The conserved quantity arising from a rotational invariance. Combine with rotational-dynamics for the classical mechanics approach and quantum-mechanics for the QM interpretation

learn more… | top users | synonyms

0
votes
0answers
26 views

what is significance of direction of vector product(torque & angular momentum)?how can one use them practically? [duplicate]

since i came across vector product or cross product i have one doubt that is what direction of torque shows.the direction of product is along axis of rotation(+ve or -ve).is there is any practical use ...
1
vote
1answer
63 views

Is it right to write $\varepsilon_{ijk} \delta_{jl}=\varepsilon_{ilk}$? (indices notation)

Consider the $l$ component of vector position $\vec{r}$, $r_l$, and the $i$ component of angular momentum $\vec{L}$, $L_i$. We have that $$L_i=[r\times p]_{i}=\varepsilon_{ijk}r_jp_k$$ ...
0
votes
0answers
26 views

What are physical observables that are connected to orbital angular momentum?

We considered a system that is confined to a curved surface. In the quantization process, we have obtained an additional orbital angular momentum that are from the surface geometrical deformation. Now ...
1
vote
0answers
69 views

Commutation between angular momentum and Hamiltonian

Consider the following Hamiltonian of a 3-dimensional system: $$H=\frac{p^2}{2m}+V(r)$$ If the components of the angular momentum, $L_i$, commute with $H$, then: $$[H,L_i]=0$$ This condition can ...
1
vote
2answers
175 views

Possible inconsistency in Bohr atom model [closed]

It is well known that Bohr model is not totally right. But I recently discovered a very curious inconsistency (if I am right) which I haven't seen explained anywhere. The first postulate of Bohr ...
1
vote
0answers
69 views

Conservation of Angular Momentum…or not?

This is my first post on physics stack exchange, but I thought the question was more appropriate than on that of math.stack. I'm currently designing a crude model of the sun-earth orbit (which I have ...
1
vote
0answers
62 views

How to measure $\mathbb{L}^2$ and $L_z $ simultaneously

What does an experiment look like, in which both quantities are measured simultanously?
0
votes
0answers
16 views

Distance needed to double the moment of inertia of a cylinder

The moment of inertia formula for a solid cylinder is $0.5MR^2$. How would I need to change the radius in order to double the moment of inertia of the solid cylinder?
2
votes
1answer
91 views

When are energy, mechanical energy, momentum, and angular momentum conserved?

I am in AP Physics and my only real hangup is knowing when the said quantities are conserved. Please define what is the SYSTEM in your answer. I kind of have the basic idea. For example, if there ...
0
votes
1answer
124 views

Proof for quantized angular momentum [duplicate]

In Bohr's model, Bohr stated that the angular momentum of the electron is quantized and stated that $$L=\frac{nh}{2\pi}$$ So what is the proof for that equation or, in other words, how did he derive ...
0
votes
1answer
51 views

Explaining conservation of angular momentum with a disconnect

A probe is rotating in space and an instrument comes loose and disconnects. I need to explain why the angular velocity $\omega$ of the probe does not change. This equation describes how the angular ...
1
vote
1answer
64 views

Comet's distance with and without gravity [closed]

I've got this question that I just can't seem to answer. The question is as follows: A comet approaches the solar system with velocity v and would, if the sun would not attract the comet, pass the ...
0
votes
0answers
38 views

Adding angular momenta of 3 spin-(1/2) particles

When adding three spin-$\frac{1}{2}$, $|\frac{3}{2}\frac{3}{2}>$ = $\frac{1}{3} (uud + udu + duu)$ Now, I know that one of the $|\frac{1}{2} \frac{1}{2}>$ states is $|\frac{1}{2} ...
0
votes
2answers
132 views

Angular momentum about a moving axis

How can we define angular momentum of a system about an axis that moves parallel to itself? For example Axis passing through CM that is perpendicular to plane of body. When we talk about ...
1
vote
1answer
155 views

Can space have angular momentum that can be transfered to/from physical objects?

This is related to another question that discusses whether space can have momentum and energy. Apparently gravitational waves or ripples in spacetime is how space stores and transfers energy/momentum. ...
2
votes
0answers
67 views

Tensor product of spin states

I just wanted to check that I carried out this problem correctly. I got the correct answer, but I'm not sure if what I did to get it is completely correct. This is from the second part of problem 3.4 ...
39
votes
2answers
7k views

Why don't galaxies orbit each other?

