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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8
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2answers
575 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 ...
1
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3answers
65 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 ...
1
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1answer
227 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 ...
2
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4answers
155 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 ...
0
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0answers
42 views
3
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0answers
41 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 ...
1
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1answer
599 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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0answers
38 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 ...
0
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1answer
39 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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0answers
16 views

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. ...
1
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1answer
47 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. ...
0
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2answers
77 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 ...
0
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1answer
64 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 ...
3
votes
2answers
101 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 ...
0
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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 ...
0
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2answers
89 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 ...
1
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2answers
72 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 ...
0
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2answers
124 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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3answers
58 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 ...
1
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2answers
77 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 $\ket{-1/2}$ ...
0
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0answers
26 views

How is angular momentum conserved in this proton+water scenario?

Consider a universe consisting of only one water molecule and one proton. ...
0
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1answer
46 views

If I start spinning a raw egg slowly why does its angular velocity increase spontaneously?

If I start spinning a raw egg very slowly in place, why does its angular velocity increase spontaneously? This is something I noticed the other day while cooking. It doesn't do the same thing with a ...
0
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1answer
40 views

Schaum explication of eigenvectors of Lz

In Schaum's Quantum Mechanics, in Chapter 6 Angular Momentum, they say "the eigenvectors of $L^2$ and $L_z$ are functions that depend on the angles $\theta$ and $\phi$ only; hence, we can represent ...
0
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1answer
37 views

Combining moments of Inertia in gear chain

I've got two objects connected by a rod along it's axis of rotation (e.g. a sphere on top of a flat cylinder rotating around it's symmetric axis). Assuming the effects of the rod are negligible, is ...
1
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1answer
54 views

Operator in Hilbert space of a spin

I'm studying quantum mechanics with Shankar's "Principles of Quantum Mechanics" 2nd edition. I'm afraid that it might be a boring question but I can't understand the following statement (389p): We ...
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0answers
76 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 ...
0
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1answer
76 views

Negative sign in rotation operator (quantum mechanics, angular momentum) [duplicate]

Schaum's Quantum Mechanics comes up with $$\exp((-i/\hbar)\cdot \theta \cdot{\hat{L}} \cdot {\overrightarrow{n}})$$ as the formula of the rotation operator. Other sources I see don't have the ...
1
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1answer
70 views

Do particles have spin because there exist spinor representations for the Lorentz group?

I am reading Peskin and Schroeder's An introduction to field theory. They first describe the spinor representation of the Lorentz group, and then they mention the fact that different particles have ...
0
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1answer
76 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 ...
0
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1answer
76 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 ...
0
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1answer
51 views

conservation of angular momentum/conservation of energy?

Perhaps a dumb question to ask, but I was given the following problem to solve: A 10 g bullet traveling at 400 m/s strikes a 10 kg, 1.0-m-wide door at the edge opposite the hinge. The bullet embeds ...
1
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2answers
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}} = ...
0
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1answer
36 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 ...
0
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1answer
18 views

Angular momentum conservation laws and GHZ article (Greenberger et al 1990)

Can anyone recommend a good book or an online source on angular momentum conservation laws in decay processes? I'm writing a master's thesis concerning Bell inequalities and currently working on GHZ ...
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2answers
50 views

Does momentum change if rotation radius changes?

Angular momentum is defined as $L = r \times p$ where r is the center of rotation and p is the momentum. Since angular momentum is conserved, if r decreases then p must increase. And since p is m*v ...
-1
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1answer
124 views

if the Earth's rotation was slowed down, would it naturally speed back up as it was before? [closed]

Fact: The Earth is rotating on it's own axis every 24 hours. Question: If, for some reason I won't specify the current speed of the Earth and could slow it down(say by 5%). Will it speed up again ...
0
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1answer
42 views

Torque in a non-inertial frame

How can we calculate torque in a non-inertial frame? Take for instance a bar in free fall with two masses, one on either end, $M_1$ and $M_2$. Taking the point of rotation to not be the center of ...
0
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1answer
60 views

Getting to spins of arbitrary direction

Let me rephrase this question: Let us assume we know that symmetry transformations always look like this: $$U(s)=e^{iKs} $$ with a hermitian Operator K. This tells us that for very small $s$: ...
1
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0answers
24 views

Expectation value in spin-orbit coupling

So I was just trying a question where it asked to find the Energy shift due to a spin-orbit coupling Hamiltonian to first order using perturbation theory. The Hamiltonian is $$H_{LS} = ...
0
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0answers
29 views

Addition of 3 angular momenta

I'm struggling to understand how the orbital angular momentum "add" in ground state Nitrogen. As I understand it N has an electron configuration of $1s^22s^22p^3$ and so the 3 outer electrons in the ...
2
votes
2answers
90 views

Deflection Effects on a Spinning Solar Sail

Suppose I have a solar-sail-powered starship flying directly away from a star. The sail is flat and perpendicular to the direction of travel. Now, in order to make the trajectory more stable (we ...
0
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0answers
75 views

Why Does Moving a Cup of Coffee Up and Down whilst carrying it Make it less Likely to Spill?

Sometimes I have a Very Full Mug of Coffee and I am trying to carry it without it spilling. I noticed that if I moved the Mug up and down when carrying it, it seemed to settle the coffee and make it ...
2
votes
1answer
59 views

Particle Physics Decay Question - Eta Prime Decay Parity/Angular Momentum Conservation

I was hoping someone could clarify why the following decay does not occur: $ \eta ^{'0} \rightarrow \pi ^{0} + \rho ^{0}$ The quark compositions and spin parity are as followed: $ \eta ^{'0} : ...
0
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1answer
61 views

Shape of galaxies [duplicate]

i want to know why galaxies are spiral in nature.. let us say there is some sort of intense mass (black hole?) at the centre of our milky way galaxy. the intense gravitaional pull is keeping evey ...
4
votes
1answer
64 views

Does Birkhoff's theorem apply to rotating collapsing stars?

Birkhoff's theorem states that every spherically symmetric vacuum solution to $R_{\alpha\beta} = 0$ is static, which greatly assists in the solution to the Schwarzschild solution by eliminating time ...
0
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1answer
42 views

Angular momentum & Energy using Yukawa's potential [closed]

I was doing my Gravitation problems and I found this one that I'm unable to solve. Yukawa's theory for nuclear forces states that the potential energy corresponding to the attraction force ...
2
votes
1answer
93 views

Angular momentum - proof for integer eigenvalues

I am confused about a proof my Quantum Mechanics textbook has left "as an exercise for the reader". So, we've got the angular momentum operator $\hat{L}$. We've also got the generalized angular ...
0
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0answers
27 views

Need clarification for Relation between angular momentum and centripetal force

I've recently started studying angular momentum, so, as far as I understand, angular momentum is conserved as long as any form of centripetal force can be maintained in the new system or otherwise it ...
1
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0answers
41 views

how to rotate scaled-vector (orientation) by scaled-vector (rotation)

Recently I seem to have gotten the physics-engine portion of my 3D simulation/game engine [apparently] working correctly. The most convenient way to store and compute position and orientation are in ...
1
vote
1answer
85 views

Why does a diver changes his body positions before and after diving?

Before a diver dives in a pool, he changes his body positions several times. When he is about to jump from board he extends his arms and legs but sometime after jumping he closes his body in a ...