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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5answers
679 views

Why does optical pumping of Rubidium require presence of magnetic field?

The optical pumping experiment of Rubidium requires the presence of magnetic field, but I don't understand why. The basic principle of pumping is that the selection rule forbids transition from ...
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1answer
47 views

Possible values for $L_x$

I've a physical system with $l=1$ and I have to calculate the values I can obtain if I measure $L_x$ and their probability. I know that: the values I can obtain are $\ m=0, \pm 1$ $\displaystyle ...
1
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1answer
448 views

Is Wikipedia's definition of angular velocity incorrect?

According to Wikipedia, the general formula for the angular velocity of a particle in three dimensions is $$\boldsymbol \omega = \frac{\mathbf r \times \mathbf v}{\left |\mathbf r\right|^2}.$$ But if ...
12
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9answers
8k views

How do you explain spinning tops to a nine year old?

Why don't spinning tops fall over? (The young scientist version) My nine year old son asked me this very question when playing with his "Battle Strikers" set. Having studied Physics myself, I am very ...
13
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1answer
486 views

How to evaluate this sum of coupling coefficients?

I would like to evaluate the following summation of Clebsch-Gordan and Wigner 6-j symbols in closed form: $$\sum_{l,m} C_{l_2,m_2,l_1,m_1}^{l,m} C_{\lambda_2,\mu_2,\lambda_1,\mu_1}^{l,m} \left\{ ...
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0answers
64 views

Klein-Gordon Field Angular Momentum Operator in Terms of Creation and Annihilation Operators [on hold]

I am computing the angular momentum operator for real Klein-Gordon field (essentially question six of here (though please note this is not a homework question, I am following through Tong's course via ...
4
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1answer
79 views

Does a Buckyball spin like an electron or like a baseball?

Does a Buckyball spin like an electron or like a baseball? We are often told that an electron does not really spin like a baseball. Only one (or two, if you count up and down) spin states, for ...
4
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0answers
74 views

To what depth can a whirlpool descend?

My question is based around comparing the physics of a tornado against, what I imagine/assume to be the marine equivalent of a tornado, that is a whirlpool located either at sea, in a tidal region or ...
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1answer
37 views

Commutation between Dirac hamiltonian and angular momentum

In reading about angular momentum and spin, I came across a derivation showing that the Dirac Hamiltonian does not commute with orbital angular momentum, and hence L is not conserved. What is it about ...
0
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1answer
88 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 ...
1
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4answers
1k views

motion in the body-fixed frame?

This is really basic, I'm sure: For rigid body motion, Euler's equations refer to $L_i$ and $\omega_i$ as measured in the fixed-body frame. But that frame is just that: fixed in the body. So how ...
2
votes
5answers
226 views

Eigenspaces of angular momentum operator and its square (Casimir operator)

The casimir operator $\textbf{L}^2$ commutates with the elements $L_i$ of the angular momentum operator $\textbf{L}$: $$ [\textbf{L}^2, L_i] = 0. $$ However, the $L_i$ do not commutate among ...
2
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2answers
120 views

Lagrangian point or dark matter?

We know that spiral galaxies spin in a way such that we have to assume that dark matter is responsible for the extra mass required to do so. My question is, can Lagrangian points (L1 and L2) be used ...
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1answer
127 views

What are phase conventions in angular momentum and rotation calculations?

I work with complicated angular momentum calculations related to atomic physics; nevertheless, I never need to use anything related to a phase convention (apparently because it's taken care of in a ...
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2answers
36 views

Intuitive interpretation of angular momentum in a macroscopic system

My professor defined the angular momentum operators in quantum mechanics as the infinitesimal rotations in the Hilbert space of quantum states. I'm looking for a qualitative, intuitive explanation of ...
1
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1answer
26 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
148 views

Total magnetic moment in an atom

I have a doubt regarding the calculation of total angular momentum of electron in an atom. Which is the right way to do it? Method 1: Total magnetic moment $$ \begin{align} \vec{\mu_J} &= ...
4
votes
2answers
562 views

Ten-ping bowling: Can a ping pong ball knock over a bowling pin?

In this video we see a rather unorthodox bowling technique on display. The gentleman appears to knock over all of the pins using only a ping pong ball. It's a fake, of course: you could never knock ...
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1answer
175 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 ...
2
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1answer
1k 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 ...
0
votes
1answer
262 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
votes
2answers
151 views

How many hours will be in a day if the radius of Earth increases by 70 m?

I am little confused about the linear momentum and angular momentum, will the linear momentum of earth change due to changing of its radius or it will stay as it was and i know that the moment of ...
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2answers
62 views

Why isn't angular velocity the moment of velocity if angular momentum is moment of momentum? [closed]

Angular momentum can be defined as $L$ = $\textbf{r}$ x $m\textbf{v}$. Why is angular velocity $\omega$ then not $\textbf{r}$ x $\textbf{v}$, but instead $v = \omega \times \textbf{r}$?
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2answers
152 views

$\hat{L}_{x}$ and $\hat{L}_{y}$ do not commute… or do they?

So $\hat{L}_{x}$ and $\hat{L}_{y}$ do not commute: $ [ \hat{L_{x}}, \hat{L_{y}}] = i\hbar \hat{L_{z}}$ But, what if we perform this operation on a state such that: $\hat{L_{z}} \phi_{l, m_{l}} = ...
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1answer
41 views

$L_y$ in terms of $L_+$ and $L_-$? [closed]

On the 5th slide of http://web.ift.uib.no/~lipniack/phys201_v08/angularmomentum.pdf, they say that: $$L_y=\frac{i}{2}(L_+-L-)$$ And this is not the only place I have seen this ...
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2answers
67 views

Stand on a black hole

Is there an theoretical possibility that an black hole rotates so fast that the acceleration pushing you out of the black hole is nearly equal to the gravity?
2
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1answer
111 views

What is this nested bracket notation?

