# Questions tagged [angular-momentum]

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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### Coupling Coefficients in SO(4)

I have two equations (from two distinct authors) for the decomposition of a coupling coefficient of SO(4) (i.e. Wigner 3j-symbol for SO(4)). In the first: \left( \begin{array}{ccc} ...
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### Spin angular momentum of a system of particles : Is there any energy associated with it?

Consider a system of point particles , where the mass of particle $i$ is $μ_i$ and its position vector is $\vec{r}_i$. Let $\vec{r}_\text{cm}$ is the position vector of the center of mass of the ...
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### 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 ...
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### On the origin of the rotation of celestial bodies [duplicate]

Possible Duplicate: Why does Venus rotate the opposite direction as other planets? Why does every thing spin? As far as I can imagine, almost each celestial body, star, planet, solar-systems, ...
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### Why do 3d spheres and gravity tend to rotating discs on one plane?

Whether is it our solar system or a whole galaxy, there is usually a massive object (star or black hole) at the centre with gas and objects rotating around it. The gravitational effect of the star/...
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### Crystal Field Theory

I am literally lost with this question: Suppose that within the set of (2L+1)(2S+1) lowest-lying ionic states the crystal field can be represented in the form a(L_x)^2 + b(L_y)^2 + c(L_z)^2, with a,...
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### What happens to a rotating rod that breaks in two?

I know that the approximation for the moment of inertia of an infinitely thin rod of mass $m$ and length $L$ spinning around an axis perpendicular to its own axis at its center is $\frac{mL^2}{3}$: ...
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### Effect of rotation on turbulence threshold for Reynolds number?

If the significance of the Reynolds number is: Then what is the effect of angular momentum on the transition from laminar to turbulent as in a convective vortex? Waterspouts, in particular, seem to ...
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### Why are spacecraft made to “spin” after launch?

At some point after launch, usually just before or after separation from the last booster stage, spacecraft are often made to "spin" (about the axis of their trajectory)? See e.g this You Tube video. ...
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### 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 ...
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### How do you combine two rigid bodies into one?

With respect to some fixed frame of reference, given the inertial tensors, positions, orientations, and angular and linear velocities of two rigid bodies, how do you combine them to make a single ...
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### Why does the Earth rotate? [duplicate]

Possible Duplicate: Why does every thing spin? So why would the Earth, or any planet for that matter, rotate along an axis? I know of no force which could come into play here, so i assume it just ...
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### Conservation of angular momentum for a nonrigid body

Question: The sun is not a rigid body but a hot ball of gas. The period of rotation varies from 37 days at the pole to 26 days at the equator. The mean radius of the sun is $7\times 10^8\text{ m}$. ...
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### 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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### Equation that tells me the rpm and mass of a spinning disk needed to keep a second large mass stable using gyroscopic effects

I am trying to figure out how large of a mass and how quickly I need to spin said mass to keep a two-wheeled robot stable. Ideally, I am looking for a formula that relates m1=mass of robot, m2=mass of ...
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### Interference of EM Waves with Orbital Angular Momentum

If you have two coherent collinear e-m beams of same frequency and polarization, but 180 degrees out of phase, they will destructively interfere. If you introduce orbital angular momentum of L=3 (...
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### Why are some galaxies flat?

What is the explanation for the flatness of some galaxies? (If it's due to their rotation then why they are rotating, why some other galaxies are not flat etc., I would like to hear a nice and ...
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### 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 ...
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### Simultaneously commuting set

How does one determine the members of an simultaneously commuting set (of operators)? For example, I have read that for orbital angular momentum, the set is {$H,L^2,L_z$}. How does one know that these ...
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### Why are our planets in the solar system all on the same disc/plane/layer? [duplicate]

I always see pictures of the solar system where our sun is in the middle and the planets surround the sun. All these planets move on orbits on the same layer. Why?
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### Where are the centers of mass for a baseball bat vs. a cricket bat?

My friend and I were comparing the rightness of a cricket bat versus a baseball bat for general violence purposes. (Eg, rioting.) Where are the centers of mass for these two instruments? Which would ...
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### confused about ball rolling and rotational energy

I was solving a practice test problem and it was just a conservation of energy problem where a spherical ball is falls from a height h to the ground such that mgh = \frac{1}{2}mv^2 + \frac{1}{2}I\...
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### What determines a progenitor's fate as a spiral or elliptical?

I was thinking about my answer to Are the inner planets on planar orbits because there was more dust in the inner solar system (early on in planetary accretion)? - when it occurred to me that maybe I ...
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### Where the angular momentum has gone?

I came across an interesting problem when I prepared for the preliminary exam on electromagnetism. Below is the problem in its original words: A metallic sphere of mass, $m$, and radius, $a$, ...
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### Spinning wheel on rotating stool - why am I also affected even when the wheel axis is horizontal?

So I can point the axis of spin in one horizontal direction - and then move it in another direction (so it stays horizontal - like the picture below). And that still changes the direction of spin (on ...
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### How is angular momentum conserved when a spinning top finally stops spinning?

Where does the top's angular momentum get transferred to? Does it very slightly change the angular momentum of the table, and then the angular momentum of the Earth?
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### Where does a star's angular momentum go as its spin slows down?