Planets orbit around stars, satellites orbit around planets, even stars orbit each other. So the question is: Why don't galaxies orbit each other in general, as it's rarely observed? Is it considered ...
0
votes
0answers
32 views

How rotational force calculation depends on the distance between the point of force application and the axis of rotation?

I don't understand how the perpendicular distance between the point of force and the axis of rotation gets involved in the calculation of the rotational effect of that force.Is it about rotational ...
-1
votes
1answer
66 views

Parity operator with other operators

I need to show the following: $$P x P^{-1} = -x, \ P p P^{-1} = -p, \ P L P^{-1} = L$$ where $P$ is the parity operator and $x$, $p$ and $L$ are the position, momentum and angular momentum ...
1
vote
1answer
103 views

Angular Momentum of a Photon

Why is it that the angular momentum of a photon is $\hbar$, irrespective of its energy? I encountered such a claim in a text about Raman spectroscopy. Is there an explanation for this using basic ...
1
vote
0answers
35 views

Why is this decay process allowed? [duplicate]

I have been given an assignment in which I have been asked to list some quantum numbers for some given allowed processes. One of them is $\Delta^+ \rightarrow p^+ + \pi^0$ I know that $\Delta^+$ ...
1
vote
1answer
69 views

Angular momentum in baryon multiplets

In the Murray Gell-Mann model, particles are brought together as a function of their angular momentum. The classification diagrams can be seen as irreducible representations of $SU(3)$, following ...
1
vote
0answers
19 views

Gyroscopic precession force translated 90 degrees? [duplicate]

I was watching a video on propeller gyroscopic effect, please take a look at this 1 minute segment (up to 6:06): https://youtu.be/QGWbjGqmoWo?t=307 Alternatively, here is a summarizing image from ...
0
votes
1answer
45 views

Angular Momentum and Eigenfunctions in QM

In Griffith's Quantum book, he starts off by finding the commutation relationships between the angular momentum and its components. He then goes on to find the uncertainty relationship ...
2
votes
0answers
72 views

Precession of angular momentum vector

I'm studying Classical Mechanics on Goldstein's book, so I'm using his terminology and notation. First I'll explain where the question comes from: consider a heavy symmetrical top and consider the ...
2
votes
0answers
28 views

How fast can an object spin? [duplicate]

Without any forces in space to stop it, assuming an object does not collide with anything or enters any kind of gravitational pull, how fast could the object spin. I mean the earth spins quite fast, ...
2
votes
3answers
599 views

Spin and Angular Momentum [duplicate]

What is the difference between spin and angular momentum, are they linked i.e. spin is a form of angular momentum. And is spin what I think it is (the way the electron/particle actually spins)
0
votes
3answers
90 views

Is Conservation of Energy maintained when the orbit of a rotating mass increases in diameter?

I read an example where someone was explaining how the law of conservation of energy does not have to be maintained within a rotating mass even though angular momentum is maintained. The given ...
1
vote
2answers
140 views

How to start an artificial gravity?

I understand how artificial gravity in space stations works. It is by normal force the wall exerts on the foot. But I wonder how to start it in the first place. I just learned about centrifugation ...
0
votes
1answer
152 views

QM angular momentum commutator solution using index notation

there are a few answered questions regarding the commutator of any two 3D angular momentum operator components $[L_i, L_j]$ , however, I am trying to go through fully using index notation so that I ...
0
votes
1answer
57 views

Conservation of angular momentum poisson brackets vs newtonian mechanics [closed]

So I have the following system. For a mass falling due to gravity the given Hamiltonian is $$ H = \frac{1}{2m}\left( P^{2}_{x} + P^{2}_{y} \right) + mgy $$ In Cartesian coordinates then, $$ x = v_o ...
0
votes
2answers
199 views

Aren't all spin states (up, down, left, right, in, out) orthogonal?

Hopefully someone can clear up a basic misconception I am having about the nature of spin state vectors. According to the book i am reading, The basis vectors of up/down spin are orthogonal to each ...
53
votes
4answers
6k views

If dark matter only interacts with gravity, why doesn't it all clump together in a single point?

I'm a complete layperson. As I understand, dark matter theoretically only interacts with the gravitational force, and doesn't interact with the other three fundamental forces: weak nuclear force, ...
0
votes
1answer
35 views

Angular momentum: why must descending and ascending chains terminate?

