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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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 ...
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1answer
55 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 ...
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1answer
73 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
71 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
87 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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143 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 ...
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1answer
64 views

What makes us twist in a somersault?

In a backwards straight somersault you can decide whether you twist early or late. Twisting early means, that you induce the twisting movement before you rotatation hits 180° and twisting late means, ...
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692 views

What stops giant cruise ships toppling over in rough seas?

A week ago, 2 of the most gigantic cruise ships in the world docked near my city. If you have seen one, or been on one, you will know how large they are. They look extremely unsafe to me, although ...
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474 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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3answers
72 views

Why does earth spin counter-clockwise?

If we observe the earth from the north pole, we can see that the earth is rotating counter clock wise direction. The earth spins due to angular momentum, but why only in counter clock wise. Why ...
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1answer
234 views

Total orbital and spin angular momentum for a closed shell

I read one Phys.SE question similar to mine, in Total angular momentum in a full shell but the question was so confusing and vague. The answer, though, was helpful for me to understand a part of my ...
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1answer
118 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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4answers
164 views

How can an infinitesimally small object rotate?

How is it possible for an object like a black hole or electron to spin since they are made up of no other components? If my understanding is correct, an electron is an elementary particle which means ...
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1answer
359 views

What does Weinberg–Witten theorem want to express?

Weinberg-Witten theorem states that massless particles (either composite or elementary) with spin $j > 1/2$ cannot carry a Lorentz-covariant current, while massless particles with spin $j > 1$ ...
3
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0answers
81 views

Protoplanetary disks, angular momentum and prograde orbits

So you've got a protoplanetary disk and you're going to gravitate yourself some planets together. The disk is made up of the usual planetary system stuff, dust and gas and whatnot, orbiting a common ...
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42 views

What variable is the conjugate momentum for angular momentum?

From the definition of conjugate momentum for a generalized coordinate we get that the conjugate for angular momentum should be proportonal to its integral with respect to time. According to my ...
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1answer
600 views

How easily can the Earth flip?

The recent media attention to sunspot activity (however warranted) reminds me of a question I had long ago. Given the angular momentum and the slight 'wobble' of the earth, and remembering the ...
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1answer
160 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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1answer
118 views

Why is orbital angular momentum quantized according to $I= \hbar \sqrt{\ell(\ell+1)}$?

I simply have no idea how this result is found $$I=\hbar \sqrt{\ell(\ell+1)}.$$ The result seems to just be dumped in textbooks rather than explained. I can get the result that $I_z=\hbar m_j$. ...
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2answers
136 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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1answer
135 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} &= ...
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3answers
1k views
0
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0answers
41 views

What will be the affect of Global Warming if Polar Ice melts? [duplicate]

Due to global warming, all the polar ice melts & sea level increases, with increase in humidity. Angular momentum of ice at pole is, very low. Due to shift of water, from pole to equator, it's ...
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3answers
152 views

Meaning of the Angular Momentum in Quantum Mechanics

There was a discussion about the angular momentum in QM in an online course that I am attending now. The discussion and the answers did not satisfy me so I wanted to ask it on Physics SE. In the ...
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1answer
42 views

Why does angular momentum change only its direction and not its value (module) in the case of a spinning top?

I have a doubt, I hope you can help me. In the case of a spinning top precessing around the $y$-axis, there's a torque $\vec \tau$ which comes from the weight of the toy. This torque is perpendicular ...
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2answers
801 views

Angular momentum for 3D harmonic oscillator in two different bases

I know that the energy eigenstates of the 3D quantum harmonic oscillator can be characterized by three quantum numbers: $$ | n_1,n_2,n_3\rangle$$ or, if solved in the spherical coordinate system: ...
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1answer
245 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 ...
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1answer
66 views

Negative sign in rotation operator again

In Wikipedia's page on the rotation operator, section "In relation to the orbital angular momentum", they write $$ R(z,t) = exp((-i/h) \varphi L_z) $$ where $\varphi$ is the angle being rotated ...
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3answers
195 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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Why is $|a,b>+ |-a,-b>$ annihilated by the ladder operator $E_{a,b}+ E_{-a,-b}$, but no other?

