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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1answer
54 views

Photon Angular Momentum

Essentially I am wanting to evaluate $$\langle j\, m \mid a^\dagger(\mathbf{k}, \lambda) \mid 0 \rangle \,,$$ where $\lambda$ indicates the circular polarization (about $\mathbf{k}$). We have that ...
2
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1answer
24 views

Does the unit of Inertia include radians? [duplicate]

The unit for angular acceleration $\alpha$ is: $$\mathrm{rad/s^2}$$ The unit for torque is $\mathrm{Nm}$: $$\mathrm{kg\ m^2/s^2}$$ And their relationship with Inertia is: $$I = \tau/\alpha$$ So ...
14
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2answers
1k views

Wouldn't angular momentum of a binary star system decrease?

Consider a binary star system, as these stars go around one another they would emit gravitational waves. Since, the graviton is a spin 2 particle. Wouldn't the angular momentum of the stars decrease? ...
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0answers
84 views
+50

Addition of spin angular momentum for massless particles

How do I add the spin angular momentum of massless particles, like photons, where only the transverse polarizations are allowed? If all three polarizations were allowed, this would be an easy ...
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0answers
18 views

Lateral forces on earths surface

If a giant stone sphere was sitting on the earths surface, would it experience a later force due to the earths rotation? For example my intuition tells me that if there was a sphere a mile high ...
2
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1answer
113 views

Sign wrong in angular momentum (Quantum Mechanics)

For small angles $\theta$ the rotation along a particular axis $n$ is given by $R(n,\theta)(r)=Id+ \theta (n \times r)+ o(\epsilon)$. Now, the rotation operator in Quantum Mechanics is given by ...
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1answer
24 views

Coordinate System vs. Angular Properties vs. Centroid

Please help me check my understanding related to the rotational motion of a 3D rigid body after reading some Physics textbooks and googling for some more materials (e.g., Wikipedia's Torque, ...
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0answers
18 views

Precessing gyroscope torque

I've been studying for an upcoming test and am completely stumped. Why is it that the weight of a gyroscope causes the torque to be directed along the horizontal as opposed to the vertical?
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1answer
52 views

Confusion about units of angular momentum

According to multiple sources the SI units for angular momentum are kg * m$^2$ / sec I am confused about the derivation for this. Here is what I have done: $$L = I \cdot \omega \\ = m \cdot r^2 ...
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1answer
75 views

Purely mechanical description of how gravity causes a gyroscope to precess

I know the vector equation that relates torque to moment of inertia and angular momentum. What I want to know is what physical mechanisms actually occur to keep the gyroscope from falling. Where is ...
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0answers
25 views

Collision of Discs and Snooker Kicks

I woke up this morning thinking about spinning discs. Could someone verify whether my reasoning below is correct? Problem 1 Suppose have two identical uniform discs constrained to move in a plane. ...
0
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1answer
63 views

How to derive the commutation relationship between $\hat{L}^2$ and $\hat{\textbf{p}}$ [on hold]

How to prove that $$[\hat{L}^2,\hat{\textbf{p}}] = i\hbar(\hat{\textbf{p}}\times\hat{\textbf{L}} - \hat{\textbf{L}} \times \hat{\textbf{p}})$$ I tried to expand $\hat{L}^2$: ...
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2answers
38 views

Describing a motion of gyroscope with gimbal

Can you tell be how to set the equations to describe the motion of this machine in movie "Contact": https://www.youtube.com/watch?v=TSaO9VGjLXc This is gyroscope with gimbal, am I right?
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0answers
97 views

Why is momentum not conserved? [on hold]

A uniform free disc in rotating in a horizontal plane ($m,R,\omega$). The surface is frictionless. A point mass of $2m$ is dropped on it from a height of $5m$ vertically at distance of $\frac R ...
3
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1answer
62 views

QM: How to compute position/momentum relation in polar coordinates

So if we are working in one dimensional space, we have the formula: $$\langle x|p\rangle = \frac{1}{\sqrt{2\pi\hbar}} e^{ipx/\hbar}$$ Suppose instead we are confined to a circle of radius $R$ so that ...
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1answer
50 views

Angular momentum of two rotating spheres

I am trying to calculate an instantaneous merger of two rotating spheres into one. Two spheres each rotating around their own axis of rotation (which are generally not aligned) and moving relative to ...
4
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2answers
263 views

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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0answers
55 views

Where do $L_+$ and $L_-$ live, if not in $\mathfrak{so(3)}$?

