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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23 views

How does frequency change with centripetal force?

Using the equation $$F_c = {{mv^2}\over{r}}$$ I can see that mass and velocity are directly proportional to centripetal force. I can also see that the radius length is inversely proportional to ...
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0answers
51 views

Precession due to mountain on Earth [on hold]

I've been stuck on this homework problem, and I could really use some help. My thought process is that when the mountain is added, the Earth will "tip" down in such a way so that the axis of ...
4
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2answers
130 views

How can mean value of a quantity $be$ an operator?

In Laundau & Lifshitz Quantum Mechanics. Non-relativistic theory in $\S29$ a problem is given: PROBLEM Average the tensor $n_in_k-\frac13\delta_{ik}$ (where $\mathbf{n}$ is a unit vector along ...
2
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1answer
40 views

Connection between half and whole integer eigenvalues for orbital angular momentum [duplicate]

I have been trying to follow this derivation from Sakurai and Shankar, pulling from both. I would like to see how the following derivation can be extended to orbital angular momentum, and thus find ...
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2answers
65 views

The uncertainty principle and spin

I realize that this may be a very basic question, but I've been unable to find the answer elsewhere so thanks in advance for the help. Suppose an electron's spin is measured about an axis, and then ...
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1answer
272 views
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180 views

Will an object falling into Earth's orbit start spinning?

Assume an object falls towards Earth (I've drawn a hyperbolic orbit, but this would apply to any orbit). The object starts at $A$, and at this point it is not rotating i.e. an observer on the object ...
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0answers
21 views

Dynamics inside a rotating spaceship

I have been thinking about this question for a long time and I din't find an explanation in the web for it lets say that we a rotating spaceship in the shape of cylinder, that is rotating in an ...
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0answers
24 views

Wigner $d$-matrix for $j=1$

In Sakurai's Modern Quantum Mechanics p.198-199, he states that for the matrix $$J_y^{(j=1)} = \frac{J_+-J_-}{2i} = \frac{\hbar}{2} \begin{pmatrix} 0 & -\sqrt{2}i & 0 \\ \sqrt{2}i & 0 ...
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1answer
56 views

Basic question about angular momentum

I've learned that the angular momentum of an object rotating about a fixed axis is $I \omega $. Also, in absence of external torques, $I_1 \omega_1 = I_2 \omega_2 $ (meaning, two different events). I ...
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3answers
98 views

QM rotation operator

I have seen the proof that for fermions a rotation of $2 \pi$ does not return a spin angular momentum eigenstate to its original form, but instead multiplies the wavefunction by $-1$. Here is an ...
4
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1answer
70 views

Complete derivation of generator of rotations

I have been look all across the internet and every book I could find trying to get a full derivation of the generator of rotations and more specifically angular momentum as a generator of rotations. I ...
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2answers
55 views

How does a wheel balance itself during circular motion? [duplicate]

A wheel (or any ring of considerable mass) hardly balances itself when it is placed vertically on ground, but when we roll it along the ground it balances itself. What causes this effect? I guess its ...
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1answer
37 views

Kepler's laws: show the planet always stays in the same plane?

I know angular momentum $L=q \times p$ is conserved, where $p=L_{\dot q}$ is linear momentum. How to apply this to a planet orbiting the star, described by the position vector $q$ relative to the ...
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1answer
58 views

Why dosen't my boomerang return [closed]

My boomerang I built will only turn just a bit back towards me, but that's it, but why? Is it my design, I incorporated the recommended dimensions from the website I used, such as an 107 degree ...
0
votes
1answer
37 views

How does angular momentum affect the trajectory of a projectile?

I am thinking about a football thrown in a very tight, very fast spinning spiral. If the football is thrown upwards at a high angle, is it possible for the football to not turn over at the top of its ...
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2answers
77 views

Why only 1 component of angular momentum?

Griffiths says that you can have only 1 well defined component of the angular momentum because of the uncertainty principle. From the uncertainty principle, we get that $$ \sigma_{L_x}\sigma_{L_y} ...
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1answer
83 views

How do you add angular momentum of three or more particles in quantum mechanics?

