The conserved quantity arising from a rotational invariance. Combine with rotational-dynamics for the classical mechanics approach and quantum-mechanics for the QM interpretation
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 ...
8
votes
1answer
487 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 ...
28
votes
1answer
441 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
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 ...
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 $p^{\mu}$, ...
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 ...
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 ...
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.
8
votes
2answers
361 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
$$[J_{ab},J_{cd}]
~=~ i(\eta_{ad} J_{bc} + \eta_{bc} J_{ad} - \eta_{ac} J_{bd} - \eta_{bd}J_{ac}),$$
...
10
votes
6answers
3k 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 ...
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 ...
3
votes
1answer
334 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 ...
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 ...
7
votes
1answer
728 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
3answers
397 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
votes
3answers
832 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 ...
4
votes
1answer
328 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, ...
2
votes
2answers
378 views
Homework about spinning top
I have a top of unknown mass that has a moment of inertia $I=4\times 10^{-7} kg \cdot m^2$. A string is wrapped around the top and pulls it so that its tension is kept at 5.57 N for a distance of .8 ...
1
vote
0answers
143 views
Will earth rotation be slowed down? [duplicate]
Possible Duplicate:
Are tidal power plants slowing down Earth's rotation?
Since we have various energy acquiring facilities that harvest energy from earth rotation. (e.g. wind, tidal ...
1
vote
3answers
796 views
Direction of torque precession of a spinning wheel
Consider a spinning wheel, which is held up by one end of it's axis like this:
To explain why the change of angular momentum is directed as shown in the figure above, one usually says that there is ...
5
votes
2answers
219 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
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
...
4
votes
2answers
483 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 ...
3
votes
3answers
393 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?
2
votes
1answer
105 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 $n$ ...
5
votes
1answer
340 views
Angular momentum and EM wave
Is there any sense in saying that circularly polarized EM waves have angular momentum?
2
votes
1answer
191 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
3answers
470 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
1answer
104 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?
1
vote
3answers
576 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 ...
1
vote
3answers
130 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 ...
1
vote
2answers
275 views
what does it mean for a particle with no size to have angular momenta?
I recently was reading about higgs boson and particle spin recently and I stubble upon an question that contains an answer to what a spin is.
It explains that electrons etc. have no size yet they ...
1
vote
1answer
276 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, ...
1
vote
1answer
161 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 ...
0
votes
0answers
100 views
Why angular momentum applies to emitted photons, and how it affects the emitting atom's quantized system
From what I've read, photons have spin of 1 (I guess possible by their relativistic mass), and when a photon is emitted from an atom, the production of this spin affects the balance of the atom's ...