This question is continuation to the previous post. The lie algebra of $ \mathfrak{so(3)} $ is real Lie-algebra and hence, $ L_{\pm} = L_1 \pm i L_2 $ don't belong to $ \mathfrak{so(3)} $. However, ...
2
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4answers
739 views

Why the center of our galaxy doesn't absorb us?

Depending on the theories, the center of our galaxy is a super massive black hole, this is easy to accept as a truth, but what I couldn't simply devour is how the solar system is orbiting around it ...
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3answers
256 views

Conservation of Angular Momentum, as related to a flywheel

Trying to work out some pesky flywheel dynamics for a project I'm working on, would love some for your assistance to better understand the underlying concepts. For a given flywheel (thin-walled ...
2
votes
3answers
47 views

Instantaneous angular momentum of a disc

Suppose we have a disk of radius $r$ and mass $m$ travelling at velocity $v$. I want to calculate the instantaneous angular momentum with axis through the edge of the disc (on the circumference). ...
0
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0answers
25 views

Calculating the $J$ value for atomic terms, having a lot of trouble with this. Already attempted

I am trying to understand this, and want to be very very clear. This is a homework question but I already attempted to answer it, so please don't put this question on hold. The question What ...
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1answer
47 views

Eigenstates of coupled Angular Momentum

SO I have a hamiltonian: $$H=\alpha J_1\cdot J_2$$ And I am asked to find the eigenstates and eigenvalues of this Hamiltonian in terms of products of the eigenstates of the z components of the ...
4
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1answer
139 views

Does total angular momentum of the Earth-Moon system include individual rotational angular momenta?

To calculate the angular momentum of a body we need to specify a point (or an axis?) from which to define the displacement vector $\vec{r}$, so that $\vec{L} = \vec{r} \times \vec{p}$. For a rigid ...
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0answers
18 views

Angular Momentum Expectation in Magnetic Field

I am trying to find the time dependent expectation value for J ($\langle J(t) \rangle$) for a spin 3/2 particle in a uniform magnetic field (in the z direction). My method is as follows: ...
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46 views

Angular momentums addition in QM

We know that the spatial inversion parity for eigenfunctions of $\hat {L}_{z}$ operator (spherical functions) is $(-1)^{l}$, where $l$ refers to angular momentum. So for product of two eigenfunctions ...
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2answers
119 views

Angular Momentum Operator in Quantum Field Theory

I'm following along with David Tong's QFT course and am trying to derive the result shown in question 6 on his 2nd problem sheet, but am running into problems when applying it to the free real scalar ...
2
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1answer
90 views

Diagonal Hamiltonian of 3 Spin 1/2 Particles

I have three Spin 1/2 Particles and a Hamiltonian given by $$H=A(S_1\cdot S_2)+B(S_2\cdot S_3+S_1\cdot S_3)$$ In order to find the energy spectrum, I want to diagonalize H in terms of ...
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3answers
151 views

Effect of incoming force on linear vs. angular velocity

First of all, I should note that I'm a programmer and have only an extremely basic understanding of physics; I only know how to explain my question in layman's terms and I apologize if I'm unclear or ...
3
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1answer
883 views

General procedure for Clebsch-Gordan expansions

I'm wondering if the Clebsch-Gordan series generalize to any orthonormal set of basis functions? If so, how would one go about deriving an expression for an arbitrary set of basis functions (perhaps ...
3
votes
1answer
152 views

Why have $n$, $\ell$, $m_\ell$, $m_s$ been picked as quantum number symbols *in this order*?

I’m learning about electron configurations and don’t quite understand why $n$, $\ell$, $m_\ell$, $m_s$ have been picked as symbols for the quantum numbers. As far as I understand it, the principal ...
0
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1answer
65 views

Total angular momentum in a full shell

I do not understand why it's supposed to be vanishing. Rather than discussing the question in its full generality I prefer to consider the following scenario, which I think sums up anything that's ...
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2answers
269 views

A sphere rolling down a rough wedge which lying on a smooth surface

A sphere of mass $m$ and radius $r$ rolls down from rest on an inclined (making an angle $\phi$ with the horizontal ) and rough surface of a wedge of mass $M$ which stays on a smooth horizontal floor. ...
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1answer
79 views

Finding angular momentum about the center of mass?

