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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36
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5answers
8k views

Why aren't there spherical galaxies? [duplicate]

According to the Wikipedia page on Galaxy Types, there are four main kinds of galaxies: Spirals - as the name implies, these look like huge spinning spirals with curved "arms" branching out ...
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0answers
45 views

How could a heavy manhole cover jump out of the ground, fly through the windshield and hit a driver in a car?

Today (12 of Feb), there was this accident in Boston where a driver was killed because a manhole cover (~200lbs) had somehow become airborne and struck her. The car looks like an SUV, so her head must ...
0
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1answer
20 views

How to apply torque impulse

In the below question, can we apply conservation of Angular Momentum? If not, why? Moreover how do we apply Torque impulse to the system ? The contact force between the cylinders will be normal to ...
0
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1answer
45 views

Navier Stokes : what about angular momentum?

I play with CFD for a while, and suddenly, a transcendantal question raises: :-) Navier Stokes is basically Newton applied on a continuum in Eulerian. For solids, we would consider linear, but also ...
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4answers
2k views

Total angular momentum of deuteron

I'm studying for my nuclear physics exam and the book we use is Introductory Nuclear Physics by K.S. Krane. In the chapter on Basic Nuclear Structure, we research the deuteron. However, when ...
0
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3answers
36 views

How does commutation between the hamiltonian and angular momentum operator (squared) imply conservation of Angular momentum?

So we are looking at central potentials in QM; The lecturer poses the question, when is $\textbf{L}$ conserved? He then considers the commutator of $\hat{H}$ and $\hat{L^2}$. We have; ...
12
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3answers
2k views

Do electrons in an atom always have the same 'direction'?

Perhaps speaking of direction of an electron isn't quite correct. But does QM indicates a kind of way whether all electrons are going e.g. 'clockwise' or not? Of course QM just gives a probability ...
6
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1answer
75 views

How can a bowling ball curve in both directions?

There is a popular video on facebook that I just don't understand. A man spins a bowling ball very fast then slightly taps it down the lane. Somehow it does half of a figure eight, curving around two ...
0
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1answer
21 views

Calculating Rolling friction of a car's wheels (NOT ON AN INCLINE)

I'm dealing with a small toy car consisting of a bottle that has a small hole in the back, covered by a thumb tack. The bottle is filled with pressurized air then the thumb tack is released, releasing ...
2
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1answer
167 views

What are phase conventions in angular momentum and rotation calculations?

I work with complicated angular momentum calculations related to atomic physics; nevertheless, I never need to use anything related to a phase convention (apparently because it's taken care of in a ...
1
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1answer
61 views

Small particle rotating around neutron star

First let me say I have read the article at "users.ictp.it › lns003 › Ruoff › Ruoff.ps.gz" about a small particles orbiting a neutron star and causing excitation of different modes of gravitational ...
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0answers
25 views

Restriction to the total angular momentum of two identical particles with spin 1

I've been asked if there is any aditional restriction to obtain the possible values of the total angular momentum J by considering that the 2 particles of spin S=1 are identical. If they are not ...
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0answers
41 views

In kerr's black hole solution can the Bekenstein-Hawking entropy be descrete?

In kerr's solution we have: $S_{BH}=\frac{k_{\beta}c^{3}A}{4G\hbar}$ where A is the area of the horizon and equal to $A=8\pi G^2 m(m+\sqrt{m^2 - a^2})$ where $a=\frac{J}{mc}$ and J is the angular ...
3
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1answer
2k views

Conservation of angular momentum in Earth-Moon system

We all know about the fact that tidal friction is slowly slowing down the Earth's rotation about its axis, and that subsequently the Moon is slowly drifting away, in order for the angular momentum of ...
-1
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1answer
38 views

Orbital angular momentum eigenstates in the $|\mathbf{r}\rangle$ representation

Consider the orbital angular momentum operators $L^2$ and $L_z$. In the $|\mathbf{r}\rangle$ representation using spherical coordinates those operators actions are given by ...
0
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0answers
23 views

Generators of cubic group: Euler angles [on hold]

I am trying to build numerically all members of the cubic group in the representation of Wigner D matrices. Angular-momentum quantum number may be small, e.g. 2, so I use the formula stated e.g. at ...
3
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1answer
544 views

How to use Clebsch-Gordan coefficients for 3 particles?

