The conserved quantity arising from a rotational invariance. Combine with rotational-dynamics for the classical mechanics approach and quantum-mechanics for the QM interpretation
37
votes
9answers
3k 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 ...
28
votes
1answer
429 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?
25
votes
4answers
2k 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 ...
20
votes
6answers
1k views
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. ...
16
votes
5answers
2k 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 ...
15
votes
4answers
614 views
Why does every thing spin?
The origin of spin is some what a puzzle to me, every thing 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 ...
15
votes
8answers
4k 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 ...
11
votes
3answers
319 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 ...
10
votes
3answers
119 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. ...
10
votes
6answers
2k 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 ...
10
votes
2answers
2k 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 $p^{\mu}$, ...
10
votes
3answers
817 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
691 views
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 ...
10
votes
2answers
375 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, $a$, ...
9
votes
2answers
77 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 ...
8
votes
3answers
488 views
Questions about the Solar System
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 ...
8
votes
2answers
343 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
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 ...
8
votes
1answer
484 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 ...
8
votes
5answers
650 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
votes
2answers
352 views
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
votes
2answers
589 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 ...
7
votes
4answers
464 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 ...
7
votes
5answers
2k 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 ...
7
votes
3answers
277 views
Can one make a ball rotate around a vertical axis using only a combination of horizontal axis rotations?
This is a nice problem that I would like to share.
Problem: In a public garden, there a statue consisting of a spherical stone and a stone cup. The ball is 1 meter in diameter and weighs at least a ...
7
votes
3answers
89 views
Rotationally invariant body and principal axis
Suppose a rigid body is invariant under a rotation around an axis $\mathsf{A}$ by a given angle $0 \leq \alpha_0 < 2\pi$ (and also every multiple of $\alpha_0$).
Is it true that in this case the ...
7
votes
1answer
726 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 ...
7
votes
1answer
266 views
Classical vs. Quantum use of the spin 4-vector
I have a few basic questions about the Pauli-Lubanski spin 4-vector S.
I've used it in quantum mechanical calculations as an operator, that is to say each of the components of S is a matrix operator ...
6
votes
3answers
849 views
Conservation of angular momentum for a rigid body rotating about a fixed point
Picture a rigid body such as a sledge hammer. Imagine that the base of the handle is attached to a fixed point such that it can rotate but not translate. I give the hammer a good push to get it ...
6
votes
1answer
138 views
Why doesn't my particle simulation end in a flat disc?
I've made a 3d particle simulator where particles are attracted to each other by the inverse of the square radius. The purpose of my experiment is to see if this alone would create a flat disk (like ...
6
votes
2answers
910 views
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 ?
6
votes
4answers
274 views
Why do 3d spheres and gravity tend to rotating discs on one plane?
Whether is it our solar system or a whole galaxy, there is usually a massive object (star or black hole) at the centre with gas and objects rotating around it.
The gravitational effect of the ...
5
votes
3answers
393 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?
5
votes
6answers
545 views
Why does the earth rotate? [duplicate]
Possible Duplicate:
Why does every thing spin?
So why would the earth, or any planet for that matter, rotate along an axis? I know of no force which could come into play here, so i assume ...
5
votes
2answers
730 views
How is angular momentum conserved when a spinning top finally stops spinning?
Where does the top's angular momentum get transferred to? Does it very slightly change the angular momentum of the table, and then the angular momentum of the Earth?
5
votes
3answers
397 views
confused about ball rolling and rotational energy
I was solving a practice test problem and it was just a conservation of energy problem
where a spherical ball is falls from a height h to the ground such that
$$mgh = \frac{1}{2}mv^2 + ...
5
votes
2answers
1k views
Relation between total orbital angular momentum and symmetry of the wavefunction
My question essentially revolves around multi-electron atoms and spectroscopic terms. I understand the idea that the total wavefunction for Fermions should be antisymmetric. Consider as an example, ...
5
votes
2answers
215 views
Do we have any effect on the rotation of he 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 ...
5
votes
2answers
96 views
What maintains quark spin alignments in baryons?
What maintains quark spin alignments in baryons?
The $uud$ proton and $udd$ neutron are both spin 1/2, implying that two of their spin 1/2 quarks are always parallel and the other is always opposed.
...
5
votes
3answers
384 views
Can the spin of a photon change during its “life”?
Or is the spin set in one of two possible states at its moment of creation and does not change for the rest of the duration of its "life"?
5
votes
1answer
192 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
...
5
votes
1answer
338 views
Angular momentum and EM wave
Is there any sense in saying that circularly polarized EM waves have angular momentum?
5
votes
1answer
343 views
Simultaneously commuting set
How does one determine the members of an simultaneously commuting set (of operators)? For example, I have read that for orbital angular momentum, the set is {$H,L^2,L_z$}. How does one know that these ...
5
votes
2answers
63 views
How do objects change their axis of rotation?
If I hold a pencil at its end and spin it, throwing it upwards, it will spin about its end, but will soon start spinning around its center. How is this?
I would draw the following torque diagram for ...
5
votes
3answers
336 views
How does Hubble's constant affect the Earth's orbit
If Hubble's constant is $2.33 \times 10^{-18} \text{ s}^{-1}$ and the earth orbits the sun with average distance of 150 million kilometers; Does that mean the earth's orbital radius increases ...
5
votes
0answers
186 views
Coupling Coefficients in SO(4)
I have two equations (from two distinct authors) for the decomposition of a coupling coefficient of SO(4) (i.e. Wigner 3j-symbol for SO(4)). In the first:
...
5
votes
1answer
109 views
Sum of angular momentum of all electrons in a magnet
Can the sum of angular momentum of all rotating electrons in all the aligned atoms in a permanent magnet have a significant contribution to the macro angular momentum of the magnet? If yes, why does ...
4
votes
4answers
3k 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.
4
votes
2answers
93 views
Where does a star's angular momentum go as its spin slows down?
So we know that stars slow down as they age. But total angular momentum must be conserved. Where does that angular momentum go?
The dissipation of Earth's tides somehow transfers Earth's angular ...
4
votes
2answers
482 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 ...
