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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32
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5answers
2k views

Why does everything spin?

The origin of spin is some what a puzzle to me, everything spin from galaxies to planets to weather to electrons. Where has all the angular momentum come from? Why is it so natural? I was also ...
42
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4answers
5k views

What is spin as it relates to subatomic particles?

I often hear about subatomic particles having a property called "spin" but also that it doesn't actually relate to spinning about an axis like you would think. Which particles have spin? What does ...
36
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2answers
2k views

Why are our planets in the solar system all on the same disc/plane/layer?

I always see pictures of the solar system where our sun is in the middle and the planets surround the sun. All these planets move on orbits on the same layer. Why?
15
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2answers
1k views

How does one experimentally determine chirality, helicity, spin and angular momentum?

If I've got an instance of a fundamental particle, how can I separate out the measurements of these three concepts? (I think) I understand the theory behind them, and why the particles in the ...
57
votes
9answers
5k views

Is Angular Momentum truly fundamental?

This may seem like a slightly trite question, but it is one that has long intrigued me. Since I formally learned classical (Newtonian) mechanics, it has often struck me that angular momentum (and ...
13
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3answers
1k views

Do mankind and manmade activities/constructions have any effect on the rotation of the Earth?

We walk or ride on our vehicles to our destinations daily. Does our movement have any effect on the rotation of the earth according to Newton's law? What will be the effect if we move all the peoples ...
10
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4answers
681 views

Why do all the planets of the solar system orbit in roughly the same 2D plane?

Most images you see of the solar system are 2D and all planets orbit in the same plane. In a 3D view, are really all planets orbiting in similar planes? Is there a reason for this? I'd expect that ...
27
votes
5answers
3k views

What if the universe is rotating as a whole?

Suppose in the milliseconds after the big bang the cosmic egg had aquired some large angular momentum. As it expanded, keeping the momentum constant (not external forces) the rate of rotation would ...
20
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6answers
7k views

Why don't spinning tops fall over?

One topic which was covered in university, but which I never understood, is how a spinning top "magically" resists the force of gravity. The conservation of energy explanations make sense, but I don't ...
27
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2answers
1k views

Why the galaxies forms 2D plane (or spiral-like) instead of 3D ball (or spherical-like)?

Question: As we know, (1) the macroscopic spatial dimension of our universe is 3 dimension, and (2) gravity attracts massive objects together and the gravitational force is isotropic without ...
14
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1answer
3k views

How to define angular momentum in other than three dimensions?

In classical mechanics with 3 space dimension the angular momentum is defined as $\mathbf{L} = \mathbf{r} \times \mathbf{p}$ In relativistic mechanics we have the 4-vectors $x^{\mu}$ and $p^{\mu}$, ...
5
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3answers
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How do the Planets and Sun get their initial rotation?

How do the Planets and Sun get their initial rotation? Why do Venus and Mercury rotate so slowly compared to other planets and why does Venus rotate in a different direction to Mercury, Earth and ...
2
votes
2answers
196 views

Angular Momentum of a rigid, extended object

Angular momentum of an object is a physical quantity that depends on the chosen point about which to calculate the angular momentum. It is often said that an object that has been thrown up in the air ...
11
votes
2answers
491 views

The secret behind the spinning, asymmetrically weighted, 2D disk-shaped top?

When you spin an asymmetrically weighted, 2D disk-shaped top, the heavy part actually rises to the top. Why is this? http://www.youtube.com/watch?v=h0SZZTBQmEs ...
11
votes
8answers
6k views

How do you explain spinning tops to a nine year old?

Why don't spinning tops fall over? (The young scientist version) My nine year old son asked me this very question when playing with his "Battle Strikers" set. Having studied Physics myself, I am very ...
7
votes
5answers
13k views

Why does a ballerina speed up when she pulls in her arms?

