The conserved quantity arising from a rotational invariance. Combine with rotational-dynamics for the classical mechanics approach and quantum-mechanics for the QM interpretation

learn more… | top users | synonyms

8
votes
4answers
6k 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 ...
8
votes
3answers
2k 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 ...
8
votes
3answers
533 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
votes
1answer
761 views

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 ...
8
votes
2answers
883 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
votes
2answers
471 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
3answers
747 views

Where does the kinetic energy go?

A uniform cylinder was placed on a frictionless bearing and set to rotate about its vertical axis. After a cylinder has reached a specific state of rotation it is heated without any mechanical support ...
8
votes
4answers
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 ...
8
votes
2answers
162 views

How to design a deliberately biased coin?

For demonstrating basic probability concepts, it would be nice to have a coin-like object that lands heads/tails not in 50/50% ratio, but biased in a way that can be revealed in a short experiment. ...
7
votes
5answers
20k 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.
7
votes
1answer
520 views

Different representations of the Lorentz algebra

I've found many definitions of Lorentz generators that satisfy the Lorentz algebra: ...
7
votes
2answers
668 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 ...
7
votes
3answers
3k views

What made Bohr quantise angular momentum and not some other quantity?

Bohr's second postulate in Bohr model of hydrogen atom deals with quantisation of angular momentum. I was wondering, though: why did he quantise angular momentum instead of some other quantity?
7
votes
3answers
592 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
1answer
269 views

ket vector with two “entries”

This is a very simple question. I am learning about angular momentum. In my lecture notes, the symbol $|\lambda,m_l \rangle$ was defined as a eigenfunction of a central potential. Two assumptions are ...
7
votes
1answer
301 views

Spin of 125 GeV Higgs boson

Can someone please explain to me why (according to decay of Higgs boson into 2 photons) Higgs boson cannot have spin $S=1$?
7
votes
2answers
736 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 ...
7
votes
3answers
352 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 ...
7
votes
2answers
1k views

Apparent violation of Newton's 3rd law and the conservation of angular momentum for a pair of charged particles interacting magnetically

Consider a system of the two identical point positive charges situated in free space (isolated from influence of any other external fields) as shown in the figure below. Particle 1 is at $(a,a,0)$ and ...
7
votes
1answer
448 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 ...
7
votes
3answers
101 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
2answers
386 views

Why don't we talk about angular momentum at all in fluid mechanics?

People usually talk about similar (or maybe not?) things like vorticity or enstrophy in fluid mechanics, but no one talks about angular momentum, why?
7
votes
3answers
565 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?
7
votes
3answers
520 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 ...
7
votes
1answer
758 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 ...
7
votes
4answers
715 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 ...
6
votes
3answers
578 views

The Asymmetry between Real and Imaginary in the three Pauli Spin Matrices

The Pauli spin matrices $$ \sigma_1 ~=~ (\begin{smallmatrix} 0 & 1 \\ 1 & 0 \end{smallmatrix}), \qquad\qquad \sigma_2 ~=~ (\begin{smallmatrix} 0 & -i \\ i & 0 ...
6
votes
2answers
1k 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 ...
6
votes
2answers
566 views

Square of the Pauli matrices and the identity matrix

The square of any of the three Pauli Spin matrices is equal to the identity. Is there any physical meaning to this? Would you expect it? Maybe in the context of the $SU(2)$ group?
6
votes
4answers
8k 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 ...
6
votes
2answers
1k views

Is there a reason why the spin of particles is integer or half integer instead of even and odd?

It seems to me that we could change all the current spin values of particles by multiplying them by two. Then we could describe Bosons as even spin particles and Fermions as odd spin particles. Is ...
6
votes
2answers
118 views

How Galaxy is formed?

Given the distance among stars (the most massive objective in the space) is so huge, the difference of order of magnitude is about 7. And also, since gravity is such a weak force, how is it likely for ...
6
votes
3answers
2k 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
163 views

How much effort would be required to fix the Earth's rotation?

Given that the earth's rotation has been slowing down by very slight amounts over time, forcing us to introduce leap seconds and so forth into our clocks and calendars, I would like to ask if this ...
6
votes
2answers
236 views

Will an object falling into Earth's orbit start spinning?

Assume an object falls towards Earth (I've drawn a hyperbolic orbit, but this would apply to any orbit). The object starts at $A$, and at this point it is not rotating i.e. an observer on the object ...
6
votes
2answers
858 views

Conservation of angular momentum experiment

I've learned in that in this experiment: ...the skater will start rotating faster when she brings her arms in and there is no net torque acting on her. But what would happen to her angular momentum ...
6
votes
3answers
389 views

Angular momentum of particle rolling around inside of sphere

I have a hemispherical bowl in which I roll a small particle around the edge, starting from the top at point A with a velocity $v_o$. It travels halfway around the sphere and reaches point B, which is ...
6
votes
0answers
272 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
2answers
250 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 ...
5
votes
6answers
998 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
855 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
3answers
3k views

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 ...
5
votes
4answers
9k views

What is the scientific reason for the inclination of earth's rotation axis?

This titled position of the earths axis is known as inclination of the earths axis. The earth's rotation axis makes an angle of about 66.5 degrees with the plane of its orbit around the sun, or about ...
5
votes
2answers
651 views

In quantum mechanics(QM), can we define a high-dimensional “spin” angular momentum other than the ordinary 3D one?

Inspired by my previous question Questions about angular momentum and 3-dimensional(3D) space? and another relevant question How to define angular momentum in other than three dimensions? , now I get ...
5
votes
2answers
1k 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
530 views

The momentum of a swinging sword

Suppose you are faced with a zombie, and the only way to kill it and save yourself is to chop its head off with your sword. However, you are very weak from illness, and can only afford to strike once. ...
5
votes
3answers
215 views

Why do we look at the representations of $SO(3)$ in QM?

I have a bit of an understanding issue why the representations of $SO(3)$ are so important for Quantum Mechanics. When looking at its Irreps one gets the Spin and Angular Momentum operators and thus ...
5
votes
1answer
219 views

Heat engines and “Angular momentum” engines?

We know that the theory of heat engines is that, if you accept the second law of thermodynamics, $\Delta S > 0$ then you can define temperature using $\frac{1}{T} = \frac{\partial S}{\partial E}$ ...
5
votes
2answers
248 views

Problem counting spin states

I can't figure out how many different spin states I can create with a four-electron system. I think I can create a spin-zero state, three spin-one states, and five spin-two states. That gives me nine ...
5
votes
1answer
638 views

What does it mean for a particle to have spin of 2? [duplicate]

When I first started to study quantum mechanics, my physics text book told that particles have spin of either 1/2 or -1/2. Then I recently read an article saying that gravitons are expected to be ...