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2 votes

How a tire send a car flying?

The energy comes from the car First of all, the tire is rolling forward, in the direction of traffic. It looks like it's coming back toward the car, because it quickly decelerates, and is not moving ...
user1167758's user avatar
0 votes

How a tire send a car flying?

I suspect the tire played a role of an inclined plane, so the car took off using its own kinetic energy. The car probably hit the tire off-center and rotated in flight as a result. I also suspect that ...
akhmeteli's user avatar
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1 vote

Where does the photon orbital angular momentum go in light-matter interactions?

You’ve posed a profound and significant question. In a circularly-polarized paraxial OAM beam, the photons possess a total angular momentum of $(\pm 1+l)\hbar$ along the propagation axis. Here, $l$ is ...
Omid's user avatar
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0 votes

Bike leaning angle computed in stationary frame

For these type of questions, it is usually conceptually easier to carry out the initial analysis in the accelerating reference frame, where everything is stationary and the 'fictitious' centrifugal ...
KDP's user avatar
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0 votes

Bike leaning angle computed in stationary frame

For organizing the computation for the stationary frame: For simplification we can instead think of it as the lean of an ice skater, going around the curve of an ice rink In order to go around the ...
Cleonis's user avatar
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5 votes
Accepted

$6j$-symbol example in Quantum Mechanics

It is a shame that most articles about $6j$-symbols (including Wikipedia) fail to mention for what they are actually used. They are used to transform between different coupling schemes in systems with ...
Thomas Fritsch's user avatar
0 votes

What creates the vertical component of the angular momentum of the whole spinning wheel and axle?

$\def \b {\mathbf}$ Lets look at the angular momentum you rotate the rotor about the Y axis with constant angular speed $~\Omega~$. the addition generalized coordinate of the gyro are the rotation ...
Eli's user avatar
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1 vote

Which Potentials lead to Kepler's second Law?

starting with \begin{align*} &\frac{d\,\vec{p}}{dt}=\vec{F}\\ &\vec{L}=\vec{r}\times\vec{p} \end{align*} where $~\vec{L}~$ is the angular momentum and $~\vec{p}=m\vec{\dot{r}}~$ is the linear ...
Eli's user avatar
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1 vote

Momentum conservation laws and explanation

See my answer to a similar question here. Conservation of momentum can be derived from Newton's Laws by considering a system of particles which each obey Newton's Second Law $\left(\sum \vec{F}_i = ...
Ben H's user avatar
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1 vote
Accepted

Momentum conservation laws and explanation

If a (mechanical) system is invariant under arbitrary spatial translations in a certain direction (say, the $x$-direction), then the corresponding component of the momentum ($p_x$ in our case) is ...
Hyperon's user avatar
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0 votes

Wigner-Eckart theorem: Completeness relation

Your notation suggests that $j$ and $m$ index the rotation group representation vectors, which are of course complete. And for $\alpha$ you need to have just one value to apply the theorem, so whether ...
Jos Bergervoet's user avatar
0 votes

How is it that some nebulae are rotating and others are not?

Turbulence. No rotation of the initial cloud is need for star formation to occur, and indeed rotation is a source of support against collapse. The molecular clouds that collapse to form stars and star ...
ProfRob's user avatar
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0 votes

How is it that some nebulae are rotating and others are not?

Ваша теория не верна,от слова-СОВСЕМ!!! Если рассматривать "схлопывание" туманности на нашей СС,то такие скорости как орбитального,так и вокруг своей оси,случайным импульсом не создать. ...
Владимир's user avatar
5 votes

Which Potentials lead to Kepler's second Law?

I think your procedure is not completely correct... When deriving the Kepler law you have to derive the product as: \begin{eqnarray} \frac{dA}{dt} &=& \frac{1}{2}\vec{r}\wedge\dot{\vec{r}} = c ...
T. ssP's user avatar
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15 votes

Which Potentials lead to Kepler's second Law?

