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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1answer
96 views

Using angular momentum in complex coordinates

So given the angular momentum operator: $$L_{z} = - ih\biggl(x \frac{\mathrm{d}}{\mathrm{d}y} - y \frac{\mathrm{d}}{\mathrm{d}x}\biggr)$$ I know how to write these in terms of polar coordinates ...
2
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1answer
131 views

Replacing an operator with its expectation value

While dealing with a circling particle in an spherical symetric potential our professor said that we can replace an operator of $z$ component of angular momentum $\hat{L}_z$ with the expectation value ...
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3answers
606 views

force applied not on the center of mass

When applying a force outside of the center of mass of the body, the body will get both linear and angular momentum. Right? Does the linear velocity from this force equal to the linear velocity from ...
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2answers
124 views

Is my physics correct or torque correct?

I would like to put this into a differential equation. This is what I have. $$r \times F = I \ddot\theta + \mu \dot\theta + k \theta$$ What I need verified: $\text{Torque} = I\ddot\theta + \mu ...
5
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2answers
156 views

Problem counting spin states

I can't figure out how many different spin states I can create with a four-electron system. I think I can create a spin-zero state, three spin-one states, and five spin-two states. That gives me nine ...
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2answers
173 views

What is the correct arrangement of the elements of Pauli matrices?

I'm dealing with angular momentum, or particularly spin, on my quantum mechanics course; I guess the Pauli matrices thing is a more general one, but I'd like to illustrate my doubt with them (maybe ...
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2answers
945 views

Slowdown rate of rotating body due to friction force [closed]

This isn't a homework question, but it might as well be. The problem I have been pondering is: If a disc (or children's roundabout if you like), of radius r, mass m, is spun around it's center ...
3
votes
4answers
267 views

If angular momentum corresponds to linear momentum, what corresponds to energy?

Angular momentum is defined from linear momentum via $\vec L = \vec r\times\vec p$, and is conserved in a closed system. Since energy is the time part of the linear four-momentum, is there a quantity ...
3
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0answers
164 views

Right-angle lever paradox in special relativity

I remember to have read somewhere an interesting special relativity "paradox" considering two perpendicular rods $A$ and $B$ of equal proper length $L$ fixed at point $O$. In the "rest" frame equal ...
8
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2answers
133 views

How to design a deliberately biased coin?

For demonstrating basic probability concepts, it would be nice to have a coin-like object that lands heads/tails not in 50/50% ratio, but biased in a way that can be revealed in a short experiment. ...
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2answers
492 views

Huge buildings affect Earth's rotation?

Does constructing huge buildings affect the rotation of the Earth, similar to skater whose angular rotation increases when her arms are closed comparatively than open?
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3answers
1k views

Origin of Ladder Operator methods

Ladder operators are found in various contexts (such as calculating the spectra of the harmonic oscillator and angular momentum) in almost all introductory Quantum Mechanics textbooks. And every book ...
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2answers
352 views

Will a spinning object come to rest?

Will a sphere spinning on its own axis come to rest given enough time, provided no other forces act upon it? I know that if you have two spinning spheres in the depths of space and orbiting each ...
3
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1answer
747 views

Can a linear momentum generate angular momentum at collision?

I'm trying to get the facts straight here. Suppose I'm throwing a ball with no angular momentum. It collides with the ground and Newton's third law tells us that a force opposite to the gravity will ...
3
votes
1answer
87 views

Why doesn't this equation for orbital motion change with position in the orbit?

The question and answer are on pg.8-10 of this PDF: At first, I went through it, thinking nothing of it. But then, I wondered: "What if we picked a final state in which the space junk was NOT at ...
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2answers
196 views

When are there enough Casimirs?

I know that a Casimir for a Lie algebra $\mathfrak{g}$ is a central element of the universal enveloping algebra. For example in $\mathfrak{so}(3)$ the generators are the angular momentum operators ...
0
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1answer
102 views

Vector cross product of $\mathbf{r}$ and $\ddot{\mathbf{r}}$ in polar coordinates

I'm struggling with the following question: Question 6 A planet of mass $m$ moves under the gravitational attraction of a central star of mass $M$. The equation of motion of the planet is ...
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1answer
251 views

Can 3 photons be combined to give a spin-0 projection?