I'm studying theory of angular momentum, but I haven't understood a step. $M_1, M_2, M_3$ are the components of angular momentum $\vec{M}$. Let's consider ladder operators $M_+=M_1+iM_2$ and ...
1
vote
0answers
72 views

Angular momentum of rolling disc

Does the angular momentum of a disc in pure rotation depend on the reference point? For example, are $L$ about the center of mass and at a distance equal to half the radius equal or different?
3
votes
0answers
89 views

Where this relation for general non rigid motion comes from?

In Goldstein's Classical Mechanics book in the chapter about the dynamics of rigid bodies the equation $$\dfrac{dL_i}{dt}+\epsilon_{ijk}\omega_jL_k = N_i$$ is presented. Now, in one exercise, we are ...
2
votes
3answers
145 views

How did planets start to spin and do all of them spin in same direction? [duplicate]

How did planets start to spin in the first place? Some say that gases which condense and form planets start spinning and hence planets acquire a spin. And some say that they start to spin to conserve ...
0
votes
1answer
178 views

Why is only angular momentum conserved for a planet and not linear momentum?

Suppose a planet is moving in an elliptical orbit with the Sun at one of its focii. I know that the forces in existence will be gravity which provides the necessary centripetal force. Now my book ...
1
vote
2answers
61 views

Angular momentum for a given Wavefunction [closed]

Problem: Give a particle in the state $\Psi = e^{\frac{-(x^{2}+y^{2}+z^{2})}{a^{2}}}(\frac{x}{a} + \frac{yz}{a^{2}})$, what are the allowed values for $l_{x}$ (and later for $l_{y}, l_{z}$). Attempt: ...
-1
votes
2answers
120 views

Are mass and angular momentum related at a quantum level?

Is the mass of an atom related to the amount of angular momentum it contains? It makes sense to me that since the waveform of an electron is much much larger than a particle in the nucleus that its ...
1
vote
0answers
89 views

Spin and polarization, QM vs QFT

On page 34 of A. Zee's book QFT in a Nutshell, he states: I expect you to remember the concept of polarization from your course on electromagnetism. A massive spin 1 particle has three degrees of ...
0
votes
1answer
108 views

Questions about the velocity of the center of gravity

I have a physics test coming up in a couple of days and I really need to have some things explained to me. It is about something that I think is called in english "the velocity of the center of ...
6
votes
1answer
272 views

Intuitive Explanation of Tippe Top Effect?

A friend showed me a tippe top (a special kind of spinning top) lately and asked me about the physics behind it. I thought about it for a while but cannot quite figure it out. So I will throw the ...
0
votes
2answers
202 views

stopping a rotating mass to achieve linear velocity

So I've been thinking about space, and I had this idea. I haven't found any prior art online for it, and from my limited understanding it seems like a viable idea. So I guess my question is, what am I ...
2
votes
0answers
42 views

Angular momentum transfer in a bottle vortex

A colleague and I were discussing the following fluid mechanics experiment, which most people have probably tried in their kitchen: take a bottle full of water (a 2-litre transparent soda pop bottle ...
4
votes
1answer
46 views

Spin $\frac{3}{2}$ representation in Georgi's book?

Georgi's book Lie Algebras in Particle Physics 2ed equation 3.32 lists the spin operators in the spin $\frac{3}{2}$ representation as: $$J_1=\left( \begin{array}{cccc} 0 & \sqrt{\frac{3}{2}} ...
6
votes
1answer
956 views

Would a double gyroscope still have gyroscopic properties?

Imagine you have a gyroscope that has two spinning parts, one on top of the other. When you pull the string, the two halves spin in opposite directions. Would this cancel out the gyroscopic ...
0
votes
2answers
67 views

What are the consequences of the angular momentum of the electron in an atom?

Well, since the electron is going around the nucleus, it must have an angular momentum (plus its spin). And since it is charged it must create an electric field. If I have understood it correctly it ...
1
vote
1answer
20 views

Arrangement of particles in g-field zero angular momentum.

Is it possible to have an arrangement of masses gravitationally interacting with each over put into motion such that the system has zero net angular momentum but no collisions or particles escaping to ...
1
vote
1answer
106 views

Matrix represenation of total angular momentum operator

I see that for total ket in QM of hydrogen atom we define a tensor product of kets of spatial and spin spaces, upon which spatial and spin operators, operate respectively. For the total angular ...