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

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264 views

What is the meaning of change of angular momentum of a ballistic object during its flight?

In a 2D world, three stones, whose magnitude of initial velocities are 5000m/s, are thrown from the North pole towards the Equator with horizontal initial angles of 15o, 30o, 45o and 60o angles. Their ...
6
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263 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 $S=1$?
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138 views

Implications of rotational invariance

The state $$|\psi\rangle ={1\over \sqrt 2}(|+\rangle|-\rangle-|-\rangle|+\rangle)$$ of system made up of 2 spin-$1\over 2$ particles is invariant under the operator $$\exp{i\theta S_y}.$$ What ...
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248 views

Angular momentum confusion

Could somebody please explain what is going on here? We have a system of two indistinguishable spin-1 bosons. We shall adopt the center of mass frame. Let $S$ = total spin $L$ = relative orbital ...
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0answers
213 views

What is the Landé g factor?

What is the Landé g factor? I know that it gives the relation between magnetic moment and angular moment, but i wanted to know why are those magnitudes related to each other and why is the magnetic ...
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0answers
76 views

Wigner $3j$ symbols

I am trying to determine the expansion that requires using $3j$ symbols; however, I am running into some conceptual snags. First, the expansion produces symbols that have m's that do not agree with ...
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2answers
2k views

Inelastic collision and conservation of linear and angular momentum

Is it possible for two spheres (a & b) to have an inelastic collision with BOTH the total linear and angular momentum preserved? I'm doing some physics simulation of some spheres attracting each ...
4
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1answer
800 views

What is the spin rotation operator for spin > 1/2?

For spin $\frac{1}{2}$, the spin rotation operator $R_\alpha(\textbf{n})=\exp(-i\frac{\alpha}{2}\vec{\sigma}\cdot\textbf{n})$ has a simple form: ...
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1answer
311 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 ...
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1answer
437 views

Holstein-Primakoff and Dyson-Maleev representation

In Holstein-Primakoff and Dyson-Maleev representation, spin operators are represented by bosonic operators. Roughly speaking, a state with $S^z=S-m$ corresponds to a state containing $m$ bosons. In ...
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1answer
303 views

Why are Euler's equations of motion coupled? Physical explanation

I have a problem with one of my study questions for an oral exam: Euler’s equation of motion around the $z$ axis in two dimensions is $I_z\dot{\omega}_z = M_z$, whereas it in three dimensions is ...
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2answers
335 views

How to write Schrodinger equation when a particle with some spin quantity and orbital angular momentum

Quantum mechanics: Suppose that there is a particle with orbital angular momentum $|L|$. But the particle also has spin quantity $|S|$. The question is, how do I reflect this into Schrodinger ...
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205 views

What is predicted to happen for electron beams in the Stern-Gerlach experiment?

The Stern–Gerlach experiment has been carried out for silver and hydrogen atoms, with the result that the beams are deflected discretely rather than continuously by an inhomogenous magnetic field. ...
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1answer
74 views

Single plane Ring system [duplicate]

Possible Duplicate: Why are our planets in the solar system all on the same disc/plane/layer? I've noticed this in many pictures, Planets are shown with a single ring around them (in some ...
3
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1answer
656 views

what happens when I roll a gyroscope along its axis of spin

Say: I have a gyroscope that is spinning in the xy plane along the z axis. I then roll its spinning axis by some angle theta Now I know the gyroscope will resist my attempting to change its axis ...
2
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1answer
182 views

Normalization of a spin-like quantity in matrix mechanics

Suppose that there is a quantity in Heisenberg picture as the following: $A=u_1\Sigma_1 + u_2\Sigma_2 +u_3\Sigma_3$ I am not sure why $u_1,u_2,u_3$ is normalized to be ${u_1}^2 + {u_2}^2 + {u_3}^2 ...
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2answers
500 views

Tensor product decomposition of SU(2)

I have a rather trivial question. I am looking for the decomposition of $1/2\otimes 1/2\otimes 1/2$. It should give, $0,1/2$ and $3/2$. I thought one must get as the overall dimension of this space 8, ...
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3answers
821 views

Conservation of linear and angular momentum

Suppose I have two rigid bodies A and B and they are connected by a spring which is attached off-center (thus possibly causing torques). Due to the spring a force $f$ acts on A and a force $-f$ acts ...
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142 views

Angular momentum of a rotating black hole

Is there an upper limit to the angular momentum of a rotating (Kerr) black hole?
3
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1answer
125 views

Determining the spin of wavefunction

We all know that by uncertainty principle, location of a wave-particle is perfectly determined when uncertainty of momentum becomes infinite. (I also heard that in reality, it is almost impossible to ...
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1answer
196 views

Can an electric motor force angular momentum not to be conserved in an isolated system?

An ice skater is in a spin, she pulls her arms in and she spins faster, she lets her arms extend outward and then she starts to slow down. She will probably weigh on a weigh scale about the same ...
2
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1answer
601 views

Conservation of angular momentum across different reference frames?

I saw the following problem from the USAPhO: A uniform pool ball of radius $r$ begins at rest on a pool table. The ball is given a horizontal impulse $J$ of fixed magnitude at a distance $\beta r$ ...
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1k views

Why do rolling disc (coin) move in circular path?