Motivation: The neutral pion decays to 2 photons ($\pi^0\to\gamma\gamma$) most of the time. For the decay of the neutral to 3 photons ($\pi^0\to 3\gamma$) we have an upper limit on the branching ...
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1answer
215 views

Physics of the point of contact for a spinning top

I understand how spinning tops don't tip over, cf. e.g. this and this Phys.SE questions. What I'm more interested is in identifying the factors that determine the direction the spinning top moves to? ...
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2answers
201 views

For mesons, or baryons, do sea quarks contribute to the angular momentum of the bound state?

The total angular momentum of a bound state of quarks, such as a meson say, can be done by studying the spin and orbital angular momentum of the 2 valence quarks. What about the sea quarks why they ...
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1answer
1k views

How is torque equal to moment of inertia times angular acceleration divided by g?

How is the following relation true $$\tau = \large\frac{I}{g} \times \alpha$$ where $\tau$ is torque, $I$ is moment of inertia, $g= 9.8ms^{-2}$, and $\alpha=$ angular acceleration.
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2answers
1k views

Angular momentum conservation while internal frictional torque is present

So this appears in a problem which looks simple enough in its context; It's something like this: Two discs, A and B, are mounted coaxially on a vertical axle. The discs have moments of inertia $I$ ...
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1answer
422 views

Calculating the moment inertia for a circle with a point mass on its perimeter

I want to calculate the tensor of the moment of inertia. Consider this situation: The dot represents a points mass, in size equal to $\frac{5}{4}m$. $m$ is the mass of the homogenous circle. I'm ...
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3answers
779 views

How can I understand a Vortex Tube and its efficiency?

A Vortex Tube takes a pressurized input stream, most typically of a gas, and creates two output streams with a temperature differential. Apparently, it has been described as a Maxwell's Demon. Both ...
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2answers
141 views

How do objects change their axis of rotation?

If I hold a pencil at its end and spin it, throwing it upwards, it will spin about its end, but will soon start spinning around its center. How is this? I would draw the following torque diagram for ...
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3answers
640 views

What does it mean if a body has kinetic energy?

What does it mean if a body has kinetic energy? Does it mean that the momentum vectors of each particle of that body has the same direction? What about angular momentum?
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1answer
649 views

Angular momentum after elastic collision

If two balls collide (elastically) and there is no friction between them, will their angular momentum change after the collision?
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1answer
217 views

Different representations of the Lorentz algebra

I've found many definitions of Lorentz generators that satisfy the Lorentz algebra: ...
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2answers
384 views

In quantum mechanics(QM), can we define a high-dimensional “spin” angular momentum other than the ordinary 3D one?

Inspired by my previous question Questions about angular momentum and 3-dimensional(3D) space? and another relevant question How to define angular momentum in other than three dimensions? , now I get ...
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1answer
90 views

Is angular momentum conserved if you move off at a Tangent?

Lets imagine a binary system of two astronauts in space connected to one another via light rope. The rope is taut and they're spinning round and round with their axis of rotation being the the axis ...
4
votes
1answer
326 views

Questions about angular momentum and 3-dimensional(3D) space?

Q1: As we know, in classical mechanics(CM), according to Noether's theorem, there is always one conserved quantity corresponding to one particular symmetry. Now consider a classical system in a $n$ ...
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1answer
73 views

interpreting aspects of rotational motion conceptually [closed]

Level - First Year Physics University I don't understand the concept of angular momentum, conceptually. What is it? if I were to explain it how would I go about doing that? without having to explain ...
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2answers
269 views

A sphere rolling down a rough wedge which lying on a smooth surface

A sphere of mass $m$ and radius $r$ rolls down from rest on an inclined (making an angle $\phi$ with the horizontal ) and rough surface of a wedge of mass $M$ which stays on a smooth horizontal floor. ...
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0answers
56 views

Conservation of angular momentum tensor $L^{\mu\nu}$ in special relativity [duplicate]

I have edited this question because I don't think that the related post answers my question fully. It refers to Noether's theorem but I would like an explicit illustration in an easier fashion: The ...
4
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2answers
412 views

Why must the angular part of the Schrodinger Equation be an eigenfunction of L^2?

