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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2answers
231 views

Thrust center in space

I have this dilemma: Suppose you have a space ship somewhere in deep space, where there is no drag force or substantial gravity. If the ship has a single engine situated in such a way that the center ...
1
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2answers
278 views

Spin of a particle and spin quantum number [duplicate]

what actually does the spin quantum number of a particle describe about? What it means when we say photon has spin 1, Higgs boson has spin 0, etc..?? What actually does that numerical value explain? I ...
3
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1answer
148 views

Mathematically, how do we deduce that angular momentum is bounded?

So, how do we know $J_{+}|j,(m=j)\rangle =|0\rangle$? I.e. that m is bounded by j. We know that $J_{+}|j,(m=j)\rangle =C|j, j+1\rangle$, but how do I know that gives zero? Is it by looking at its ...
2
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1answer
2k views

Is angular momentum always conserved in the absence of an external torque?

Consider either the angular momentum of the earth around the sun or equivalently swinging a ball horizontally on a string. I know that with respect to the point of rotation of the swinging ball, ...
2
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1answer
658 views

How can a satellite's speed decrease without its orbital angular momentum changing?

I have no idea what the answer is. I'm supposed to answer it within 3-4 sentences.
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2answers
182 views

Internal/Rotational angular momentum

I have some difficulties to understand the relation between the internal and the rotational angular momentum of a rigid body which is also known as König's theorem, so what physical intuition lies ...
3
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3answers
141 views

Trilinear gauge couplings: Spin

In non-abelian gauge theories self interaction of gauge fields is permitted, allowing coupling such as $WWZ$ (i.e. $Z$-boson decaying to $W^+W^-$) or ggg (i.e. gluon splitting into two new gluons). ...
3
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2answers
2k views

What causes precession or nutation in a spinning object?

What causes precession in a spinning object? What causes nutation in a spinning object? What causes a top, gyroscope, and the earth to wobble? Just because it's a simple question, I'm not ...
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0answers
1k views

How is multiplicity given by 2S+1?

Suppose there are two electrons in an atom with $s_1 = \frac{1}{2}$, $l_1 = 1$ and $s_2 = \frac{1}{2}$, $l_2 = 1$. Hence the total $S$ (of the atom) may be +1 or 0. And total $L$ is either $+2$, $+1$ ...
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0answers
59 views

What exactly is the spin of a particle? [duplicate]

Possible Duplicate: What is spin as it relates to subatomic particles? I'm having a hard time grasping the concept of spin, my textbook describes it very vaguely: Stable matter contains ...
1
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1answer
91 views

Relationship between angular momentum of Earth and recession rate of the Moon

So the problem goes like this: Two masses $m_1$ and $m_2$ orbit each other with semimajor axis $a$. The orbit is circular, and $m_1 \gg m_2$. The body $m_1$ has a rotational moment of intertia $I_1$ ...
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1answer
517 views

Having hard time with Angular Momentum and Parallel axis theorem

I'm having hard time with Angular Momentum and Parallel axis theorem. Please explain these 2 formulas. Is one formula derived from the other? $$J = J_{cm} + R_{cm} \times P_{cm}$$ $$I = I_{cm} + ...
0
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1answer
527 views

How do I find the eigenvalues for the angular momentum ladder operators?

I am trying to calculate the normalising constants for the angular momentum ladder operators but am stuck when I need to calculate expected values. How can I find the expected values
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1answer
130 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?
3
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2answers
298 views

Spinning spheres colliding

In an ideal environment with no friction, in a vacuum, what happens to the velocity of the spin of two spheres spinning in perfect parity at two different velocities when they come into contact?
4
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1answer
275 views

Clarifications about Poisson brackets and Levi-Civita symbol

I need some clarifications about Poisson brackets. I know canonical brackets and the properties of Poisson Brackets and I also know something about Levi-Civita symbol (definition and basic ...
4
votes
1answer
487 views

Can any physical rigid body be represented by an ellipsoid with the same angular dynamics?

