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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151 views

Para and ortho hydrogen angular momentum values

In Wikipedia, it is said that: Orthohydrogen, with symmetric nuclear spin functions, can only have rotational wavefunctions that are antisymmetric with respect to permutation of the two protons. ...
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170 views

Can we prove Conservation of Angular Momentum without assuming internal forces are central?

The only proof I've seen of Conservation of Angular Momentum assumes that the internal forces of the system act along the line joining particles i and j (i.e. - all internal forces are central.) Can ...
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1answer
20 views

L-S Coupling (Atomic Physics) Ground State [on hold]

Can someone please explain to me why in the second configuration the ground state is associated with $L=F=3$ and $J = 7/2 $? ** Another question: Should we always take $J$ as even? if yes, why?
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0answers
63 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 ...
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1answer
135 views

Sequential Stern-Gerlach devices - realizable experiment or teaching aid?

At least one textbook [1] uses sequential Stern-Gerlach devices to introduce to students that the components of angular momentum are incompatible observables. Viz., the $z$-up beam from a SG device ...
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1answer
20 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
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3answers
1k views

Has a body angular momentum and torque only in a circular path?

In different contexts, my book(Principles of Physics by Resnick, Halliday ,Walker) , they wrote For torque, the path need no longer be a circle and we must write the torque as a vector ...
2
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0answers
58 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 ...
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1answer
62 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, ...
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1answer
30 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 ...
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2answers
694 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 ...
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1answer
42 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 ...
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1answer
33 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 ...
2
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1answer
81 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 ...
3
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2answers
938 views

acceleration of rings in aerotrim (human gyroscope)

I'm working on a graphic simulation (just for fun, for an open-source screensaver) of an Aerotrim - a "human gyroscope", one of those exercise/training machines with a human in the middle, perched on ...
0
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1answer
39 views

Expressing angular velocity of solid body [closed]

The problem: We have a circular disk of radius $R$ and mass $M$ that is mounted on a rotation axis that is not the axis of symmetry of the disk. The moment of inertia with respect to the axis of ...
2
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0answers
130 views

Movement of a gyroscope with non-fixed axis

Assume one has a gyroscope rotating around an axis with both ends leaning on a dedicated semiplane as shown on the picture below. There is no friction either between the rotor and the axis or between ...
0
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1answer
149 views

Expectation value of total angular momentum $\langle J \rangle$

[I am working with Griffiths Introduction to Quantum Mechanics, 3rd Edition. My problem is general but if you want to look I am reading from ch 4.1 in which the weak-field Zeeman Effect is being ...
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39 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} ...
2
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2answers
189 views

Angular momentum matrices (Schiff section 27)

On page 203 3rd edition of Schiff we are given the angular momentum matrices ${J}$ for $j=1$. I am curious as to how these relate to orbital angular momentum for $j = 1$. If we take the corresponding ...
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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
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1answer
56 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\, ...
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6answers
331 views

How do point particles transfer angular momentum between each other?

I know that quantum physics says that one can't change the magnitude of spin of a point particle but that still leaves the question of how one changes the direction of spin. One possible way point ...
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66 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 ...
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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 ...
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1answer
73 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 $\theta$, ...
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31 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 ...
13
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1answer
2k views

Can one black hole suck in another black hole?

In the recent news, scientists at NASA have found “unprecedented” black hole cluster near Andromeda’s central bulge. I wonder why doesn't all these black holes merge and such each other in until just ...
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3answers
104 views

Does angular momentum of a system whose moment of inertia is changing remains constant?

An equilateral triangle $ABC$ formed from a uniform wire has two small identical beads initially located at $A$. The triangle is set rotating about the vertical axis $AO$. Then the beads are ...
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0answers
18 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 ...
4
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3answers
43 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 ...
3
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1answer
199 views

Pulsar beam radiant intensity distribution

I'm curious about the radiant intensity distribution of pulsars: what's the general dependence of intensity on angle, and what are typical angular beam widths? How much does the beam width vary ...
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0answers
76 views

Does electron spin? [duplicate]

Spin quantum number I was reading above article on spin quantum number. It says Uhlenbeck, Goudsmit, and Kronig introduced the idea of the self-rotation of the electron, which would naturally ...
0
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1answer
266 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 ...
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2answers
79 views

What factors will make Earth re-rotate again if it stopped? [closed]

"What will happen if Earth stopped rotating?" have been answered multiple times with a lot of informative and interesting answers. Continuing this hypothetical question, I have another one in mind. ...
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0answers
34 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 ...
0
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3answers
938 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 ...
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1answer
81 views

Transforming to a rotating frame in the $x$-basis

I was reading this paper on analytically Solvable driven time-dependent two level quantum systems. The Hamiltonian considered in the paper is the following: $$H=\sigma_z\cdot J(t)/2)+\sigma_x\cdot ...
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1answer
218 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 ...
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2answers
53 views

Transformation of $| JM\rangle$ under the group of rotations

I am following the Quantum Mechanics I, Galindo A., Pascual P. and in page 207 explaining the matrix representations of the Rotation Operators in the angular momentum it appears the next (obvious) ...
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2answers
56 views

What does “transfer” of angular momentum mean?

The Moon’s gravity produces tidal deformations or “bulges” in the Earth. Because of the Earth’s rotation, the line that goes through the bulges is not aligned with the line between the Earth and the ...
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1answer
113 views

Angular velocity of disc from induced motion

I came across a question regarding linear momentum $L$ and it's conservation, however I tried and got confused. It reads: A $40kg$ girl stands on the very edge of a rotating disc of mass $50kg$ and ...
3
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5answers
358 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 $| ...
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2answers
131 views

Angular momentum about a moving axis

How can we define angular momentum of a system about an axis that moves parallel to itself? For example Axis passing through CM that is perpendicular to plane of body. When we talk about ...
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3answers
436 views

Classical proof of the gyromagnetic ratio $g=2$

I was reading Representing Electrons: A Biographical Approach to Theoretical Entities, by Theodore Arabatzis. At a certain point, where he is explaining the history of the magnetic moment of the ...
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2answers
94 views

Pauli Matrices & 2D Rotation Operators?

I was doing a strange calculation with my teacher the other day: find the eigenvalues and eigenvectors of the 2D rotation operator. Intuitively, there should be no solution to this problem in ...
0
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1answer
62 views

Understanding work with rotational momentum/moment of inertia

Apologies for the basic question but between the vectors and the spinning, I'm getting confused. If I have a wheel with moment of inertia $I$ spinning at some rate $\vec\omega$ around an axis, what ...
0
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2answers
32 views

Protecting astronauts from G's when taking off/landing

When landing from orbit or launching from the ground to orbit (with chemical rockets or other means of fast acceleration), could one place the astronauts in a centrifuge and spin it to protect them ...
3
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2answers
81 views

Could 1 force cause a pure moment?

A friend of mine told me if there is only one force, it cannot cause only rotation. I wasn't convinced so I proposed a thought experiment, and now we are both confused. Suppose that we put a rod ( ...
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2answers
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Why 2s state is lower in energy that 2p state in atoms?

The s orbital have higher probability to be closer to the core and feels larger attraction than the p orbital and on average is further away and in addition p has repulsive potentilal l(l+1)h^2/2mr^2. ...