We have a coin that is rolled such that it's tilted at an small angle $ \theta $. Question:: What turns around rolling disc so that it traces circular motion (spiral as it's speed decreses)? ...
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191 views

Multiplicity of eigenvalues of angular momentum

Reading Dirac's Principles of Quantum Mechanics, I encounter in § 36 (Properties of angular momentum) this fragment: This is for a dynamical system with two angular momenta $\mathbf{m}_1$ and ...
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2answers
3k views

Why Silver atoms were used in Stern-Gerlach experiment?

For the Stern-Gerlach experiment done in 1922: Why were silver atoms used? Silver atoms contain many electrons in different shells (with different angular momemtum quantum numbers. Why are those not ...
2
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1answer
4k views

What's the right way to calculate the principal moment of inertia?

I am writing a program that incorporates calculating the principal moment of inertia for a protein residue based on its component atom XYZ coordinates. I am exceedingly confused about which formulas ...
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782 views

motion in the body-fixed frame?

This is really basic, I'm sure: For rigid body motion, Euler's equations refer to $L_i$ and $\omega_i$ as measured in the fixed-body frame. But that frame is just that: fixed in the body. So how ...
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479 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 ...
5
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2answers
700 views

How is angular momentum measured in experiments/in practice? [duplicate]

Possible Duplicate: How does one experimentally determine chirality, helicity and spin? How do you find spin of a particle from experimental data? We read about and study angular momentum ...
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2answers
136 views

Why isn't the maximum eigenvalue of $J_z$ squared equal to the maximum eigenvalue of $J^2$?

During a standard derivation of the eigenvalues of the angular momentum operators, $J^2$ and $J_z$, where $$J^2|\alpha, \beta\rangle =\hbar^2\alpha|\alpha, \beta\rangle$$ and $$J_z|\alpha, ...
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1answer
370 views

Angular momentum conservation in a central field through the Hamiltonian

In my teacher's notes there is a discussion of the Hamiltonian for a central force field with potential $V(r)$. The Hamiltonian is formulated in spherical polar coordinates: ...
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2answers
417 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 ...
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What does it really mean that particle has a spin of up/down? And how is spin actually meassured?

I been reading some physics articles (related to the recent discovery of the particle that could be a Higgs boson) posted online and it was talking about electron spin and how it can only have values ...
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1answer
413 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 ...
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1answer
523 views

Double gyroscope: Can a spinning pencil tumble on only one axis?

Picture an object such as item 7 on this page .. http://en.wikipedia.org/wiki/List_of_moment_of_inertia_tensors Call that the x axis and z is in to the distance. See diagram below. We are in deep ...
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3answers
953 views
2
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3answers
3k views

Proving angular momentum is conserved for a particle moving in a central force field $\vec F =\phi(r) \vec r$

A problem I am trying to work out is as follows: A particle moves in a force field given by $\vec F =\phi(r) \vec r$. Prove that the angular momentum of the particle about the origin is constant. ...
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574 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?
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98 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 ...
3
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1answer
573 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, ...
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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 ...
3
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2answers
347 views

Why is there a phase factor when the two composite angular momentum is exchanged in Clebsch–Gordan coefficients

An identity exists for CG coefficients: $$\langle j_1 m_1 j_2 m_2 |J M \rangle = (-1)^{j_1+j_2-J} \langle j_2 m_2 j_1 m_1|J M\rangle,$$ But why is there a phase factor $(-1)^{j_1+j_2-J}$? It seems ...
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3answers
232 views

Should any theory of physics respect the principle of conservation of angular momentum or linear momentum?

Is it possible that a theory that can describe the universe at the planck scale can violate things that we now consider fundamental in nature?For example can it violate rotational and translational ...
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777 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?
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2answers
484 views

Moment of inertia of a football and its angular momentum

What are the ways to create a mathematical model for the moment of inertia of a football? Can the moment of inertia of the football be simplified to two cones stack against each other? I'm trying to ...
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1answer
490 views

Wigner-Eckart projection theorem

I'm following the proof of Wigner-Eckart projection theorem which states that: $$\langle \bf{A} \rangle ~=~ \frac{\langle \bf{A} \cdot \bf{J} \rangle}{\langle {\bf{J}}^2 \rangle} \langle \bf{J} ...
8
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2answers
621 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 $$[J_{ab},J_{cd}] ~=~ i(\eta_{ad} J_{bc} + \eta_{bc} J_{ad} - \eta_{ac} J_{bd} - \eta_{bd}J_{ac}),$$ ...
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1answer
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Angular momentum operator and expectation values

I was reading some notes and it says that $\langle L_z^2\rangle=\langle L^2\rangle$ IFF the system is radially symmetric. I can see that in order that the LHS of the statement implies that $\langle ...
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2answers
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Conservation of angular momentum in helicopter

I have a small RC-controlled toy helicopter with removable tail rotor. Suppose I remove the tail rotor, hold the tail with my hand, start the rotor until it moves with constant angular velocity and ...
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3answers
823 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"?