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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883 views

Counter Rotating Bicycle wheels on same axis-> Will they still cause me to spin on a stool?

So people are familiar with the idea of holding a spinning bicycle wheel while on a stool (whose seat can spin). You then tilt the spinning wheel and lo and behold you start to spin on the stool. Ok ...
2
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2answers
915 views

Mech stability through gyroscope

I recently read up about gyroscopes, angular momentum and mechs (the big Cockpit controlled robots) and was wondering if it would be possible to get a stable walking mech (only as example, not meant ...
2
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1answer
788 views

Does ABS cause a force that resists turning a car into a corner?

ABS systems work by allowing a tire to continue to rotate rather than "locking-up" (stop turning) due to loss of traction with the road surface. A rotating tire can influence the direction of the ...
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2answers
475 views

Homework about spinning top [closed]

I have a top of unknown mass that has a moment of inertia $I=4\times 10^{-7} kg \cdot m^2$. A string is wrapped around the top and pulls it so that its tension is kept at 5.57 N for a distance of .8 ...
2
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1answer
112 views

Angular momentum, what is it, is it conserved, and how do we know?

Firstly, most definitions of angular momentum assume a point about which you define angular momentum. I realize that you can consider the angular momentum about any point, and have many angular ...
2
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1answer
76 views

Rotation from Goldstein's Classical Mechanics

I apologize for the ambiguity in my title. It was rather difficult to figure out what is the most appropriate title for my questions. My questions come from chapter 4 and chapter 5 of Goldstein, ...
2
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2answers
120 views

How to explain spin of electron? [duplicate]

How can we explain spin of electron, or the spin of other fundamental particles? If we think the spin of electron is similar to the spin of a ball or planet we make a mistake. We say it is an ...
2
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2answers
58 views

Why do rotations of a multicomponent state function take this form?

I am reading Leslie Ballentine's Quantum Mechanics, section 7.2, which is all about the explicit form of the Angular Momentum operators. I understand how he gets the form for the single component ...
2
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1answer
55 views

Formalism and representation in Quantum Mechanics

I am just curious about the formalism of basic Quantum Mechanics. Lets take for instance the system of a spin-$\frac{1}{2}$ particle. The state of the particle is described by a vector in an abstract ...
2
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1answer
67 views

Angular momentum of anyons

Why is it true that anyons can have angular momentum taking any real value? Why aren't they restricted to the $j(j+1)$ integer values most are familar with?
2
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1answer
43 views

Pulsars with accreting disk in binary system

Following this line, I am wondering about the following question. Accreting pulsars in binary systems are usually thought to accrete from a prograde disk, so increasing their spin in the process. ...
2
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1answer
144 views

Why the orbital angular momentum equal zero for electron in s state? does it mean that the electron doesn't orbiting in s [duplicate]

Why is the orbital angular momentum $l$ equal to zero for electrons in the $s$ state? Does it mean that the electrons aren't actually orbiting?
2
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1answer
39 views

Angular momentum of a black hole

I recently read this Phys.SE post and, since I didn't know that black holes had a spin, a question came to my mind: how can I calculate the spin velocity of a black hole? Does mass or radius affects ...
2
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3answers
88 views

Instantaneous angular momentum of a disc

Suppose we have a disk of radius $r$ and mass $m$ travelling at velocity $v$. I want to calculate the instantaneous angular momentum with axis through the edge of the disc (on the circumference). ...
2
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1answer
134 views

Sign wrong in angular momentum (Quantum Mechanics)

For small angles $\theta$ the rotation along a particular axis $n$ is given by $R(n,\theta)(r)=Id+ \theta (n \times r)+ o(\epsilon)$. Now, the rotation operator in Quantum Mechanics is given by ...
2
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1answer
419 views

Hamiltonian matrix off diagonal elements?

I'm trying to understand how Hamiltonian matrices are built for optical applications. In the excerpts below, from the book "Optically polarized atoms: understanding light-atom interaction", what I ...
2
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1answer
206 views

Does the spin precession change sign when the angular momentum does?

Say you have a charged particle moving circularly in an electromagnetic field. Basic quantum mechanics tell us that its spin will precess with a certain frequency. If the same particle were traveling ...
2
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1answer
824 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 $\mathbf{L}$, ...
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2answers
185 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 ...
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1answer
698 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.
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1answer
626 views

How does weight/mass affect angular momentum?

How does weight/mass affect angular momentum? For my 8th gr science fair project I have to do an experiment on angular momentum. My problem is that we have not been taught any of that in physics yet, ...
2
votes
1answer
179 views

Normalization of a spin-like quantity in matrix mechanics

Suppose that there is a quantity in Heisenberg picture as the following: $A=u_1\Sigma_1 + u_2\Sigma_2 +u_3\Sigma_3$ I am not sure why $u_1,u_2,u_3$ is normalized to be ${u_1}^2 + {u_2}^2 + {u_3}^2 ...
2
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2answers
191 views

Multiplicity of eigenvalues of angular momentum

Reading Dirac's Principles of Quantum Mechanics, I encounter in § 36 (Properties of angular momentum) this fragment: This is for a dynamical system with two angular momenta $\mathbf{m}_1$ and ...
2
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1answer
4k views

What's the right way to calculate the principal moment of inertia?

I am writing a program that incorporates calculating the principal moment of inertia for a protein residue based on its component atom XYZ coordinates. I am exceedingly confused about which formulas ...
2
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1answer
514 views

Double gyroscope: Can a spinning pencil tumble on only one axis?

