The conserved quantity arising from a rotational invariance. Combine with rotational-dynamics for the classical mechanics approach and quantum-mechanics for the QM interpretation

learn more… | top users | synonyms

1
vote
2answers
610 views

Too big to revolve like an atom? [on hold]

At what point do objects naturally start revolving as a disk? From an atom, with which the electron revolves as a sphere, to a galaxy, that revolves in the same direction? I herd about rigid ...
0
votes
1answer
42 views

How to calculate the linear momentum on a dumbbell? [on hold]

In this picture there is a dumbbell and a mass in motion that hits one of the masses of the dumbbell. Now the problem is I have to find the velocity of the CM and the rotational speed around the CM. ...
-1
votes
1answer
34 views

Can light change the shape of a black hole?

If light orbits a black hole without ever getting closer or further from it, and the black hole pulls on the light from all directions, does the black hole extend at its equator? Would more light make ...
-1
votes
0answers
52 views

Frequency's relationship to Angular velocity? [closed]

I have an issue regarding the concept of getting the angular velocity. I know that angular velocity relationship to frequency is w=2π*f, however I have a problem where a right circular cylinder with ...
0
votes
0answers
37 views

Period of a Neutron star? [closed]

I need help understanding this concept of rotational motion. I have a problem that uses a star in which the star has a radius initially of 7*(10^7) km and it is treated as a solid sphere(which means ...
2
votes
1answer
33 views

Center of gravity of the photon beam

I have a conceptual question: In singular optics the orbital angular momentum (OAM) is represented by two components: intrinsic (no relation to spin!) and extrinsic. The first one is associated to ...
2
votes
0answers
52 views

Efficient Method for Multiplying Angular Momentum Operators

I'm doing a calculation that involves canonical symmetrization of angular momentum. For example: $H_{\text{classical}} = J_x J_y \rightarrow \hat{H}_{\text{quantum}} = \frac{1}{2}(\hat{J_x}\cdot \...
0
votes
3answers
193 views

How do we know that an electron “spins”?

As far as I know, you can't necessarily isolate an electron to observe it, you can only observe its effects on other particles due to fields. Moreover, we can't know an electron's exact location or ...
4
votes
2answers
77 views

Is there a relation between spin and the spin group?

In Quantum Mechanics spin appears as one type of angular momentum. Indeed, in Quantum Mechanics one angular momentum on the state space $\mathcal{E}$ is a triplet of observables $\mathbf{J}=(J_1,J_2,...
17
votes
2answers
2k views

What is black hole spin?

First of, congrats to the people at LIGO. In this article, the BBC notes that the latest LIGO results show that a new black hole was formed with a spin of $0.2$ (dimensionless number). What exactly ...
2
votes
2answers
45 views

Does a circularly polarized electromagnetic wave transfer angular momentum from the transmitter to a receiving antennae?

This question is about the rotation of macroscopic objects and looks at the magnetic vector of an electromagnetic wave. As basis for comparison, we consider an induction motor. The stator induces a ...
0
votes
2answers
102 views

Total spin of system of two spin-$1/2$ particles

Consider a quantum system of two spin one half particles. Let $\alpha(1)$ be 'spin up' for first system, and $\beta(1)$ 'spin down' for first system, and likewise for second system. We have $$ \chi = \...
3
votes
1answer
61 views

Tensor product representation of $SO(3)$ in the Hilbert space of particle with spin $S$

For a particle with a spin $S$, the rotation operator is given by $$ e^{iJ_i\theta/\hbar} $$ where $J_i$ is the component of the total angular momentum along the direction of the rotation axis. The ...
-1
votes
1answer
26 views

Calculating the work done by friction on a rigid body due to the piston

I have a uniform rod of length 0.5m and mass 0.1kg, and on this rod are two balls of mass 0.03kg both at a distance of 9.997cm away from the center of the rod. There is a pin about the center of the ...
1
vote
0answers
52 views

