# Tag Info

### 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, ...
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### 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.
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### 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 ...
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### 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....
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### 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. ...
• 73.7k

### 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 $l$?" ...
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1 vote
Accepted

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### 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 ...
• 959

### 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 ...
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### 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 ...
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### 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 &...
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### 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 ...

### 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 ...
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### 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 ...
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### 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 ...
• 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. ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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^...

### 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 ...
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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 ...
• 29.9k
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 ...
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