According to wikipedia, the inertia tensor of an ellipsoid with semi-axes $a,b,c$ and mass $m$ is $\left[\begin{array}{ccc} \frac{m}{5}(b^2+c^2)&0&0\\ 0&\frac{m}{5}(a^2+c^2)&0\\ ...
3
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3answers
369 views

Quantum mechanical angular momentum and spin formalism/notation

I am currently stuck on the following notation: $\frac{1}{2}\otimes\frac{1}{2} = 0 \text{ (antisym) } \oplus 1 \text{ (sym) }$ No matter what I tried, I couldn't derive the identity. I am sure that ...
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1answer
928 views

Poisson brackets and angular momentum

I'm trying to find $[M_i, M_j]$ Poisson brackets. $$\{M_i, M_j\}=\sum_l \left(\frac{\partial M_i}{\partial q_l}\frac{\partial M_j}{\partial p_l}-\frac{\partial M_i}{\partial p_l}\frac{\partial ...
4
votes
2answers
715 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 ...
4
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4answers
4k 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 ...
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4answers
850 views

Angular momentum power plant on Earth

If tidal power plants are slowing down Earth's rotation then is it theoretically possible to build a power plant that would drain energy from Earth's angular momentum (thus slowing down it's ...
2
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2answers
460 views

Why for a spin half particle, possible outcomes of measuring spin projection along any direction are the same?

If one measures the projection of spin of a spin half particle along the x axis one will always get plus or minus half $\hbar$ Measuring it along the y axis one will always get plus or minus half ...
7
votes
1answer
517 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 ...
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2answers
431 views

Angular Momentum Operators Non-Degenerate

Typically one writes simultaneous eigenstates of the angular momentum operators $J_3$ and $J^2$ as $|j,m\rangle$, where $$J^2|j,m\rangle = \hbar^2 j(j+1)|j,m\rangle$$ $$J_3 |j,m\rangle = \hbar ...
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1answer
374 views

Angular Momentum of Diatomic Molecules

I have run into a problem trying to calculate angular momenta and I wonder if someone can set me straight. I think I know that the lowest order rotational mode should have angular momentum of h, and ...
2
votes
1answer
560 views

How does weight/mass affect angular momentum?

How does weight/mass affect angular momentum? For my 8th gr science fair project I have to do an experiment on angular momentum. My problem is that we have not been taught any of that in physics yet, ...
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1answer
135 views

Commutation relation of $J^2$ and $R(\alpha,\beta,\gamma)$

If $R(\alpha,\beta,\gamma)$ is the Rotation operator and $\alpha,\beta,\gamma$ are Euler angles and $J$ is the total angular momentum then how to get to this: $$[J^2,R]~=~0?$$ This is stated in ...
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0answers
43 views

Calculate Rotational Intertia

If a can of soup, and a can of beans (tightly packed), are set in a race down a rough hill (has friction), the soup wins, because the inside of the can (soup) is not drawing energy from the system. ...
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3answers
261 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 ...
2
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1answer
204 views

Appearing To Reverse Object's Rotation

Can it be done, and if so, how does one you explain mathematically the ability to cause a rotating object to appear to change the direction of rotation? I believe it has something to do with angular ...
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2answers
342 views

Ice skater increase of energy

This may be a very basic question but I am not seeing how it works. Consider the standard example of an ice skate rotating about his/her center of mass and pulling in his/her arms. The torque is zero ...
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2answers
159 views

Directionality of angular momentum

I was told that the sum of linear and angular momentum is conserved. Given that angular momentum's direction as a vector is completely arbitrary (I believe there is no physical reason for choosing ...
5
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2answers
163 views

What maintains quark spin alignments in baryons?

What maintains quark spin alignments in baryons? The $uud$ proton and $udd$ neutron are both spin 1/2, implying that two of their spin 1/2 quarks are always parallel and the other is always opposed. ...
2
votes
2answers
426 views

Question on Total, Orbital and Spin Angular momentum

I am reading about the total, orbital and spin angular momentum, and I am not clear as to what these generators actually do after exponentiating. Could you give me a physical picture of what happens ...
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0answers
326 views

Moment of Inertia Tensor about non-principal axis

I'm part of the Western Martial Arts/Historical European Martial Arts community, and a debate that often comes up is parrying with the edge vs parrying with the flat of a blade. I want to do some ...
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2answers
4k views

Torque And Moment Of Inertia

I am reading the two concepts mentioned in the title. According to the definition of torque and moment of inertia, it would appear that if I pushed on a door, with the axis of rotation centered about ...
4
votes
1answer
618 views

How does Delta baryon decay conserve angular momentum?

I'm a chemist so bear with me: I understand the Delta baryons $\Delta^{+}$ and $\Delta^{0}$ to be in some sense spin (and isospin) quartet states of the proton and neutron. These can decay straight ...
0
votes
1answer
250 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
votes
1answer
258 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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1answer
134 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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0answers
230 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 ...
3
votes
0answers
203 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 ...
1
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0answers
72 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 ...
1
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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 ...
3
votes
1answer
679 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: ...
6
votes
1answer
291 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 ...
4
votes
1answer
399 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 ...
2
votes
1answer
294 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
306 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 ...