3 gimbal gyroscope stability

Apologies if this has been answered elsewhere but I´d rather put my trust in a dedicated community before youtube or wikipedia. Once the rotor/flywheel is up to speed the rotation and centrifugal ...
0
votes
1answer
34 views

Cross-product within commutator

I've been trying to prove some commutator identities of angular momentum, and I don't want to go brute force and prove for each coordinate seperately. So I tried using the Levi-Civita formalism for ...
-2
votes
1answer
52 views

Gravity and angular momentum

When a mass moves towards a bigger mass at a constant velocity, they will be attracted to each other such that the smaller mass will revolve around the bigger mass with the same speed as before. ...
0
votes
2answers
36 views

Conceptual understanding behind moments of force for a rigid body cylinder

I have a question behind the conceptual understanding of the following equation: $$\frac{\text{d}}{\text{d}t}\mathbf{L}_G = \sum_i \ \mathbf{r}_i\times \mathbf{f}_i$$ where $\mathbf{L}_G$ is the total ...
0
votes
1answer
24 views

Balancing an object with two loads

Suppose a bar (black) sitting on a suspended ball (blue) has two rigid loads of equal weight attached to it (red): Will the ball balance on the blue ball given even when the connection points of ...
1
vote
1answer
24 views

Would a celestial body in a horseshoe orbit be tidally locked to the planet?

A smaller celestial body like a moon or an asteroid can be in a horseshoe orbit around a planet. Since it might go inside the tidal lock radius (but does not stay inside it all the time), during the ...
0
votes
2answers
34 views

Total Angular Momentum of Hadrons

Hadrons are made of 2 or 3 quarks. Quarks have spin 1/2, so Mesons can have spin S = 1 or spin S = 0, and Baryons can have spin S = 3/2 or spin S = 1/2. Is there orbital angular momentum of the quarks ...
0
votes
1answer
43 views

Correct Definition of Angular Momentum of a Charged Particle in an Electromagnetic Field? (Classical Mechanics) [duplicate]

What is the more correct definition of angular momentum $\vec{\mathbf{M}}$ in three dimensions? (I.e. classically/Lagrangian/Hamiltonian, not necessarily quantum or relativistic) $$\vec{\mathbf{M}}...
0
votes
0answers
39 views

First order time-independent perturbation theory: How to practically calculate the perturbed wave-function

This is one of the problems that draws the line between academically learning something, and having to use it. While I learned the formulas relevant to this, I just want to make sure I'm using them ...
5
votes
1answer
172 views

Our choice of basis surely cannot effect possible outcomes of a measurement?

Common sense says that, of course, the outcome of a measurement on a quantum system cannot be affected by what base we choose to represent it in. However, while studying QM text, it seems like they ...
0
votes
0answers
56 views

Could a photon also be a fermion? [duplicate]

Some phycisits have found photons that has a spin of 1,5. Now fermions has always a half spin and bosons like photons always with a whole spin. But if those photons really exists are they than ...
0
votes
1answer
23 views

Spin on the rack

Bike mounted on hitch rack. Why wheels spin constantly while I drive? I can't find anything on the internet. The kids in the other cars love to watch them
0
votes
0answers
78 views

Parity operators and spin

Consider the following excerpt from Weinberg's Lectures on Quantum Mechanics: I follow everything up until the last statement in the excerpt. In fact, from other things I've read, it seems that one ...
2
votes
0answers
60 views

Measurement of $L_z$ in a state which includes spin

I'm working through a problem on finding probabilities for measurements performed for quantities associated with one electron in three dimensions with spin. In that case we know that the state space ...
1
vote
1answer
68 views

Under what condition is angular momentum conserved in both classical and quantum physics?

Classically, angular momentum is only conserved in a central potential by considering the torque (correct me if I am wrong). In quantum mechanics, it is also true, isn't it? If this is the case, ...
2
votes
1answer
91 views

Can light be a spinor?