I'm trying to find some information on how to add the angular momentum of three or more particles, but all the sources I look at deal with only two. In this case I understand that if the angular ...
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1answer
31 views

How to get moment from angular momentum

I have a mass spinning while attached to a string as shown in the diagram: I can calculate the angular momentum of the mass as I know it's shape and rate of rotation (in deg/s). I want to calculate ...
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2answers
199 views

An identity of Pauli matrices

I am studying spin recently, and textbook gives some identities of Pauli matrices, one said that for any two unit vectors $\bf m$ and $\bf n$, $[\bf m \cdot \bf{\sigma},\bf {n \cdot \sigma}]= ...
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2answers
96 views

How to associate a Hilbert space with a QM system?

I couldn't really find a fitting title for this question. I'm still relatively new to QM and am trying to get the basics down. I understand that a physical system is associated with a Hilbert Space, ...
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0answers
32 views

Conservation of angular momentum in a plane

Suppose i have an object that moves circulary in a conical basin like at the picture. I know that there no azimuthal forces. But if take torque about the center of rotation then $R$ and $mg$ take part ...
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1answer
68 views

Tensor operators and transformation of $O^s_{\ell}|j,m,\alpha\rangle$

In H. Georgi's Lie Algebras in Particle Physics one defines a tensor operator transforming under the spin-$s$ representation of $SU(2)$ as the set of operators $O^s_{\ell}$ (for $\ell=-s...s$) such ...
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1answer
63 views

orbital angular momentum of the silver atom

In a silver atom, the first 46 electrons are all paired and according to David McIntyre in Quantum Mechanics, The electrons in the closed shells can be represented by a spherically symmetric cloud ...
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1answer
68 views

Why do planets not stop revolving around the Sun? [duplicate]

Why do planets revolving around the Sun not stop revolving? Note I am not asking why planets do not collapse with Sun.
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0answers
19 views

Simplification of matrix-element given the Wigner-Eckardt theorem and Clebsch-Gordon coefficients of a 1,1/2 system

How can I simplify the following matrix-elements $$\left\langle 1,1/2;m_1,m_2\left| S \right| 1,1/2;m_1^{'},m_2^{'} \right\rangle$$ given the Wigner-Eckard theorem $$\left\langle j,m|S|j^{'},m^{'} ...
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1answer
75 views

Why do particles have spins such as $1/2$, $3/2$, $5/2$? [duplicate]

What does it mean to have 'half' spin? I have looked on Wikipedia and a few youtube videos on spin but they don't explain what it means to have $1/2$ spin. I am 18 and only starting to learning about ...
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0answers
54 views

How to get from momentum to force

Situation: I have a solid object (black) attached to a rod (blue) as shown below: The rod is fixed at the top. The solid object is a cylinder as shown, with a rate of rotation ...
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1answer
21 views

Azimuthal angle in bloch sphere

I was wondering if there is any direct physical meaning behind the Bloch sphere parametrization in the sense that if I choose the angle $\phi =0$, then what does this mean for my spin state? Does ...
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2answers
105 views

Proving that conservation of momentum doesn't apply to electron in H-atom

To prove that the conservation of linear momentum doesn't apply to electron in H-atom, is it sufficient to show that angular momentum operator ($\hat L$) and momentum operator ($\hat p$) do not ...
3
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1answer
72 views

Question about surface term in QFT problem

I am trying to follow the solution of the following problem (Srednicki 39.2): To show that: $$J_z b_s^\dagger(p\hat z)|0\rangle=\frac{1}{2}\ s\ b_s^\dagger(p\hat z)\ |0\rangle, $$ where $J_z$ ...
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1answer
41 views

Boomerang angular momentum

So I'm building a boomerang to fly 200 feet in order to do that I was told to increase the moment of inertia to increase the resistance from change in state, and I was told that it would increase the ...
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3answers
103 views

How can you conclude that the angular momentum of a particle moving in a central field of force will be constant?

