The conserved quantity arising from a rotational invariance. Combine with rotational-dynamics for the classical mechanics approach and quantum-mechanics for the QM interpretation
10
votes
2answers
85 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
votes
1answer
62 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
vote
1answer
72 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 ...
1
vote
1answer
54 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?
...
3
votes
1answer
59 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
votes
1answer
70 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.
2
votes
1answer
110 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 $I$ ...
0
votes
1answer
39 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 ...
3
votes
1answer
52 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 ...
5
votes
2answers
63 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 ...
1
vote
2answers
131 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?
3
votes
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?
3
votes
1answer
87 views
Different representations of the Lorentz algebra
I've found many definitions of Lorentz generators that satisfy the Lorentz algebra: ...
2
votes
2answers
144 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 ...
1
vote
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 ...
2
votes
1answer
102 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 $n$ ...
1
vote
1answer
34 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 ...
0
votes
1answer
59 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. ...
0
votes
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 ...
4
votes
2answers
177 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
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 ...
4
votes
2answers
88 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
vote
1answer
54 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 ...
1
vote
0answers
57 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
votes
2answers
85 views
quantization of angular momentum
What is the most direct way of observation of quantization of angular momentum?
0
votes
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 ...
2
votes
2answers
120 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 ...
7
votes
4answers
471 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 ...
2
votes
0answers
89 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 ...
2
votes
1answer
100 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
328 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 ...
8
votes
5answers
651 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
188 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
137 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
124 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 ...
5
votes
2answers
215 views
Do we have any effect on the rotation of he earth?
We walk or ride on our vehicles to our destinations daily. Does our movement have any effect on the rotation of the earth according to Newton's law? What will be the effect if we move all the peoples ...
2
votes
2answers
144 views
A universe of angular momentum?
I read this on Wikipedia:
[...] That most tangible way of expressing the essence of quantum mechanics
is that we live in a universe of quantized angular momentum and the
Planck constant is the ...
4
votes
2answers
91 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
vote
2answers
109 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
votes
1answer
90 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
votes
1answer
183 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
votes
1answer
183 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.
0
votes
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 ...
3
votes
3answers
73 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).
...
2
votes
2answers
412 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 ...
1
vote
0answers
96 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 $s2 = \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 or 0.
Now ...
0
votes
0answers
43 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
vote
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$ ...
1
vote
1answer
134 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} + ...
1
vote
1answer
247 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