My friend thinks it's because she has less air resistance but I'm not sure.
8
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2answers
641 views

Lie bracket for Lie algebra of $SO(n,m)$

How does one show that the bracket of elements in the Lie algebra of $SO(n,m)$ is given by $$[J_{ab},J_{cd}] ~=~ i(\eta_{ad} J_{bc} + \eta_{bc} J_{ad} - \eta_{ac} J_{bd} - \eta_{bd}J_{ac}),$$ ...
4
votes
1answer
513 views

Why is the value of spin +/- 1/2?

I understand how spin is defined in analogy with orbital angular momentum. But why must electron spin have magnetic quantum numbers $m_s=\pm \frac{1}{2}$ ? Sure, it has to have two values in ...
2
votes
2answers
693 views

Angular momentum of a translating and rotating body

If a rod is rotating about one end, does it have pure rotation or do you also consider the translation of centre of mass when calculating its angular momentum? Also, how would one calculate the ...
8
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2answers
705 views

Huge buildings affect Earth's rotation?

Does constructing huge buildings affect the rotation of the Earth, similar to skater whose angular rotation increases when her arms are closed comparatively than open?
9
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2answers
998 views

Dynamics of counter-rotating flywheels

I've wondered about this for ages. If we create a pair of flywheels that rotate in the opposite direction with the same angular momentum, but are co-located and have the same mass and inertial moment ...
14
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4answers
2k views

Why does each celestial object spin on its own axis?

AFAIK all the celestial objects have a spin motion around its axis. What is the reason for this? If it must rotate by some theory, what decides it's direction and speed of rotation? Is there any ...
12
votes
2answers
4k views

Adding 3 electron spins

I've learned how to add two 1/2-spins, which you can do with C-G-coefficients. There are 4 states (one singlet, three triplet states). States are symmetric or antisymmetric and the quantum numbers ...
10
votes
3answers
599 views

Why does spin have a discrete spectrum?

Why is it that unlike other quantum properties such as momentum and velocity, which usually are given through (probabilistic) continuous values, spin has a (probabilistic) discrete spectrum?
7
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3answers
184 views

What is the origin of spin of celestial objects?

In an older question from June 2011, Why does each celestial object spin on its own axis?, apparently revived by the system, a user is asking about the origin of the rotation of celestial bodies. The ...
9
votes
2answers
666 views

Spin - where does it come from?

I study physics and am attending a course on quantum field theory. It is hard for me to draw connections from there to the old conventional theories. In quantum field theory spin originates from the ...
8
votes
1answer
510 views

Effect of the tail of the cat in the falling cat problem

To explain why a falling cat can turn by 180 degree without external torque and without violation of the conservation of angular momentum, one usually models the cat as two cylinders as in ...
4
votes
4answers
6k views

What determines the direction of precession of a gyroscope?

I understand how torque mathematically causes a change to the direction of angular momentum, thus precessing the gyroscope. However, the direction, either clockwise or counterclockwise, of this ...
9
votes
1answer
1k views

Why do galaxies and water going down a plug hole spin?

We all experience things spinning, whether it's water down a drain, the earth on its axis, planets round the sun, or stars in a galaxy - even electrons round an atom. But why is spin so common in ...
5
votes
4answers
493 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 ...
33
votes
5answers
6k views

Why aren't there spherical galaxies? [duplicate]

According to the Wikipedia page on Galaxy Types, there are four main kinds of galaxies: Spirals - as the name implies, these look like huge spinning spirals with curved "arms" branching out ...
12
votes
3answers
2k views

Origin of Ladder Operator methods

Ladder operators are found in various contexts (such as calculating the spectra of the harmonic oscillator and angular momentum) in almost all introductory Quantum Mechanics textbooks. And every book ...
21
votes
9answers
2k views

Physical meaning of the angular momentum

Still reading Classical Mechanics by Goldstein, I'm struggling on a very basic notion: angular momentum. I physically understand it as the momentum of an object rotating around something given a ...
7
votes
2answers
445 views

Quantization of a particle on a spherical surface

Suppose we have a particle of mass $m$ confined to the surface of a sphere of radius $R$. The classical Lagrangian of the system is $$L = \frac{1}{2}mR^2 \dot{\theta}^2 + \frac{1}{2}m R^2 \sin^2 ...
11
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2answers
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How can a singularity in a black hole rotate if it's just a point?