If we have a couple of particles of an equal, unknown mass: $$r_{+} = (c + e^{-Bt} \cos({\theta}))\textbf{x} + (d + e^{-Bt} \sin({\theta}))\textbf{y}$$ $$r_{-} = (c - e^{-Bt} ...
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0answers
36 views

Angular momentum of 2d harmonic oscillator

So, I have the problem of determining the spectrum of H and L, in terms of creation and annihilation operators of angular momentum... The problem goes along with what is happening on this page. ...
5
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2answers
701 views

Conservation of linear and angular momentum

Suppose I have two rigid bodies A and B and they are connected by a spring which is attached off-center (thus possibly causing torques). Due to the spring a force $f$ acts on A and a force $-f$ acts ...
0
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1answer
60 views

Addition of Angular Momentum

I am tring to find the eigenvectors of a two spin system, with $j_1=3/2$ and $j_2=1/2$. To start, $$m_1 =-3/2,-1/2,1/2,3/2$$ $$m_2=-1/2,1/2$$ For $j_1$, there are 4 possible states, and 2 possible ...
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0answers
23 views

Spherical Harmonic projection on axis

I am trying to solve for the Spherical harmonics $Y^m_{l=1}$ with a second axis at an angle $\alpha$ with respect to the z axis. Then this can be used to find the probability that a particle with ...
0
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1answer
83 views
12
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3answers
424 views

Do particles have different spins in different frames of reference?

Let's say we have two photons, whose momentum vectors point to opposite directions. Also spin angular momentum vectors of the photons point to opposite directions. (Sum of spins is zero) Now we ...
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0answers
69 views

Difference between expectation values of $L^2$, $L_z$ and measuring $L^2$, $L_z$

I was given with this hydrogen radial wavefunction $$ R_{21} =\left(\sqrt{\frac{1}{3}}Y^0_1 + \sqrt{\frac{2}{3}}Y^1_1\right) $$ and was asked to find a) What are the expectation values of the ...
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0answers
42 views

How does $\bar{r}\times(\bar{\nabla}\times) - \bar{\nabla}\times(\bar{r}\times)$ relate to the orbital angular momentum operator?

When I attempted to calculate the following by hand $$\bar{r}\times(\bar{\nabla}\times\bar{F}) - \bar{\nabla}\times(\bar{r}\times\bar{F}),$$ I noticed some of the terms I extracted looked similar to ...
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0answers
64 views

What makes a wrist-energized gyroscope rotate faster?

I'm considering a wrist-energized gyroscope, shown below (after my daughter let it fall and it broke open). That one was sold as Roller Ball, but variants are known as Powerball, DynaBee, Dynaball, ...
0
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1answer
40 views

Construction of Angular Momentum eigenvectors

I have a problem that asks (verbatim) Carryout the construction of the eigenvectors of total angular momentum and its z component for $j_1$=3/2 and $j_2$=1/2 I am not completely sure where to ...
0
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1answer
32 views

Thrust to Weight ratio in Space with an off set CoM

With regards to this thread, Thrust center in space My question is, if the thrust to weight ratio was increased so that it was much higher than the weighted mass of the sphere (ship), would the ...
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1answer
82 views

What is $\langle \sigma_\mu \rangle$ $\langle \sigma_\mu \rangle$ for the Pauli Matrices?

What is \begin{align} \sum_{\mu=0}^{3} \langle \sigma_{\mu} \rangle^2 = ? \end{align} $\sigma_{\mu}$ are the Pauli matrices. The Bra-Ket notation is used in this question: \begin{align} \langle ...
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0answers
64 views

Imagine a 50-mile tower spanning from desert floor to the Karman Line

CORRECTION: The structure weighs 1.568E15 kg.s Does the structure effect the equilibrium of earth's rotation? Would momentum from Earth's rotation apply lateral force to the structure? What else do ...
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2answers
2k views

How can a singularity in a black hole rotate if it's just a point?

I guess nobody really knows the true nature of black holes, however, based on everything I know about black holes, there is a "singularity" at their center, which has finite mass but is infinitely ...
0
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1answer
93 views

How do I find angular and linear velocity after normal force and “infinite” friction force?

Look at this picture: http://i.imgur.com/mY8ShkV.png Here we have a ball resting on top of a platform (the contact point is marked red). I know the normal vector (marked green). I also know the mass, ...
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0answers
36 views

Transforming the angular momentum operator (from spherical to Euler and the internal valence angle) for a reduced 3-body problem

Let me introduce the problem: In a two electron fixed nucleus problem the "body" is the atom, whose electrons are located relative to the nucleus by the coordinates $r_1$ and $r_2$, and the angle ...