The following is an excerpt from K. Varga's paper, Precise solution of few-body problems with stochastic variational method on correlated Gaussian basis: ...The function $θ_{LM_L}(\mathbf{x})$ in ...
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1answer
29 views

Time-reversal procedure for spin

What's the physical reason/explanation for the fact when time is reversed then, in addition to momentum of fermion, spin is also reversed?
2
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3answers
205 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 $| ...
0
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2answers
36 views

Conservation of Energy vs Conservation of Momentum in Rotational Dynamics

It is clear to me why angular momentum is always conserved, and how in some cases energy is not necessarily conserved within the system (in those cases where bodies deform, or friction is involved). ...
2
votes
1answer
151 views

What is the physical importance of the commutation relations of angular momentum?

What is the physical meaning of these commutation relations: $$[L_{z},L_{\pm}]=\pm\hbar L_{\pm}\tag{1}$$ and $$[L_{+},L_{-}]=2\hbar L_{z} ~?\tag{2}$$
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0answers
127 views

Spin 1/2 particles hamiltonian, addition of angular momentum confusion

Suppose I want to compute $S^{1}_z -S^{2}_z$ on a singlet state $|0,0>$. (where $S^{i}_z$ are two particles' spin operators). $$|0,0> = \frac{1}{\sqrt{2}} (|\frac{1}{2},-\frac{1}{2}> - ...
0
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1answer
46 views

Why is the tilt of Earth in sync with an orbit around the Sun?

Is there any physical reason the changing tilt of Earth (which gives rise to our seasons: Spring, Summer, Autumn and Winter) is in sync with an orbit of the Sun (i.e. one year)? It can't just be ...
0
votes
1answer
27 views

Resultant center of rotation due to multiple moments

Say, there are multiple moments (M1, M2, M3) acting on a body (of irregular shape) at points P1, P2, P3 respectively. The body is free to rotate about any point. Now, which resultant center (the ...
0
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3answers
721 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 ...
2
votes
0answers
40 views

Relativistic rotational squeezing?

I would like to consider a sphere rotating at very high angular speeds, such that the speed in its equator would be relativistic. This is very similar to Ehrenfest paradox situation, except that ...
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0answers
31 views

Angular momentum of satellite including momentum wheel

I have consulted textbooks, online sources and professionals (including spacecraft experts, dynamics lectures and mechanical engineers) without a consensus to the answer to this question. I am ...
3
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1answer
257 views
0
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1answer
43 views

Find the expression of $j_+$ and $j_-$operators [closed]

I have just started to do exercises about quantum mechanics and I have some difficulties. I have a particle with spin $j=1$ and the Hamiltonian is $H=\gamma(j_xj_y+j_y j_x)$ (where $\gamma$ is a ...
0
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1answer
30 views

Advent of our solar system

When the solar system was born why did Sun not consume all the planets by its immense gravity, as the planets were all gases, so it would have been very easy?
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2answers
54 views

Force needed to deflect a gyro

Although all related articles (and also question/answers here) say that a gyro resists any attempt to change its plane of rotation, I haven't been able to find the formula/ rule that specifies the ...
0
votes
0answers
8 views

trace of spherical components of an angular momentum multiplet

My basic mathematical question is whether or not there exist selection rules regarding the traces of the spherical tensor components of some operator acting on some subspace of definite total angular ...
31
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3answers
3k views

Why the galaxies form 2D planes (or spiral-like) instead of 3D balls (or spherical-like)?

Question: As we know, (1) the macroscopic spatial dimension of our universe is 3 dimension, and (2) gravity attracts massive objects together and the gravitational force is isotropic without ...
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2answers
335 views

Does conservation of momentum mean a gyroscopic inertial thruster cannot work?

There is a device called the gyroscopic inertial thruster. Here is a Wikipedia article on it. I believe that this device cannot possibly work and that conservation of momentum proves that it cannot ...
2
votes
1answer
60 views

Why don't things balance after they stop spinning?

When I spin a penny, I spin it on its "edge" (circumference). So why is it that when the penny inevitably stops spinning, it never comes to rest on its edge, instead falling onto one of its faces? It ...
0
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1answer
81 views

How is angular momentum conserved?

A uniform vertical turntable (mass M and radius R center O) is at rest on the xy plane and is mounted on a frictionless axle, which lies along the vertical z axis. I throw a lump of putty mass m with ...
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3answers
77 views

Can we reduce a hurricane's power using wind turbines?

Below is the abstract of an article in Nature: Taming hurricanes with arrays of offshore wind turbines, describing computer simulations that indicate that wind turbines could disrupt a hurricane ...
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1answer
90 views

Why do $H$ and $L^2$ commute in spherically symmetric potential?

In this PDF document (a lecture by Shivaly Reddy, page 13), he says that $L^2$ is independent of $r$; therefore it commutes with any function of $r$. This seems related to a problem in ...
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3answers
147 views

Why is only one quantity of angular momentum i.e. $L_z$ quantized & not $L_x$ & $L_y$?

This is quoted from Arthur Beiser's Concepts of Modern Physics: Why is only one quantity of $\mathbf{L}$ quantized? The answer is related to the fact that $\mathbf{L}$ can never point in any ...