I guess nobody really knows the true nature of black holes, however, based on everything I know about black holes, there is a "singularity" at their center, which has finite mass but is infinitely ...
8
votes
2answers
3k views

Why Silver atoms were used in Stern-Gerlach experiment?

For the Stern-Gerlach experiment done in 1922: Why were silver atoms used? Silver atoms contain many electrons in different shells (with different angular momemtum quantum numbers. Why are those not ...
4
votes
1answer
748 views

Is all angular momentum quantized?

Angular momentum is definitely quantized in elementary particles and electrons in atoms. Molecules also have characteristic rotation spectra. Is it true that all angular momentum is quantized, ...
7
votes
4answers
567 views

What's is the origin of Orbital Angular Momentum of electrons in atoms?

Consider the Hydrogen 1s electron. We know that, in the quantum picture, the electron isn't orbiting or rotating at all, rather we simply state that the electron is spread over the entire space with ...
6
votes
2answers
556 views

Meaning of spin

I'm pretty astounded that I did not hear about this sooner, but in my course on QFT our professor told us that the concept of spin can be used to mean three things: Mechanical spin (apparently a ...
5
votes
2answers
495 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 ...
5
votes
2answers
880 views

Why do many people say vector fields describe spin-1 particle but omit the spin-0 part?

We know a vector field is a $(\frac{1}{2},\frac{1}{2})$ representation of Lorentz group, which should describe both spin-1 and spin-0 particles. However many of the articles(mostly lecture notes) I've ...
4
votes
3answers
334 views

Moment of Inertia, why $r^2$and not $r$?

So my engineering mechanics book includes a brief discussion on area moments of inertia. Unfortunately, the ensuing chapter is predominately computational in nature. I don't have a thorough grasp of ...
4
votes
3answers
3k views

Proving angular momentum is conserved for a particle moving in a central force field $\vec F =\phi(r) \vec r$

A problem I am trying to work out is as follows: A particle moves in a force field given by $\vec F =\phi(r) \vec r$. Prove that the angular momentum of the particle about the origin is constant. ...
3
votes
4answers
599 views

Why, for a spin-½ particle, are the possible outcomes of measuring spin projection along any direction the same?

If one measures the projection of spin of a spin half particle along the $x$ axis one will always get $\pm\tfrac12\hbar$. Measuring it along the $y$ axis one will always get $\pm\tfrac12\hbar$. ...
8
votes
3answers
2k views

How can I understand a Vortex Tube and its efficiency?

A Vortex Tube takes a pressurized input stream, most typically of a gas, and creates two output streams with a temperature differential. Apparently, it has been described as a Maxwell's Demon. Both ...
7
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3answers
416 views

Are there planetary systems where the planes of orbits vary greatly?

Inspired by this question, are there any known planetary systems with largely varying planes of orbit? For example a system where two planets have perpendicular planes?
5
votes
1answer
439 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 ...
4
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2answers
2k views

Which force makes a wheel roll down the hill? What causes friction?

A wheel rolling down a hill has two axis of rotation. One is where the center or mass is and the other is the point of contact with the surface which acts as a fulcrum. I was trying to understand ...
4
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3answers
877 views

$\hbar$, the angular momentum and the action

Is there anything interesting to say about the fact that $\hbar$, the angular momentum and the action have the same units or is it a pure coincidence?
3
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1answer
619 views

Cases in which angular velocity and angular momentum point into same direction

I know that angular momentum $\vec{L}$ and angular velocity $\vec{\omega}$ of a rigid body doesn't point into the same direction in general. However if your body spins around a principal axis, ...