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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0answers
9 views
MIT algebraic question - Elliptic Orbits, Kepler's Second Law, Energy Conservation - What just happened?
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 ...
10
votes
2answers
127 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 ...
1
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1answer
90 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 ...
3
votes
3answers
796 views
Could life survive a pole shift caused by an asteroid collision?
Could life on earth survive a large pole shift caused by an asteroid collision?
I became aware that there are people who believe that the earth's pole suddenly shifts. That is, its rotational ...
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2answers
96 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 ...
7
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4answers
481 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 ...
0
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1answer
65 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
...
1
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1answer
55 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?
...
2
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1answer
112 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 $I$ ...
3
votes
1answer
60 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 ...
0
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1answer
79 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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0answers
53 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 ...
2
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0answers
90 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 ...
15
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8answers
4k views
Why don't spinning tops fall over?
One topic which was covered in university, but which I never understood, is how a spinning top "magically" resists the force of gravity. The conservation of energy explanations make sense, but I don't ...
5
votes
2answers
64 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 ...
3
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1answer
53 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 ...
0
votes
1answer
41 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 ...
2
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1answer
103 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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2answers
132 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
75 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?
2
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2answers
148 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 ...
3
votes
1answer
90 views
Different representations of the Lorentz algebra
I've found many definitions of Lorentz generators that satisfy the Lorentz algebra: ...
4
votes
2answers
92 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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1answer
250 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
29 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 ...
10
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2answers
2k views
How to define angular momentum in other than three dimensions?
In classical mechanics with 3 space dimension the angular momentum is defined as
$\mathbf{L} = \mathbf{r} \times \mathbf{p}$
In relativistic mechanics we have the 4-vectors $x^{\mu}$ and $p^{\mu}$, ...
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votes
1answer
61 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. ...
1
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1answer
35 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 ...
4
votes
2answers
181 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 ...
1
vote
2answers
284 views
Conservation of angular momentum in propeller planes and helicopters
Consider a propeller plane with only one propeller in the front. If the propeller rotates, I would expect by conservation of angular momentum, that the body of the plane would spin in the opposite ...
4
votes
2answers
90 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) ...
1
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0answers
44 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 ...
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1answer
55 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 ...
4
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2answers
728 views
Why Silver atoms were used in Stern-Gerlach experiment?
For the Stern-Gerlach experiment done in 1922:
1-why silver atoms were used?
2-Silver atom contains many electrons in different orbits (different $l$'s). Wouldn't the inner -shell electrons be ...
1
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0answers
59 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 ...
8
votes
1answer
485 views
How does one experimentally determine chirality, helicity, spin and angular momentum?
If I've got an instance of a fundamental particle, how can I separate out the measurements of these three concepts?
(I think) I understand the theory behind them, and why the particles in the ...
4
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2answers
85 views
quantization of angular momentum
What is the most direct way of observation of quantization of angular momentum?
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1answer
59 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
1answer
251 views
Angular Momentum Addition Theorem - Sanity Check
Looking back at my quantum mechanics notes, the angular momentum addition theorem is listed as:
$j=j_1+j_2,j_1+j_2-1, ..., |j_1-j_2| $ (Using conventional notation)
, but I'm a little unsure how to ...
2
votes
2answers
121 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 ...
5
votes
1answer
343 views
Simultaneously commuting set
How does one determine the members of an simultaneously commuting set (of operators)? For example, I have read that for orbital angular momentum, the set is {$H,L^2,L_z$}. How does one know that these ...
1
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1answer
46 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 $I_1$ ...
3
votes
1answer
174 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\\
...
2
votes
1answer
104 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
votes
2answers
334 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 ...
7
votes
1answer
268 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 ...
8
votes
5answers
653 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
190 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.
...
2
votes
0answers
139 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 $\mathbf{L}$, ...
3
votes
2answers
128 views
Space Quantization of Quantum Angular Momentum
I am trying to understand what my book is trying to convey.
Quantum angular momentum is $L_z = m_l \hbar$
"Choosing arbitrarily a z axis and using an appropriate experimental technique, we measure ...