Picture an object such as item 7 on this page .. http://en.wikipedia.org/wiki/List_of_moment_of_inertia_tensors Call that the x axis and z is in to the distance. See diagram below. We are in deep ...
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1answer
231 views

How could $\textbf{S}^2$ not be a multiple of the identity?

I'm self-studying quantum mechanics with Sakurai's book (Modern Quantum Mechanics, 2nd edition) and came across the following in reference to the operator $\textbf{S}^2$: As will be shown in ...
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1answer
977 views

Converting angular velocity to linear velocity through friction

A very basic question here; it's related to this one, but not quite the same. If a rotating rigid body (a sphere for the sake of discussion) with mass $m$, radius $r$ and inertial tensor $I$ has ...
2
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1answer
320 views

Measuring the mass using angular velocities

I have 2 objects which are intially connected together, $O_1$ and $O_2$. When they are connected together, they have a rotation rate about their center of mass of $w_1$. $O_2$ is cleanly released from ...
2
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1answer
623 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 ...
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0answers
25 views

In 2-dimensional and 3-dimensional universes, stellar systems and galaxies are flat and disky. But what about in 4-dimensional universes?

I just watched that interesting video: https://www.youtube.com/watch?v=tmNXKqeUtJM In 2 dimensions a cloud of particles rotating in a plane is flat by definition since it's in 2 dimensions. ...
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0answers
23 views

What is the relationship between the angular speed and the diameter of the eye of a water vortex?

In a water vortex formed in a plastic bottle, what is the relationship between the angular speed of the water and the diameter of the hole in the cap? I would have expected that according to the ...
2
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0answers
40 views

When Did Structures Begin to Orbit in the Universe?

In Big Bang Cosmology, I am familiar with the radiation era, and the moment of last scattering, but I am just not familiar with the physics of orbits, or of the “falling outward,“ if you will, that ...
2
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1answer
42 views

Why does the raising and lowering operator not affect total angular momentum?

My notes define: $$ L_{\pm} = L_{x} \pm i L_{y} $$ and states: $$ [L_{z},L_{\pm}] = \pm \hbar L_{\pm} $$ I'm fine with this as it's easy to show the result with some ugly algebra. It then says: ...
2
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2answers
49 views

How to model energy loss in a rotating body?

I recently asked a question about modeling instability in a rotating rigid body. I now realize that I was mentally confounding two different effects: The "Dzhanibekov effect" in which a rigid ...
2
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1answer
46 views

Transfer of angular momentum during oblique impact with(out) adhesion

I am solving a problem of 2 identical spherical particles colliding. The impact is oblique. I consider both normal and tangential contact forces. Tangential force is a combination of elastic force ...
2
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0answers
40 views

How do I calculate integer and half integer spin? [closed]

How do I calculate integer and half integer spin, and how do I use the calculations?
2
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2answers
200 views

Angular Momentum Operator in Quantum Field Theory

I'm following along with David Tong's QFT course and am trying to derive the result shown in question 6 on his 2nd problem sheet, but am running into problems when applying it to the free real scalar ...
2
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0answers
92 views

What are the assumptions behind “term symbols”?

In multi-electron atoms, the electronic state of the optically active "subshell" is often expressed in "term symbols" notation. I.e. $^{2S+1}L_J$. This presumes that the system of electrons has ...
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0answers
49 views

Stern Gerlach experiment - only two discrete beams?

The Stern Gerlach experiment was meant to prove the orbital quantization of electrons where there should be +ml,0,-ml states. So for l=2, there should be 5 beams. But they saw 2 beams, which was ...
2
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0answers
67 views

Spin of a decay product

A particle A decays into particles B, C and D. The spin of A, B and C particles is 1/2 each. What are the possible spins of particle D? My attempt is the following: Since B and C have spin 1/2 ...
2
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1answer
313 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 ...
2
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0answers
253 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 ...
2
votes
1answer
408 views

Angular momentum components as independent integrals of motion

I was told that in order to solve the Kepler problem (6 degrees of freedom in total) you have to proceed, step by step, to reduce those degrees of freedom using the integrals of motion. You do so ...
2
votes
1answer
263 views

Will a precessing spinning wheel fall down if there is no friction at all?

If there where no friction at all, would a spinning wheel held up by one end of the axis spin precess forever without falling down? I just asked another question about the same problem: Direction ...
2
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0answers
238 views

Why do control moment gyroscopes exhibit “torque amplification”?

There are a number of articles that describe the benefits of using control moment gyroscopes (CMGs) over reaction wheels in inertial navigation applications. One of the primary benefits of using a CMG ...
2
votes
1answer
74 views

Single plane Ring system [duplicate]

Possible Duplicate: Why are our planets in the solar system all on the same disc/plane/layer? I've noticed this in many pictures, Planets are shown with a single ring around them (in some ...
1
vote
3answers
498 views

Is it possible to deduce the conservation of angular momentum from the conservation of energy?

Is it possible to deduce the law of conservation of angular momentum from the law of conservation of energy? If possible, by what sense the conservation of angular momentum has the status of law, if ...
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2answers
104 views

Differentiating a vector product

$$m_i\mathbf{r}_i\times\frac{\mathrm{d}^2\mathbf{r}_i}{\mathrm{d}t^2} = \frac{\mathrm{d}}{\mathrm{d}t}\biggl(m_i\mathbf{r}_i\times\frac{\mathrm{d}\mathbf{r}_i}{\mathrm{d}t}\biggr)$$ I do not ...
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2answers
655 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 ...
1
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3answers
829 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?