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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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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1answer
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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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1answer
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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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1answer
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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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1answer
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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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1answer
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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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1answer
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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,
$$
\langle \textbf{k}' |V|\textbf{k}\rangle = \frac2\pi\sum_{lm} V_l (k', k) Y_{...
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Why are there are no acceptable solutions of the Dirac equation that are eigenstates of the orbital angular momentum?
The nonrelativistic wave function in free space is simply a product of the coordinate part and the spin part; the orbital angular momentum and the spin are separately conserved. In the relativistic ...
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2answers
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Angular momentum as an operator on triple product space
General arguments about introduction of angular momentum to QM is that under a transformation of coordinates the x and y position operators mix (as it is usually written)
$$\hat{x}' = \cos(\theta) \...
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1answer
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Mcintyre Quantum Mechanics - Angular Momentum Conservation
I have two questions regarding this topic.
1.
I captured the part of the section I'm referring to. If I didn't my question would probably not make sense. My first question is to the second to last ...
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286 views
Newton's second law in angular form
I'm rather confused about the correct form of Newton's second law in angular form and how matrices of inertia could be converted from one coordinate system to the other.
Consider the system below:
...
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1answer
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Rotating Black Holes
All stars rotate. And the more they contract the faster the rotation, so is there such a thing as a non-rotating black hole? And as gravity is less at the equator of a rotating star, assuming that ...
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1answer
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Notation - angular momentum for composite systems
In the discussion for the addition of angular momentum for composite systems, my lecturer uses the following notation in his notes when referring to a composite system of two spin-half particles:
$ ...
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2answers
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Conservation of Angular Momentum w.r.t a Reference point
When angular momentum is conserved, does it mean that it does not matter what the reference point is at? Say for example with this image below, the observer stands at two possible points P1 and P2. ...
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What is this angular momentum coupling notation? $\langle \ell 2 m_\ell 0|\ell 2\ell' m'_\ell\rangle \langle \ell 2 0 0|\ell 2\ell' 0\rangle$
I'm reading this unsigned powerpoint presentation of the Nilsson model in nuclear structure physics. On p. 15, they have this:
$$\langle \ell'm'_\ell|Y_{20}|\ell m_\ell\rangle = i^{\ell-\ell'}\sqrt{\...
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Angular velocity of rotating rod
Consider the following system:
Newton's second law for rotational motion:
\begin{equation}\tau=I\alpha \Leftrightarrow rF=\frac{1}{3}mr^{2}\alpha \Leftrightarrow \frac{d\omega}{dt}=\frac{3F}{mr}\end{...
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1answer
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Representations of the rotation group
(I have already done a similar question, but I did not express myself very well and the question was a bit confusing, so let me try again. If you find the question repetitive, I apologize and you can ...
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Why does zero $x$ angular momentum imply nonzero $z$ angular momentum?
Assume we have a state $\psi =|n, L =1, L_x =0\rangle$. If we compute it's reprentation in $L_z$ basis we get:
$$\psi = \frac{1}{\sqrt{2}}|n, L =1, L_z =1\rangle - \frac{1}{\sqrt{2}}|n, L =1, L_z =-1\...
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Would conservation of angular momentum make it difficult to fall sideways in an O'Neill space colony?
It's always bothered me that the O'Neill space wheel puts forth centrifugal force as a suitable replacement for gravity. However, it seems the effects of conservation of angular momentum would induce ...
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Why are the vectors canceled out in this scenario for angular momentum of a particle?
I have a study guide for our next test, and I'm trying to understand the professors answer but I don't understand why i^ * i^ = 0?
Here is his work,
Why do we know that the P Vector is on direction ...
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2answers
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There's only time, no space in Quantum Mechanics
In this lecture (44:23) Nathan Seiberg: Topics in 2+1 Dimensional Quantum Field Theories 2.
Nathan Seiberg says there's no space in QM and therefore fermions have spin 0. This sounds pretty revolting ...
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1answer
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$\mathrm{SU}(2)$ as a representation of the rotation group
I have read in a book that the group $\mathrm{SU}(2)$ is one of the irreducible representations of the rotation group. The book begin saying that the rotation group has 3 generators $J_{1}, J_{2}$ and ...
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Rotationally invariant metrics and conservation of angular momentum
This was prompted by an exam question, though the questions are more general:
A 2D Riemannian space has the metric:
$ds^2=dr^2 + \gamma^2 r^4 d\phi^2$
State what conserved quantity ...
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1answer
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Rotation of a Point Particle
I wonder if there is a meaning of rotation for a point particle.
Does a point particle have angular momentum and does he reply to torque?
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2answers
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What is the physics behind a pirouette?
Around last week, I watched a ballet production at the Melbourne Arts Centre, and boy was I amazed! These people dressed up in costumes were spinning on their toes in all kinds of ways, and I was ...
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Alternative classical explanation of the Stern-Gerlach Experiment?
Many questions have been asked on this site about the Stern-Gerlach experiment, but as far as I can tell this one hasn't. Does the following classical explanation of the SG experiment work?
Model ...
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1answer
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Angular momentum conservation during collision
If I have a disk which is pure rolling and it strikes with a ladder, so can I conserve angular momentum about point O?
I think I can because normal reaction passes through O, so torque due to it will ...
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What is particle spin in terms of waves? [duplicate]
If particles are waves, then what really is spin?
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If angular momentum of an electron in $s$-orbital is zero, then is it true that the electron doesn't move?
If the electron does move, then what is the factor that leads angular momentum of the electron in s-orbital to be zero?
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Precise value of spin in Nms?
What is the exact value of the spin of a particle with a 'spin' of 'one'? In units of Nms (Newton-meter-second)?
And does a boson really have a spin of exactly one, or has that been 'normalized'?
...
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Questions about finding “top rung” and “bottom rung” of angular momentum operator (Proof in Griffiths)
The problem is like this:
Let
$$L_x = yp_z - zp_y, L_y = zp_x - xp_z, L_z = xp_y- yp_x, \\
L^2 = {L_x}^2 + {L_y}^2 + {L_z}^2 \\
L_\pm \equiv L_x \pm iL_y
$$
We wish to find a "top rung" $f_t$ and ...
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1answer
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Rising/lowering operators and trigonometric functions
I've just started learning about angular momentum and spin theory, and when I came across the definitions of the rising and lowering operators, I noticed the inverse form looks suspiciously like the ...
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3answers
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How do inspiraling black holes get closer?
In Newtonian mechanics, binaries are stable. We here on earth are very glad that it will not emit its angular momentum and spiral into the sun. What is different about the black holes and neutron ...
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2answers
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Wigner-Eckart theorem and vectors
Let's consider a system in state $^3$D$_1$:
$$\vec{L}^2=L(L+1)=6 $$
$$\vec{S}^2=S(S+1)=2$$
$$\vec{J}^2=J(J+1)=2$$
According to Wigner-Eckart theorem, if this is an irreducible representation, all ...