A recent discovery suggests that photons can have half-integer spins. This seems to contradict the well understood notion that photons are vector (1-form) fields What does this mean for the ...
14
votes
2answers
957 views

Photons with half integer angular momentum - what's happening?

I have just read this article - what is happening? Analysing these beams within the theory of quantum mechanics they predicted that the angular momentum of the photon would be half-integer, and ...
1
vote
1answer
45 views

Momentum Conservation

The Problem: There are three masses all of equal mass $m$. One mass breaks of with velocity $v$ at an angle $\theta$ to the rod. I have to find max velocity of $A$ and the time at which this ...
1
vote
1answer
34 views

Finding the Mass of a Precessing Top

Consider a symmetric, non-nutating precessing top with one point fixed (the tip if you will). It's symmetry axis is at an angle $\theta$ to the vertical and it steadily precesses at some angular ...
1
vote
0answers
45 views

Showing classical spin tensor is time independent for free particle

Reading through Weinberg's gravitation book, the following definition is given for the spin tensor (Pauli-Lubanski psuedovector): $$ S_\alpha = \frac{1}{2}\epsilon_{\alpha\beta\gamma\delta} J^{\beta\...
0
votes
1answer
32 views

Rotation and Momentum

I understand that according to one of Euler's theorems, any solid object's 3D rotational orientation can be represented by a single 3D vector and an amount, i.e. a 4D vector. However, is it correct ...
0
votes
1answer
25 views

How high does a slide need to be if the person at the bottom grabs a pole and rotates the pole 72 degrees?

My attempt: $mgh = \frac{1}{2}I \omega^2$ $\omega^2 = 2 \alpha\Delta \theta$, so $mgh = \frac{1}{2}I 2 \alpha \Delta \theta$ $mgh = I \alpha \Delta \theta = \tau \Delta\theta$ $\tau = rF\sin \...
2
votes
1answer
59 views

Expressing eigenstates of $\mathbf{L}^2$ and $L_z$ in terms of the Cartesian eigenstates $|n_x\, n_y\, n_z\rangle$

I want to express the degenerate eigenstates of the three-dimensional isotropic harmonic oscillator written as eigenstates of $\mathbf{L}^2$ and $L_z$, in terms of the Cartesian eigenstates $|n_x\, ...
5
votes
0answers
78 views

What type of fields are continuous spin representations?

Continuous spin representations (infinite dimensional representations of the Lorentz group) are pretty rarely discussed, and usually not in that much mathematical details. And usually it is done in a ...
0
votes
1answer
17 views

Angular momentum energy loss

Suppose a man sits on a freely rotatable light chair holding 2 dumbbells to his chest, he then extends his hands while maintaining the height of each dumbbells (so that gravitational of the system is ...
1
vote
1answer
84 views

Pendulum question- Angular momentum-impulse

The pendulum of mass m and length l is released from rest at $\theta=0$. Using only the principle of angular impulse and momentum, determine the expression for $\ddot \theta $ in terms of $\theta$, ...
0
votes
0answers
20 views

Precession or projection?

A spin of 1/2 in a magnetic field is known to rotate around the direction of the field. But then it is also stated that it must be projected spin up or down. Is this simultaneous or happens after ...
5
votes
3answers
53 views

Why are pulsar's radiation beams collimated?

Every picture of a pulsar a see shows a very collimated radiation beam. What is the mechanism generating such a collimation? Note: I am not talking about "relativistic jets". I am talking about ...
0
votes
0answers
36 views

Heisenberg equation of motion for angular momentum operator

I am working on problem 5, from chapter 3 of Sakurai's Modern Quantum Mechanics. The problem has the following Hamiltonian: $$ H = \frac{1}{2}\left (\frac{K_1^2}{I_1}+\frac{K_2^2}{I_2}+\frac{K_3^2}{...
1
vote
0answers
46 views

Spinning black hole laser?

Is a laser that uses a rotating black hole's ergosphere as the gain medium possible? The idea is that the coherent light feeds off of the black hole's rotation. Assume that the black hole is ...