I have a Hamiltonian for 3 particles of spin 1 that I boiled down to: \begin{equation} k(\textbf{S}^2+\cdots), \end{equation} where: \begin{equation} \textbf{S}=\textbf{S}_1+\textbf{S}_2+\textbf{S}_3. ...
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1answer
78 views

Adding cinnamon to my coffee makes it stop whirling much faster: Why is thats?

When I stir my coffee in a cup, the fluid spins a long time, but when I pour cinnamon into the cup, the spinning fluid slows and stops very rapidly - why?
0
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1answer
235 views

Equivalency of conditions involving angular momentum of a rolling ball hitting a wall

(59th Polish Olympiad in Physics) A ball of mass $m$, radius $r$ and a moment of inertia $I = \frac 25 mr^2$ is rolling on the floor without sliding with the linear velocity $v_0$. It hit the wall ...
1
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1answer
332 views

Transfer of angular momentum during oblique impact with(out) adhesion [duplicate]

I am solving a problem of 2 identical spherical particles colliding. The impact is oblique. I consider both normal and tangential contact forces. Tangential force is a combination of elastic force ...
0
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1answer
40 views

How to show the finite rotation of a spin-1/2 system?

I'm reviewing my quantum mechanics by going through Sakurai and Napolitano again and working out all of the derivations. I'm stumped (though I probably shouldn't be) on some algebra in the finite ...
2
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2answers
54 views

Measuring Rotation of Sun

If the sun had a uniform surface (i.e., if there were no sunspots to look at), is there a practical way to measure its rotation? In other words, if some external force flipped the sun's spin ...
0
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2answers
47 views

What is relationship between linear and angular momentum?

I'm confused about imparting momentum to a sphere, which causes it to rotate without slipping. Does the momentum applied go: only to the rotational motion and the linear is a consequence of the ...
3
votes
5answers
3k views

Why Does Angular Velocity Increase as Radius Decrease?

Suppose a child were to ask you why a tetherball (picture below) seems to speed up as it wraps around the pole. How would you explain this to them? Certainly you wouldn't say something like, "Angular ...
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2answers
78 views

How has the world remained in balance?

In the center of our galaxy, there is a Supermassive black hole. We were told in early astronomy units of school that black holes are giant vacuums that will absorb/consume the area around it. My ...
2
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2answers
4k 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 ...
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1answer
51 views

Quantum bases conversion ($S_x$, $S_y$, $S_z$)

As part of several of my homework problems on the subject, I've had to convert between bases, for instance $|+\mathbf{x}\rangle$ in the $S_z$ basis $\left( \frac{1}{\sqrt{2}}\left( |+\mathbf{z}\rangle ...
1
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1answer
34 views

An impulse is given to a sphere out of the center?

I'm wondering what will happen if there is an impulse $J$ given to a sphere mass $M$ out of its center? I'm sure that it will rotate about the center, but what is its translational motion? It will ...
1
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1answer
21 views

Precession on a heavy rod: Angular momentum and torque contradiction

Say I got a so massive rod and a relatively light spinning flywheel. Fixing an end on a pivot, and the disk on the other endpoint, as expected, the rod would undergo precession. If we call the plane ...
1
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1answer
48 views

Conservation of angular momentum of system of two objects

This may be a silly question, but I just want to clarify something. Say we have two spinning spheres, each spinning about an axis going through their own center of mass: All of the conservation of ...
0
votes
1answer
173 views

What is really the force required to open a door?

