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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Balance of a spinning coin
If we place a typical coin on a table, it will almost immediately fall due to gravity. However, with a little push it will roll and not fall anymore until friction eventually slows it down enough to ...
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How many illusionary axes of rotation can coexist?
Consider the answer to this question:
How many different axes of rotation can coexist?
Any rigid body, at any time, can only be rotating about one instantaneous axis of rotation.
Now, that ...
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Transformation of the derivative of the scalar field in Ramond's book about QFT
In the book by Pierre Ramond about quantum field theory, he explores in chapter 1.4 (p.13) the behavior of fields under Poincaré transformations. He starts by explaining that infinitesimal ...
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Quantization of angular momentum of system of particles
Suppose there is a system of particles interacting with each other. Is it the angular momentum of each particles which would be quantized as $\sqrt{n(n+1)} \hbar$ or is the angular momentum of the ...
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Does asymmetric rigid body experience torque-free precession?
I know that a top (or any axis symmetric body) experience torque-free precession.
and I know that asymmetric body, with 3 different dimensions has stable rotation when the angular velocity is near the ...
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Equivalent definitions of total angular momentum
Consider the equality
\begin{equation}\exp\left(-\frac{i}{\hbar}\boldsymbol{\phi J}\right)\left|x\right>=\left|R(\phi)x\right>,\end{equation}
where $\left|x\right>$ denotes a position ...
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Angular momentum of a cylindrical system in general relativity
The definition of energy and enegry flux of a cylindrical symmetric system in general relativity is given by Kip Throne in Phys. Rev. 138, B251 and generalized by Chandrasekhar in Proc. Roy. Soc. Lond....
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How is angular momentum conserved for the orbiting body if the centripetal force disappears? [duplicate]
When the centripetal force on an orbiting body disappears (e.g. if it the body is a ball and the force was exerted by a string and the string rips, or, more unrealistically, if the body is the earth ...
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Why is the angular momentum of a 3D kicked rotor non-negative?
We know that for a 2D kicked rotor the angular momentum quantum number can be any integer from minus infinity to infinity. However, for a 3D kicked rotor this is not the case: it can only be positive ...
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Why conserve angular momentum about COM
In many questions involving collisions between Rigid bodies angular momentum is conserved about center of mass
If bodies stick together after collision they estimate com and then conserve about ...
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Linear momentum of a rotating system
So say we have a thin rod resting horizontally on a flat frictionless surface. The rod is pinned at its center, and a small mass collides perfectly inelastically with one end of the rod after moving ...
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Physical meaning of constants (momenta?) generated by Noether's theorem via an ${\rm SO}(3)$-action
Let $\Bbb R^3$ be our configuration space. Consider the Lagrangian $L\colon T\Bbb R^3 \cong \Bbb R^6 \to \Bbb R$ given by$$L(x,y,z,\dot{x},\dot{y},\dot{z}) = \frac{m}{2}(\dot{x}^2+\dot{y}^2+\dot{z}^3) ...
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Angular momentum operator in different bases
The Eigenvectors of $L_3$ (for spin 1) are $\left| m \right>$ with $m=1,0,-1$.
One can compute the matrix
$D_i=\begin{pmatrix}\left< 1 \middle| L_i \middle| 1 \right> & \left< 1 \...
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What would be the direction of force exerted on two stationary posts by pivoting levers which are spring loaded? [closed]
I am having a difficult time with visualizing/determining what would be the direction of force exerted on two stationary metal rods by two pivoting levers which are spring-loaded.
To help explain ...
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Quantized value of spin angular momentum and underlying mysteries
I think the quantized value of the spin angular momentum is $\hbar/2 $ rather than $\hbar $ is the basic reason for the $4\pi$ rotation of a wave function to retain its initial state again? Is it true?...
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Uranus: The Spin
In his prog. , on the outer planets, Brian Cox stated that Uranus spins on its side because it once endured an interplanetary collision.
Such a cataclysm would normally be devastating for both ...
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Particle interactions simulator
I'm an A-Level student trying to write a program that will take in two particles (like a proton and electron) and output the new particles. I'm planning to implement the conservation laws so that the ...
