Skip to main content

New answers tagged

0 votes

Is the kinetic energy of a rotating system just the sum of the instantaneous kinetic energies of the individual particles?

What I am trying to establish is if kinetic energy calculated treating the system as a rotating system is just an alternative point of view from treating the kinetic energy as a sum of linear motions, ...
KDP's user avatar
  • 5,891
0 votes

Is the kinetic energy of a rotating system just the sum of the instantaneous kinetic energies of the individual particles?

There is no rotation of masses, you just have movement with v=sin(wt) of several masses in different direction. The video shows, that the projection of circular motion is a sin function.
trula's user avatar
  • 6,362
4 votes

Is the kinetic energy of a rotating system just the sum of the instantaneous kinetic energies of the individual particles?

There's no "linear KE" nor "angular KE", there's only KE. KE of a particle. The KE of a particle is defined as $$K = \frac{1}{2} m |\mathbf{v}|^2 \ .$$ You just need to take the ...
basics's user avatar
  • 10.7k
0 votes

Energy eigenvalue of hydrogen-like atoms using Laplace-Runge-Lenz vector

Your first task is to absorb all superfluous constants into your nondimensionalized variables, and do the same for the nice review by Valent which is required reading, if you cannot follow WP or Pauli....
Cosmas Zachos's user avatar
3 votes

Angular momentum quantum number $l$ either integer or half integer

The book is correct in using “either - or”. But the reason relies upon more fundamental instances of QM than the structure of angular momentum operator. More precisely a certain superselection rule. ...
Valter Moretti's user avatar
0 votes

Angular momentum quantum number $l$ either integer or half integer

The other answers and comments are all great; I will solely focus on the word either as emphasized in the question. The book is answering the question "what are the possible values of $l$?" ...
Quantum Mechanic's user avatar
1 vote
Accepted

Calculating the expectation value of the angular momentum operator

How do come up with $$ \frac{1}{\pi}\frac{\hbar}{i} \frac{1}{2\phi}\sin^2{2\phi \pi}? $$ The answer for the integral must be a number, not a function of $\phi$. The integral $$ \int_0^{2 \pi} \cos\...
mike stone's user avatar
  • 54.5k
1 vote

Reference on partial wave expansion in the context of QFT

Apart from Weinberg QFT vol1, section 3.7, one can look at the paper: "On the general theory of collisions for particles with spin", Jacob and Wick 1959. A recent review that I found useful ...
1 vote
Accepted

Doubt on conservation of angular momentum for Kepler's laws

The definition of a plane can be written as $\vec{a}\cdot \vec{r} = 0$, where $\vec{a}$ is any vector perpendicular to the plane. In this case, you have a vector quantity $\vec{L}$, which is from its ...
ProfRob's user avatar
  • 133k
1 vote

Doubt on conservation of angular momentum for Kepler's laws

The angular momentum ${\bf L}$ of a point-like particle is proportional to the vector product of position ${\bf r}$ and velocity ${\bf v}$. It is a vector orthogonal to the plane containing ${\bf r}$ ...
GiorgioP-DoomsdayClockIsAt-90's user avatar
2 votes

Is it possible to reproduce tennis racket theorem instability with a gymbal under earth gravitational field?

I'm posting a new answer for the following reason: a totally different way of implementing a Dzhanibekov effect demonstration occurred to me. Manufacture an object that is spherical on the outside, ...
Cleonis's user avatar
  • 21.4k
0 votes

Quick question regarding Larmor precession and bar magnets

https://en.m.wikipedia.org/wiki/Ferromagnetic_resonance: ‘ Ferromagnetic resonance, or FMR, is coupling between an electromagnetic wave and the magnetization of a medium through which it passes. This ...
my2cts's user avatar
  • 25.3k
0 votes

Why does angular momentum shorten the Schwarzschild Radius of a black hole?

Black holes aside, adding the freedom of rotation within the 3 standard volumetric dimensions essentially increases dimensionality. Rotation is a place to store momentum and energy without ...
Ike Kiefer's user avatar
2 votes

Is it possible to reproduce tennis racket theorem instability with a gymbal under earth gravitational field?