I found a few Phys.SE threads in which an impulse is used to exert a torque on a rod, is it possible to get a realistic description of the force required to open a door?: If we have a free 'door' ($l ...
3
votes
2answers
52 views

Intuitive explanation of rotational inertia with respect to angular momentum

I understand that there are proofs (e.g. proof, another proof) of why the angular momentum about two points for an object is the same. However, could someone give an intuitive explanation of why this ...
1
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4answers
92 views

Spinning disk touches stationary disk [closed]

Suppose we have a solid disk of mass $M$ and radius $R$ that is spinning at an angular velocity of $\omega_0$ about an axis going out its cm. It is brought to touch a stationary disk of mass $m$ and ...
2
votes
1answer
283 views

Find angular momentum about any point

How do I find the angular momentum of a body about any point? We know that $L=I\omega$ for a body rotating in space, where $L$ denotes the angular momentum, $I$ denotes the moment of inertia and ...
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1answer
437 views

Independence of angular momentum with respect to origin for rotation about center of mass

Why is angular momentum for rotation about the center of mass independent of origin of the coordinate system?
4
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2answers
95 views

Radial quantum number for infinite circular well

For completeness, I will sketch the solution of a particle in an infinite circular well first and then get to my question. I apologize in advance since the introduction is standard undergraduate ...
2
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2answers
67 views

Two particles have the same linear momentum but their angular momentum differ. Which's harder to stop?

Which one is harder to stop, a 2 kg particle moving in a circular path of radius 5 m , with angular velocity of 10 rad/s or a 2 kg particle moving in a circular path of radius 2 m with a angular ...
4
votes
2answers
11k 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 ...
0
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0answers
22 views

Conservation of angular momentum in a system under torque

Let's say we have a particle $A$ like this which is located in the disk $c$. Consider that the particle itself is not moving, but in general it is constrained to the semicircle $d$, in that if it ...
1
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2answers
105 views

Find the error: If $L_x$ and $L_y$ are zero, then $L_z$ is conserved

From Goldstein's Classical Mechanics (2nd ed.), problem 38 of chapter 9 basically says the following: It's been shown that the Poisson bracket of two constants of the motion is also a constant of ...
1
vote
1answer
58 views

Decomposition of tensor product space into direct sum [closed]

Consider a tensor product space of two representations $j = \frac{3}{2}$ and $j = 1$. How to show $4 \otimes 3 = 6 \oplus 4 \oplus 2$?
3
votes
1answer
61 views

Second Kepler's law implies that constant velocity

I was trying deduce that if we suppose that the planet's orbits are circular and de Kepler's secong law is true: A line joining a planet and the Sun sweeps out equal areas during equal intervals of ...
2
votes
5answers
306 views

Physical interpretation of applying a unitary operator to a state

When we apply one of the Pauli matrices $\sigma_y$ on one of its eigen-vectors $| \odot \rangle$, what does the eigen-value tell us about $| \odot \rangle$? Is this considered a measurement of $| ...
3
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1answer
426 views
1
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0answers
13 views

Assigning values of angular momentum transfer

How do the shapes of the experimentally measured differential scattering or transfer cross sections help in assigning reliable angular momentum transfer values?
0
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3answers
850 views

Conservation of Angular Momentum, as related to a flywheel

Trying to work out some pesky flywheel dynamics for a project I'm working on, would love some for your assistance to better understand the underlying concepts. For a given flywheel (thin-walled ...
3
votes
2answers
299 views

$\hat{L}_{x}$ and $\hat{L}_{y}$ do not commute… or do they?

So $\hat{L}_{x}$ and $\hat{L}_{y}$ do not commute: $$ [ \hat{L}_{x}, \hat{L}_{y}] = i\hbar \hat{L}_{z}$$ But, what if we perform this operation on a state such that: $$\hat{L}_{z} \phi_{l, m_{l}} ...
0
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1answer
39 views

If a system is in a state $L^2 =2 \hbar^2$ and $L_x=0$ why can't $L_z$ be 0?

A particle is in a state where $L_x=0$ and $L^2 = 2\hbar^2$. This means $l=1$ and $m_x = 0$. I will call this state $Y^x_{lm} = Y^x_{10}$ I wanted to know what possible values $L_z$ could have in ...
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0answers
13 views

Coupling between angular momenta of particles conserve angular momentum of each particle?

Suppose there are two particles in angular momentum numbers $j_1$ and $j_2$ respectively. Suppose there is some interaction that couple together the particles' angular momenta. As there is no external ...
3
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1answer
34 views

Conservation of Angular Momentum in Einstein - de Haas effect

I am not really sure why the law of conservation of angular momentum should hold true in the Einstein - de Haas effect. Consider the following excerpt about the phenomenon (taken from Magnetism in ...