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Radius vs speed for flywheel energy storage
If I understand the formula correctly, the equation for kinetic energy of a flywheel is $mw^2r^2$ whereas the formula for "centrifugal force" is $mw^2r$.
So how come so much focus is on the speed of ...
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Why don't all electrons contribute to total orbital angular momentum of an atom?
There are 47 electrons in a Silver atom, but talking about its orbital angular momentum we only take the outermost valence electron which occupies the 5s orbital. Why don't the remaining inner 46 ...
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Angular momentum and angular velocity
The angular velocity $\vec{\omega}$ lies along the axis of rotation. And the angular momentum $\vec{J}$ is the cross product of $\vec{r} \times \vec{p}$. Which according to me should also lie along ...
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Conservation of Angular Momentum in Spherically symmetric potential
In Goldstein Book it is given that:
Since the problem is spherically symmetric, the total angular momentum vector $$\boldsymbol{L}=\boldsymbol{r}\times \boldsymbol{p}$$ is conserved.
What does the ...
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Confusion in conservation of angular momentum
Problem statment: A rod hinged at one end is released from the horizontal position. When it becomes vertical its lower half separates without exerting any reaction at the breaking point. Then find the ...
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Angular momentum and Gyroscopic precession of a top [closed]
A top is spinning in the counterclockwise direction as seen from above. Its axis of rotation makes an angle of 15º with the vertical. If frictional forces can be neglected, which of the following is ...
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Is the velocity of the spinning rod constant after it's hit?
Say we've got a rod floating around in space, with two masses of $m_0$, one attached at each end. Let's say the rod has a length of $l$.
There's another mass, $m_1$, moving at some velocity $v$ ...
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Spacial Wavefunction Symmetries and Identical particles
I was reading this and it mentions in the 3-electron section, that for a spacial wave function to be symmetric under fermion swapping, it must be a function of even parity. Similarly for anti-symmetry ...
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Ground state of an odd, deformed nucleus: intuition for what happens to the $j_x$ and $j_y$ of the odd particle
This is something that relates closely to my long-ago PhD research, and it's a point that I never satisfied myself thoroughly on. I have a copy of a standard text that covers this general topic, de ...
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How can a non-rotating black hole or singularity be created?
Every star or other massive body in the universe rotates, if only a little. If such a body collapses, its spin, any spin at all, and thus, angular momentum approach infinity as r approaches 0. Angular ...
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If there are eigenstates of $L_z$ in a degenerate subspace, are there also eigenstates of $L^2$?
The question arises from an exercise but tackles deeper understanding of angular momentum operators.
Suppose we have a 2D harmonic oscillator and an infinite square well in the third dimension:
\...
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If the mass of the Earth is decreasing by sending debris in space, does its angular momentum also decrease? [duplicate]
We are sending huge amount of debris into space from earth, and also very heavy satellites and rockets, then the mass of earth must be decreasing over time.
If the mass will decrease, then ...
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What is the significance of having two formulas for area moment of inertia?
What is the significance of calculating area moment of inertia twice?
I mean calculating area moment of inertia w.r.t axis and
calculating same area moment of inertia w.r.t centroidal axis?
Why not ...
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What's the relation between the Lorenztz group and spin of particles?
I know that particles are defined in terms of irreducible representations of the Poincaré group, and that the state of a massive particle is defined by its mass and spin, which are the eigenvalues of ...
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An ice cube orbiting the Earth
Recently I am stuck with a question about an ice cube that is orbiting the earth from a certain radius and it starts to melt down by the sun.
Which of the followings are wrong?
The cube will start ...
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Wicks contractions of stress-energy tensor and plane partitions
I am working out the number of wick contraction of a number $n$ of stress-energy tensor in 4D CFT.
The strategy is as follows:
For 1 stress energy tensor $T_{\alpha\beta}$, you have only one ...
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Conservation of Angular momentum or Work = 0 , which is valid?