So we know that stars slow down as they age. But total angular momentum must be conserved. Where does that angular momentum go? The dissipation of Earth's tides somehow transfers Earth's angular ...
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### Converting Angular Momentum?

I am aware of three apparently different forms of angular momentum: spin, orbital and macroscopic, like a spinning crystal or baseball. Can angular momentum be transferred or converted from one of ...
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### How does Hubble's constant affect the Earth's orbit

If Hubble's constant is $2.33 \times 10^{-18} \text{ s}^{-1}$ and the earth orbits the sun with average distance of 150 million kilometers; Does that mean the earth's orbital radius increases ...
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### N particles, will there be any rotation after a period of time or everything will collapse

This is in context of classical Newtonian physics. Consider a system of n different point mass particles. Initially all are spread around on one plane. No particle possess any velocity to begin with. ...
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### Why does everything spin?

The origin of spin is some what a puzzle to me, everything spin from galaxies to planets to weather to electrons. Where has all the angular momentum come from? Why is it so natural? I was also ...
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### maximum rotational speed

I am wondering if there is a limit to rotational speed of an object just like there is one for translation speed ? what are the implications of general relativity for rotating objects ?
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### Clebsch-Gordan Identity

I'm trying to take advantage of a particular identity for the sum of the product of three Clebsch-Gordan coefficients, however, the present form of my equation is slightly different. Is there a ...
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### generalizing spin rotations

I have a question about the relation: $\exp(-i \vec{\sigma} \cdot \hat{n}\phi/2) = \cos(\phi/2) - i \vec{\sigma} \cdot \hat{n} \sin(\phi/2)$. In my texts, I see $\phi\hat{n}$ always as c-numbers. My ...
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### Sum of angular momentum of all electrons in a magnet

Can the sum of angular momentum of all rotating electrons in all the aligned atoms in a permanent magnet have a significant contribution to the macro angular momentum of the magnet? If yes, why does ...
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### How does one experimentally determine chirality, helicity, spin and angular momentum of a fundamental particle?

If I've got an instance of a fundamental particle, how can I separate out the measurements of these four quantities? (I think) I understand the theory behind them, and why the particles in the ...
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### Why does each celestial object spin on its own axis?

AFAIK all the celestial objects have a spin motion around its axis. What is the reason for this? If it must rotate by some theory, what decides it's direction and speed of rotation? Is there any ...
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### QM interpretation of Larmor precession

Typically when I think of a spin moment in an external field, I visualize it classically in terms of a magnetic moment precessing around the external field vector. Now how is this described quantum ...
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### Integral of the product of three spherical harmonics

Does anyone know how to derive the following identity for the integral of the product of three spherical harmonics?: \begin{align}\int_0^{2\pi}\int_0^\pi Y_{l_1}^{m_1}(\theta,\phi)Y_{l_2}^{m_2}(\...
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### How to define angular momentum in other than three dimensions?

In classical mechanics with 3 space dimension the angular momentum is defined as $\mathbf{L} = \mathbf{r} \times \mathbf{p}$ In relativistic mechanics we have the 4-vectors $x^{\mu}$ and $p^{\mu}$, ...
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### Modeling and Simulating Pendulum Motion

I've been having difficulty creating a mathematical model of a pendulum in my code. While there is plenty of info on general equations describing a the motion of a pendulum, I seem to be having ...
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### 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 ...
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### resistance of a flywheel to change of angular momentum

I've got a flywheel with angular momentum $\vec L$. Now I'd like to change the orientation of $\vec L$ by an angle $φ$ (in degrees). How do I calculate the angular momentum $\vec M$ for that change?
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### Relation between total orbital angular momentum and symmetry of the wavefunction

My question essentially revolves around multi-electron atoms and spectroscopic terms. I understand the idea that the total wavefunction for Fermions should be antisymmetric. Consider as an example, ...
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### Are there planetary systems where the planes of orbits vary greatly?

Inspired by this question, are there any known planetary systems with largely varying planes of orbit? For example a system where two planets have perpendicular planes?
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### Why do all the planets of the solar system orbit in roughly the same 2D plane?

Most images you see of the solar system are 2D and all planets orbit in the same plane. In a 3D view, are really all planets orbiting in similar planes? Is there a reason for this? I'd expect that the ...
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### How can a point-particle have properties?

I have trouble imagining how two point-particles can have different properties. And how can finite mass, and finite information (ie spin, electric charge etc.) be stored in 0 volume? Not only that, ...
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### Angular momentum in string theory

Since strings are extended objects, is all angular momentum in string theory essentially "orbital" angular momentum? Or is there still a kind of intrinsic angular momentum assigned to a string? ...
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### Intrinsic angular momentum in classical mechanics

Please note, I am only interested in classical mechanics discussion on this. Please do not involve quantum mechanics. Inspired by this question: Is Angular Momentum truly fundamental? My question ...
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### Why does Venus spin in the opposite direction?

Given: Law of Conservation of Angular Momentum. Reverse spinning with dense atmosphere (92 times > Earth & CO2 dominant sulphur based). Surface same degree of aging all over. Hypothetical large ...