Kepler's second law is just conservation of angular momentum. Angular momentum is conserved for any spherically symmetric potential. In particular, as you note, the geometrical interpretation of the ...
Sten's user avatar
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2 votes
Accepted

Addition of angular momenta with relative coefficients

Well, assuming these represent rotation of a tensor product space, so operators of different subscripts commute, and they satisfy the rotation group Lie algebra, $$ [J^a_i,J^b_j]=i\epsilon^{abc} J^c_i ...
Cosmas Zachos's user avatar
0 votes

Rotational states in higher dimensions: multiple magnetic quantum numbers

Thanks to LPZ's answer, I just want to graphically show the restrictions on the magnetic quantum numbers $m_{12}$ and $m_{34}$ at least in 4 dimensions, to show how wrong my guesses were: $m_{12}$ ...
Nanite's user avatar
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4 votes
Accepted

Projector onto Adjoint and Singlet Representations for $SU(N)$

Indeed. Review for su(2), in your notation, where $\vec S$ are the normalized 3-vector generators, so $\vec \sigma /2$ for the fundamental and anti fundamental, so you have $$ \vec{S}_1\cdot \vec{S}_2=...
Cosmas Zachos's user avatar
0 votes

How do we know the creation and annihilation operators for angular momentum give rise to a complete basis?

The irreducible representations of the Lie algebra of $\rm SU(2)$ (defined by $[T_k,T_\ell]= i \varepsilon_{k \ell m}T_m$) can be classified by the "weights" $j=0,\, 1/2,\, 1,\, 3/2, \,2, \...
Hyperon's user avatar
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0 votes

Acting forces on a curve ball (billiards)

The poster is correct that the ball would normally veer to the right with the left-side hit causing clockwise rotation. This is not a regular hit on ball on the left side of cue ball, however. This ...
Paul Bell's user avatar
1 vote

Proof of Newton's second law of rotation for rigid body

Use the equation for a single particle and apply summation over all of them. Then use newton's third law to cancell out internal forces.
mathemaster's user avatar
1 vote
Accepted

Rotational states in higher dimensions: multiple magnetic quantum numbers

I’ll start by a quick refresher on $\mathfrak{so}(d)$. More generally, the Lie bracket of two basis vectors is: $$ [L_{ij},L_{kl}]=i(\delta_{ik}L_{jl}+\delta_{jl}L_{ik}-\delta_{il}L_{jk}-\delta_{jk}L_{...
LPZ's user avatar
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0 votes

What is the prevailing opinion in scientific community about Hans C. Ohanian's description of spin?

It answers the question: what does "spinor" have to do with "spin"? How does "spinor" turn into "spin"? Ohanian tells us that, when the spinor is coupled to ...
Nanite's user avatar
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5 votes

Can a stationary object acquire angular momentum?

Yes, a stationary macroscopic object can have a net spin, with the most familiar example being a ferromagnet where the magnetic field is generated by the magnetic dipole moments (due to electron spins)...
David Bailey's user avatar
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0 votes

Can a stationary object acquire angular momentum?

If you are talking about electrons, there is spin angular momentum and orbital angular momentum. The spin angular momentum is not the angular momentum of spinning electrons. In fact there is no such ...
EagerToLearn's user avatar
0 votes

Can a stationary object acquire angular momentum?

No, unless another object imparts angular momentum to it (since angular momentum is a conserved quantity)
Señor O's user avatar
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0 votes

How much force is required to break precession?

This is a good question, because when you search the internet there is not one single formula for the maximum reaction torque of a gyroscope. The formula generally given for the reaction torque $T_p$ ...
KDP's user avatar
  • 2,140
1 vote
Accepted

Proof of Newton's second law of rotation for rigid body

For a particle in the rigid body we have $$\tau = \frac{dL}{dt}$$ And $\mathbf{\tau} =\mathbf{ r\times F}$ This gives us $$\frac{dL_i}{dt}=\mathbf{ r_{i}\times F_{net,i}}$$ Where $$F_{net,i}$$ is the ...
Aarush Saharan's user avatar
4 votes

Conservation of spin angular momentum at the vertex having two fermions and graviton

No, total angular momentum conservation does not fail. Spin and orbital such are not separately conserved. The graviton-energy-momentum-tensor coupling is Lorentz invariant, and so total angular ...
Cosmas Zachos's user avatar
1 vote

Conservation of spin angular momentum at the vertex having two fermions and graviton

While it is typically more important that conserved quantities are the same between the initial and final states of an entire process in QFT, it is certainly true that vertices, since they are ...
Wintermute's user avatar
3 votes

At what angle should an object be thrown to get it into orbit?

Suppose you throw the object hard enough for it to orbit the earth in an ellipse. The point where you are throwing it is on the ellipse. It has a large upward velocity at that point, so the ellipse is ...
mmesser314's user avatar
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-1 votes

Conservation of spin angular momentum at the vertex having two fermions and graviton

The end product will necessarily have at least two gravitons. Compare to QED where electron-positron annihilation produces at least two photons. Without proof or reference, in general, at any order of ...
my2cts's user avatar
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