A gimbal suspension for the purpose of demonstrating the Dzhanibekov effect (when weightlessness is not available) presents special challenges. In a comment I already linked to the video about the ...
Cleonis's user avatar
  • 21.4k
0 votes

Why doesn't centrifugal force change instantly?

Looking from above, when any spinning wheel is nudged anticlockwise it always responds by trying to rotate the spin axis so that the axis is vertical and the wheel is rotating anticlockwise around the ...
KDP's user avatar
  • 5,891
5 votes
Accepted

Why doesn't centrifugal force change instantly?

This behavior is not caused by centrifugal force, but rather by conservation of angular momentum. If you take any spinning object, and draw an arrow aligned with the axis of rotation, that arrow ...
RC_23's user avatar
  • 9,463
3 votes
Accepted

Gravitational collapse - proof that energy dissipation is required?

The virial theorem tells us that for an isolated cloud (no external pressure, magnetic fields or rotation) that $$2K + \Omega = 0\ , $$ where $K$ is the kinetic energy of the cloud particles and $\...
ProfRob's user avatar
  • 133k
0 votes

Why does rotation make black holes smaller?

@Yukterez: the area $A=16\pi\mathcal{M}^2$ comes from the expression $A=\int \sqrt{|\gamma|} d\theta d\phi$ (being $\gamma_{\mu\nu}$ the induced metric on the event horizon), which describes exactly ...
Alfred's user avatar
  • 1
0 votes

Can I use any linearly independent, orthogonal, eigenkets as starting basis to construct $S_x$, $S_y$ and $S_z$?

I think the confusion partially comes from the use of row- and column-vector "tuple" notation when talking about a basis. Think about the ordinary 2D Cartesian coordinate system that we ...
Marius Ladegård Meyer's user avatar
0 votes

Why is half-integer spin not observed classically?

Electron spin has been interpreted classically in the context of the theory of stochastic electrodynamics (classical electromagnetism + zero-point field - the field causing the Casimir force): Cetto, ...
Andrei's user avatar
  • 813
0 votes

Can I use any linearly independent, orthogonal, eigenkets as starting basis to construct $S_x$, $S_y$ and $S_z$?

Elementary computation starting with $$ M=\begin{pmatrix} a& b \\ b^* &c\end{pmatrix} $$ show that $$ \begin{pmatrix} a& b \\ b^* &c\end{pmatrix}\begin{pmatrix}1\\ 0\end{pmatrix}= \...
ZeroTheHero's user avatar
  • 46.1k
2 votes

Can I use any linearly independent, orthogonal, eigenkets as starting basis to construct $S_x$, $S_y$ and $S_z$?

Of course, you can write the spin operators in the basis you prefer. If you choose to work in the basis of the eigenstates of $S_z$ $\{|\uparrow\rangle,|\downarrow\rangle\}$, you get $S_x = \frac{\...
Matteo's user avatar
  • 3,014
1 vote

Why is half-integer spin not observed classically?

Ferromagnets are a classical manifestation of electron spin. MRI is a classical manifestation of nuclear, mostly proton, spin. Both are spin half. What you are looking for is a -1 factor upon 360$^\...
my2cts's user avatar
  • 25.3k
5 votes

Why is half-integer spin not observed classically?

The other answers are great, and it's very much true that you can totally write down a classical field theory with half-integer-spin fields. That notion still feels kind of odd, though, because all ...
Rokas Veitas's user avatar
2 votes

Why is half-integer spin not observed classically?