Ladder operators act on states $|a,b>$ by $$E_{c,d}|a,b> = |a+c,b+d> $$ Other possible ladder operators in my example are $E_{-a,b}$, $ E_{a,-b}$ or some linear combination of them. ...
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1answer
53 views

Angular Momentum Operators - Commutation Relations

I was going over past PGRE exam questions, and came across this one. The components for the angular momentum operator $\mathbf{L}=(L_x,L_y,L_z)$ satisfy the following commutation relations. ...
2
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1answer
173 views

Problem on Einstein - de Haas experiment

I am a Physics student (4th year) and I'm trying to study the Einstein - de Haas effect in laboratory. That is what I got: a suspended Iron cylinder with about 5 cm height and a radius of 0.8 cm is ...
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2answers
79 views

If 1% of total water in earth evaporates to the atmosphere due to Global Warming, what will happen? [closed]

My views Atmospheric volume increases. Mesosphere's temperature will increase. Resulting no rainfall. Some H2O molecules will escape to the space. Rotation of Earth will slow down, resulting the ...
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4answers
2k 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 ...
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3answers
698 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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2answers
493 views

How to write Schrodinger equation!

Quantum mechanics: Suppose that there is a particle with orbital angular momentum |L|. But if the particle also has spin quantity |S| the question is: How do I reflect this into Schrodinger equation? ...
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133 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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2answers
108 views

Free rotation of a rigid body

So I am currently reading Fowles and Cassidy and there is something I'm confused about in the section about geometric description of free rotation of a rigid body. I will present the stuff first that ...
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1answer
55 views

Drag in low earth orbit

So I'm looking at the following problem; Arrow type configuration in orbit. Each end of the arrow has a mass and a cross sectional area (we can assume the head and tail are connected by a ...
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1answer
222 views
0
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91 views

Generalization of torque and angular momentum

Question: in the simple equations $\tau = r \times f$ and $L = r \times p$, what is the origin of the vector $r$? In many textbook discussions on rotation of a rigid body about a fixed axis, $r$ is ...
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4answers
7k views

What is spin as it relates to subatomic particles?

I often hear about subatomic particles having a property called "spin" but also that it doesn't actually relate to spinning about an axis like you would think. Which particles have spin? What does ...
3
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1answer
249 views

How does the Gordon Decomposition of Dirac Current give rise to spin angular momentum?

How does the Gordon Decomposition of Dirac Current give rise to spin angular momentum? I used the Gordon Decomposition to split the Probability Current of the Dirac Field into its orbital current and ...
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2answers
74 views

Larmor Precession - What does precession actually means?

Larmor Precession - What does precession actually means? Is it change in the orientation of the axis with which electron revolves around the orbit or what. But, shouldn't the radius of the orbit ...
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2answers
78 views

Using rotation matrix for spin to write x oriented spin in z-spin basis

$\newcommand{\ket}[1]{\left| #1 \right>}$The problem is to write the ket vector for a particle with spin +1/2 along the x axis, in terms of the standard basis vectors $\ket{+1/2}$ and $\ket{-1/2}$ ...
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3answers
60 views

Why can't the angular momentum vector be parallel or anti-parallel to the applied magnetic field?

This is the excerpt from my book, Arthur Beiser's Concepts of Modern Physics: An atom with a certain value of $\displaystyle{m_l}$ will assume the corresponding orientation of its angular ...
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2answers
1k views

Apparent violation of Newton's 3rd law and the conservation of angular momentum for a pair of charged particles interacting magnetically

Consider a system of the two identical point positive charges situated in free space (isolated from influence of any other external fields) as shown in the figure below. Particle 1 is at $(a,a,0)$ and ...
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1answer
552 views

Definition respective derivation of angular momentum formula

I am reading An Introduction to Mechanics by Kleppner and Kolenkow (2014). On page 241 is the definition of the angular momentum: Here is the formal definition of the angular momentum $\vec{L}$ ...
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28 views