnetic moment [duplicate]

Since magnetic moment come from circulation of current or magnet. Because spin of electron is not classical spin of body so what is origination of spin magnetic moment and angular momentum? Is ...