Why is half-integer spin not observed classically? Why do you single out half-integer spin? Are you implying that integer spin can be observed classically? If neither integer spin nor half-integer ...
MadMax's user avatar
  • 4,452
2 votes

How can rotation about Z be a superposition of rotations in X ($|\uparrow \rangle_z = |\uparrow\rangle_x + |\downarrow\rangle _x $)

(I’m sorry to say) there is so much confusion in the title and the post… First, a rotation about $\hat z$ is not a superposition of rotations about $\hat x$. In fact, what you have written has ...
ZeroTheHero's user avatar
  • 46.1k
2 votes

How can rotation about Z be a superposition of rotations in X ($|\uparrow \rangle_z = |\uparrow\rangle_x + |\downarrow\rangle _x $)

Think about spin as an internal degree of freedom, similar to the polarization of an electromagnetic wave. This is the approach taken to explain the Stern-Gerlach experiment at the start of Sakurai's &...
agaminon's user avatar
  • 1,715
0 votes

Physical meaning of Russell–Saunders and $jj$ coupling

There's a pretty good explanation on this site: http://www.pci.tu-bs.de/aggericke/PC3e_osv/Kap_V/Russel.htm The main take aways are: When you do a Russel-Saunders coupling, you evaluate the sum of all ...
Mosakon's user avatar
0 votes

Why surface and bulk states of topological insulators (TI) have different topological invariants and how it leads to conductive states?

In the standard sense, when we think about topological classification/topological order - we think of dividing ground states of local and gapped Hamiltonians (with the symmetry eigenvalue if we are ...
Adam's user avatar
  • 187
0 votes

How come the magnetic field disappears when a neutron star becomes a black hole, while the rotation remains?

Árpád Szendrei asked: "How come the magnetic field disappears when a neutron star becomes a black hole?" If a net electric charge remains, the star would collapse to a Kerr Newman black ...
Yukterez's user avatar
  • 12.4k
-1 votes

Angular Velocity of 3D object rotating in space

Angular velocity comes from time derivative of rotation, the direction of the angular velocity vector can be interpreted as the direction of instantaneous rotation axis (changing it's direction as ...
basics's user avatar
  • 10.7k
1 vote

Direct experimental observation of magnetic orbital quantum number $m_l$

OP wants to observe orbital angular momentum directly without spin angular momentum being involved. The simplest way to do this is if the total spin is zero. Atomic term symbols make the search easy. ...
Dr. Nate's user avatar
  • 419
3 votes

Is intrinsic spin a quantum or/and a relativistic phenomenon?

There is nothing that distinguishes the spin from the magnetic dipole Spin was introduced into physics when it was realized that, in addition to its interaction with electric fields, the electron also ...
HolgerFiedler's user avatar
0 votes

Doubt regarding angular momentum conservation

System: small disc, large disc and massless motor. No external forces and torques act on the system thus angular momentum about an axis is conserved. The massless motor affixed to the outer rim of the ...
Farcher's user avatar
  • 97.9k
0 votes

Doubt regarding angular momentum conservation

In classical mechanics, for a fixed pole $H$, the balance equation of angular momentum reads $$\frac{d}{dt}\boldsymbol{\Gamma}_H = \mathbf{M}_H^{ext} \ ,$$ i.e. time derivative of the angular momentum ...
basics's user avatar
  • 10.7k
0 votes

The expectation of $L^2_x$

I don't know where you got those formulas from, they might apply to some specific system, but in general it is always true that $$ S^2 = S_x^2 + S_y^2 + S_z^2 \\ = \frac{1}{2}(S_+S_- + S_-S_+) + S_z^...
Perttu Hilla's user avatar
0 votes

Doubt regarding angular momentum conservation

The only situations where angular momentum is ''not conserved'' are where your system of interest is coupled to some other system which you aren't explicitly considering so you can take or give ...
ors's user avatar
  • 549
1 vote

Does the direction of the torque acting on a car tire change depending on which direction the tire is rotating?

car tires will fly off perpendicular to the direction of a moving car I'm not sure this is true. I've seen cases where they move in about the same direction the car was. because of the torque ...
joseph h's user avatar
  • 29.9k
19 votes
Accepted

Is intrinsic spin a quantum or/and a relativistic phenomenon?

SPIN ORIGIN Spin is a purely relativistic property. It comes in fact from the representation theory of the Lorentz group (the relativistic symmetries group). In classical mechanics, you have ...
LolloBoldo's user avatar
  • 1,611

Top 50 recent answers are included