In the figure, the block on the smooth table is set into motion in a circular orbit of radius "r" around the Center hole. The hanging mass is identical to the mass on the table and remains in ...
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Some Clebsch-Gordan coefficients for $j_{1}=1$ and $j_{2}=1$
I've successfully derived every coefficient, but not the one that has $j=0$.
Starting from $|J=2,M=2⟩$ and applying $J_{-}$ we derive $|2,1⟩$ and $|2,0⟩$ and using orthonormality (and the Condon-...
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Show that when angular momentum $L_x$ and $L_y$ commute with operator $G$, then $L_z$ also commutes with $G$
I want to prove that if Angular momentum $L_x$ and $L_y$ commute with an operator $G$, angular momentum $L_z$ also commutes with $G$.
if $[L_x , G] = [L_y, G] = 0$
then $[L_z , G] = 0$
I know that $...
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Strange bra-ket notation
I encountered a question, where I need to find the constant. But the state is given like this: $$|\psi\rangle = A(|1,1\rangle -i|1,-1\rangle+2|1,0\rangle)$$ So normally eg. when the state is given ...
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Angular velocity of thrown object?
I was reading this and came across the statement
After releasing the knife, it will fly forward and continue to rotate around its center of gravity with the same angular velocity it
had during ...
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Reaction wheel: angular momentum conservation or action-reaction?
Reaction wheel are commonly used in spacecraft to change its attitude: an onboard inertia wheel is accelerated or decelerated along an axis to make the spacecraft rotate around the same axis.
While ...
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Spin of elementary particles
Going by the explanation given by Stephen Hawking (as given in Brief History of Time) , the spin of a particle is no. of rotation you give to that particle so that it looks the same.
Like you give ...
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Angular momentum and external torque
In John Taylor - Classical mechanics it was mentioned that the equation
$L' = \Gamma^{ext}$
is true even with respect to the center of mass. Here we are working with a system of particles, $L = \sum ...
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**Mathematical Derivation** of the fact that all planets will orbit on the same plane
There is some discussion about this Here. If an isolated system of particles under gravitational force is allowed to decrease its energy by means such as inelastic collision, then eventually all ...
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Symmetries of Wigner $3j$-symbols by exchange
I know that Wigner $3j$-symbols have certain symmetry factors arising by exchange of two columns within one symbol.
But what happens if you have two 3j symbols and do an exchange like this:
$ \left(\...
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How are these two versions of the conservation of angular momentum different?
Here are two versions of the conservation of angular momentum.
The total angular momentum is constant if there is no external moment on the system
The total angular momentum of a particle is constant ...
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Why is $L_z$ operator more important the $L_x$ or $L_y$ operators?
When we talk about orbital angular momentum, we always use L_z but never talk about L_x or L-y. Why is that?
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Symmetry relation of Wigner-Eckart
I saw a symmetry relation following from the the Wigner-Eckart Theorem looking like this
$$(\xi j|| T_L || \xi'j') = (-1)^{j-j'} (\xi' j'|| T_L || \xi j)^*$$
I know that it must come somehow under ...
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Noether current Lorentz rotation massive vector field
I'm considering a massive vector field in classical field theory.
With the Lagrangian density
$$\mathscr{L}=-\frac{1}{4}V^{\mu\nu}V_{\mu\nu}+\frac{1}{2}m^2V^{\mu}V_{\mu}.$$
I want to prove from the ...
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Why does electron-positron annihilation conserve parity?
I think I'm missing something quite basic here but consider the process:
$$ e^- + e^+ \rightarrow 2\gamma$$
Fermions have opposite parity to antifermions so the parity quantum number before the ...
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Matrix representation in angular momentum basis
I'm trying to find a way to verify that the following expansion is valid for any potential, including noncentral ones,
$$
\langle \textbf{k}' |V|\textbf{k}\rangle = \frac2\pi\sum_{lm} V_l (k', k) Y_{...
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Angular momentum as an operator on triple product space
General arguments about introduction of angular momentum to QM is that under a transformation of coordinates the x and y position operators mix (as it is usually written)
$$\hat{x}' = \cos(\theta) \...
