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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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 ...
42
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4answers
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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
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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?
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How can the Earth keep spinning with a liquid core?

In regards to the 'conservation of angular momentum' being the explanation of why celestial objects spin... If you fill a ball or any other container with a liquid and try to spin it, you will not ...
33
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5answers
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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 ...
32
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5answers
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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 ...
27
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5answers
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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 ...
27
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2answers
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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 ...
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6answers
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Rotation angle of a giant lily when a child crawls on its rim

Below is a picture of Giant Water Lily. Scientific Name: Victoria Amazonica. Leaves of some of these could be as big as 3 m diameter and carry a weight of 45kg spread evenly and can support a child. ...
21
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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 ...
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 ...
15
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3answers
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Wouldn't angular momentum of a binary star system decrease?

Consider a binary star system, as these stars go around one another they would emit gravitational waves. Since, the graviton is a spin 2 particle. Wouldn't the angular momentum of the stars decrease? ...
15
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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 ...
14
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4answers
398 views

Why are spacecraft made to “spin” after launch?

At some point after launch, usually just before or after separation from the last booster stage, spacecraft are often made to "spin" (about the axis of their trajectory)? See e.g this You Tube video. ...
14
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4answers
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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 ...
14
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1answer
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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 $p^{\mu}$, ...
13
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1answer
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Can one black hole suck in another black hole?

In the recent news, scientists at NASA have found “unprecedented” black hole cluster near Andromeda’s central bulge. I wonder why doesn't all these black holes merge and such each other in until just ...
13
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3answers
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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 ...
13
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3answers
938 views

Where the angular momentum has gone?

I came across an interesting problem when I prepared for the preliminary exam on electromagnetism. Below is the problem in its original words: A metallic sphere of mass, $m$, and radius, $a$, ...
12
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3answers
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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 ...
12
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2answers
241 views

When are there enough Casimirs?

I know that a Casimir for a Lie algebra $\mathfrak{g}$ is a central element of the universal enveloping algebra. For example in $\mathfrak{so}(3)$ the generators are the angular momentum operators ...
12
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3answers
473 views

Do particles have different spins in different frames of reference?

Let's say we have two photons, whose momentum vectors point to opposite directions. Also spin angular momentum vectors of the photons point to opposite directions. (Sum of spins is zero) Now we ...
12
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2answers
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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 ...
12
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1answer
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Are the orientations of spin-axes and binary/planetary orbits random or is there any relationship with the Galactic plane?

In an answer to another question, a claim has been made that orbit/spin orientations are random (at least within our own Galaxy), except perhaps towards the Galactic centre. I have dabbled in this ...
12
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0answers
370 views

How to evaluate this sum of coupling coefficients?

I would like to evaluate the following summation of Clebsch-Gordan and Wigner 6-j symbols in closed form: $$\sum_{l,m} C_{l_2,m_2,l_1,m_1}^{l,m} C_{\lambda_2,\mu_2,\lambda_1,\mu_1}^{l,m} \left\{ ...
11
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8answers
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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 ...
11
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3answers
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An electron has no known internal structure, does that imply it has an unknown one?

I'm currently reading Alonso and Finn's Electromagnetism book. It explains that the spin contributes to the magnetic moment and is somewhat comparable to a rotation of the particle around its own ...
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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 ...
11
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2answers
492 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 ...
10
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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?
10
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4answers
682 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 ...
10
votes
1answer
2k views

Why exactly does a boomerang return back to the thrower?

I was always intrigued by the phenomena that govern the returning back of a boomerang to the thrower. Even if it is dependent on various factors such as velocity, aerodynamics, wind resistance and ...
10
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5answers
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Why does a curling rock curl?

In the game of curling, players "curl" a granite "rock" (of precise size and roughly a flattened cylinder) down a "sheet" of ice towards a target; the "rock" will curve in its path in the direction of ...
9
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4answers
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If angular momentum is conserved, what's wrong with this scenario?

I understand that, in a given system with no external torques applied, angular momentum is conserved. However, consider the following situation: Let's say the earth revolves around the Sun in a ...
9
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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 ...
9
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2answers
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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 ...
9
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1answer
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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 ...
9
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1answer
367 views

What makes a wrist-energized gyroscope rotate faster?

I'm considering a wrist-energized gyroscope, shown below (after my daughter let it fall and it broke open). That one was sold as Roller Ball, but variants are known as Powerball, DynaBee, Dynaball, ...
9
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5answers
730 views

Will freely rotatable polarizers align?

Will two freely rotatable linear polarizers (placed in sequence and at some angular offset less than, say, 45 degrees) eventually align if you shine (plenty of) unpolarized light at the first one? If ...
8
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2answers
706 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?
8
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4answers
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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 ...
8
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2answers
642 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 $$[J_{ab},J_{cd}] ~=~ i(\eta_{ad} J_{bc} + \eta_{bc} J_{ad} - \eta_{ac} J_{bd} - \eta_{bd}J_{ac}),$$ ...
8
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3answers
439 views

What do the Pauli matrices mean?

All the introductions I've found to Pauli matrices so far simply state them and then start using them. Accompanying descriptions of their meaning seem frustratingly incomplete; I, at least, can't ...
8
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2answers
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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 ...
8
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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 ...
8
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2answers
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maximum rotational speed

I am wondering if there is a limit to rotational speed of an object just like there is one for translation speed ? what are the implications of general relativity for rotating objects ?
8
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3answers
418 views

Addition of spin angular momentum for massless particles

How do I add the spin angular momentum of massless particles, like photons, where only the transverse polarizations are allowed? If all three polarizations were allowed, this would be an easy ...
8
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2answers
779 views

Intrinsic angular momentum in classical mechanics

Please note, I am only interested in classical mechanics discussion on this. Please do not involve quantum mechanics. Inspired by this question: Is Angular Momentum truly fundamental? My question ...
8
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Addition of Angular Momementa in deeply bound situations, proton spin crisis

In Landau and Lipshitz's introductory book on Quanum Mechanics, "Quantum Mechanics Non-Relativistic Theory, Third Edition: Volume 3", chapter XIV (page 433 in the edition on Amazon) is "Addition of ...
8
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Is it expected that all stellar black holes will be spinning near the maximum allowed $\omega$-velocity?

Using a bit of classical reasoning I'm imagining black hole formation to be much like an ice skater pulling in her arms: Now, the size difference between a star and its black hole can't even be ...