When determining the magnitude of the angular momentum vector $|\vec L |$, for a particle in a central field, my textbook concludes the following: $L=|\vec{r}\times m\vec{v}| = mr^2\dot{\theta}$ = ...
4
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1answer
111 views

How to interpret spin observables constructed by non-standard phase choices?

If we try to find matrix elements of ladder operators ( $J_{\pm}$) for spin when they act on eigenstates of $J^2$ and $J_z$ ( $\newcommand{ket}[1]{\left|#1\right\rangle} ...
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0answers
36 views

Relative velocity between a ball hitting a rod [closed]

A ball of mass $m$ travelling with a velocity $v_0$ collides elastically, and perpendicularly with a rod at a distance $d$ from the center of the rod. The rod has a mass $M$ and lies on a frictionless ...
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1answer
102 views

Conservation of angular momentum in a free rod

When a collision is elastic and no external torque acts on a system, angular momentum is conserved I found this example and checked the results: A ball (m = 1 Kg , v = p =+22 m/s, Lm = +11, Ke = 242 ...
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2answers
61 views

How's equilibrium possible here?

Here's the question.......Two point masses $m$ and $2m$ are attached at each end of a light rod. The rod is pivoted at the center and is free to move in a vertical plane. Then find the angle $A$ when ...
1
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1answer
29 views

Is the distance involved in calculating angular momentum to an axis or a point?

I'm a high school student.I still don't really understand angular momentum and moment of inertia. I know the moment of inertia of a point mass is defined as $mr^2$. For any other shape, we integrate ...
2
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1answer
33 views

Angular momentum effect on quantum energy

I'm doing some computational research into quarkonium states and I've written a code that determines energy levels by finding a solution to the Schrodinger equation for a given angular momentum. I.e. ...
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1answer
38 views

Find angular velocity of motor

I'm quite bad at this, but I'm trying to change that and I need some assistance. Please bare with me while I attempt to explain what I'm trying to figure out and correct me where I'm wrong. Basically ...
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2answers
45 views

Dumbbell rotation

What if apply impulse to dumbbell consisting of two masses and massless rod? It is clear for me that left dumbbell will move straight line. But it is not clear for me what kind of motion will have ...
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2answers
39 views

Do comets spin? Why do satellites/space station not spin?

Do comets spin? Why don't satellites or space-station spin? If spin is fundamental thing, then it should be found in all (moving) objects.
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3answers
116 views

$F=ma$ contest problem on angular momentum [closed]

Problem #25 from the 2009 $F=ma$ contest: Two discs are mounted on thin, lightweight rods oriented through their centers and normal to the discs. These axles are constrained to be vertical at all ...
3
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1answer
107 views

Paradox: electric current in a coil on a disc - will this disc spin if the circuit is opened?

I encountered this problem in a book, but there were no solution written there. The setup: there is a plastic (insulator) circular disc, that is suspended in a way, that can very easily rotate (so ...
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1answer
53 views

What is the ultimate “goal” of two particles in a gravitational field? [closed]

What is the ultimate "goal" of two particles in a gravitational field? Will the particles eventually occupy the same point at the same time if nothing stops them? What stops them from achieving the ...
2
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0answers
45 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 ...
0
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1answer
59 views

Scalar field gives spin $0$ particles

Related to this question. What needs to be shown is that the total angular momentum (derived from the Klein-Gordon lagrangian) acting on a ket with $0$ momentum, gives 0. This would mean that a ...
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2answers
128 views

Boomerang physics and aerodynamics

I posted a question before on this website asking how to build a boomerang for a project which can fly at least 200 feet, so how would I increase the flight path. A user responded with: slow down the ...
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1answer
71 views

Total angular momentum in QFT

Can anyone show explicitly how the QFT total angular momentum operator $$\hat{\vec{J}} = - i \int \frac{d^3p}{(2 \pi)^3} \hat{a}^{\dagger}_{\vec{p}} ( \vec{p} \times \nabla_{\vec{p}}) ...