I was reading about the solution to the Schrodinger Equation in spherical coordinates with a radially symmetric potential, $V(r)$, and the book split the wavefunction into two parts: an angular part ...
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0answers
104 views

Closed-form equation for orientation and angular velocity over time

If a rigid body, rotating freely in 3d, experiences no friction or other external forces and has an initially diagonal inertia matrix $\mathbf{I}_0$ (with $I_{11}>I_{22}>I_{33}>0$) and ...
4
votes
2answers
168 views

Solve the angular part of Schrodinger equation numerically

I would like to solve the angular part (the one for what is usually called the $\theta$ angle) of a time-independent 3D Schrodinger equation $$ \frac{\mathrm{d}}{\mathrm{d}x}\left[ (1-x^2) ...
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1answer
174 views

Fundamental properties of motion

The first paragraph of the Wikipedia article on the angular momentum operator states that In both classical and quantum mechanical systems, angular momentum (together with linear momentum and ...
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0answers
215 views

Conservation of Angular Momentum: atomic transitions vs exciton decay

I have a question about the role of photon angular momentum in two different sets of selection rules: In atomic transitions within the dipole approximation, I've seen the selection rule as: $\Delta ...
4
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2answers
127 views

quantization of angular momentum

What is the most direct way of observation of quantization of angular momentum?
0
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1answer
215 views

Angular Momentum Addition Theorem

If I have, for example a particle with $s = 3/2$ and $\ell = 2$, what are the allowed values of $j$? I'm slightly confused because I know that $j = \ell + s$, so surely there is only one allowed ...
3
votes
2answers
470 views

Quantization of orbital angular momentum

Probably a very simple question, but I can't find the answer on the Internet. I know nearly to nothing about quantum mechanics, but in statistical physics I'm confronted with the idea that the orbital ...
8
votes
4answers
2k views

What causes a soccer ball to follow a curved path?

Soccer players kick the ball in a linear kick, though you find it to turn sideways, not even in one direction. Just mid air it changes that curve's direction. Any physical explanation? Maybe this ...
3
votes
1answer
771 views

Elastic collision of rotating bodies

How would you explain in detail elastic collision of two rotating bodies to someone with basic understanding of classical mechanics? I'm writing simple physics engine, but now only simulating ...
6
votes
2answers
404 views

Meaning of spin

I'm pretty astounded that I did not hear about this sooner, but in my course on QFT our professor told us that the concept of spin can be used to mean three things: Mechanical spin (apparently a ...
2
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1answer
369 views

Conservation of Angular momentum in the dipole selection rules

If the total angular momentum J of an atom is not changing during a dipole transition, where does the angular momentum for the photon come from?
4
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2answers
730 views

Quantum Mechanics: Show that the expectation value of angular momentum does not change with time

The potential is given by $V\left(\left\|(x,y,z)\right\|\right)$, so $[\hat{L}, \hat{H}] = 0$. Using the definition of $\langle \hat{L} \rangle$ and the time-dependent Schrödinger equation, show that ...
9
votes
5answers
710 views

Will freely rotatable polarizers align?

Will two freely rotatable linear polarizers (placed in sequence and at some angular offset less than, say, 45 degrees) eventually align if you shine (plenty of) unpolarized light at the first one? If ...
3
votes
3answers
287 views

Where do the conservation laws come from?

I know the conservation of energy comes from Noether's theorem via the time-translational symmetry, and if I remember correctly, the conservation of momentum comes from space-translational symmetry. ...
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1answer
619 views

How is parity relevant to determining angular momentum?

Question: Particle A, whose spin $\mathbf{J}$ is less than 2, decays into two identical spin-1/2 particles of type B. What are the allowed values of the orbital angular momentum $\mathbf{L}$, ...