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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2answers
185 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
34 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
68 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
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0answers
88 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
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3answers
143 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
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1answer
169 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 ...
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2answers
60 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: ...
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2answers
116 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
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0answers
86 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
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1answer
96 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
241 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 ...
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2answers
180 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
40 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
942 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
66 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
19 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 ...
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1answer
104 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 ...
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1answer
93 views

Doubt related to rotational motion (rolling down an inclined plane)

I have doubt regarding when an object ( sphere , ring , cylinder etc ) rolls down a FRICTIONLESS inclined plane. Let us suppose the angle of inclination of inclined plane is θ. Now the forces acting ...
1
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1answer
49 views

Trouble Understanding the Concept of Invariance

I am reading the book by Brian Cox & Jeff Forshaw: "Why does E=MC^2". It is getting to the point of explaining what invariance is. According to Cox & Forshaw, invariance states that the laws ...
0
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0answers
33 views

Explanation for Spiral galaxies [duplicate]

Can anyone explain to me why our galaxy is spiral and not irregular or spherical? Please be specific and if maths is required to state what you mean precisely, use it. I will understand it much better ...
1
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1answer
74 views

Rotation, Boosts and their relation to Spin

Angular momenta are the generators of rotations. For example, $L_1,L_2,L_3$ represents the orbital angular momentum operators which represents rotations in 3-D space in $xy$, $yz$, $zx$ plane. Spin ...
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3answers
130 views

Does orbital angular mometum has no meaning for single photons?

In the quantization of free electromagnetic field, it is found that the left-circularly polarised photons corrsponds to helicity $\vec{S}\cdot\hat p=+\hbar$ and right-circularly polarised photons ...
4
votes
1answer
380 views

The uncertainty in angular momentum

It is known that the different spatial components of the angular momentum don't commute with each other. $$ [L_x,L_y] \propto L_z \\ [L_y,L_z] \propto L_x \\ [L_z,L_x] \propto L_y $$ Also it is known ...
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0answers
98 views

How angular momentum conservation is related to the isotropy of space?

In Landau & Lifshitz Vol. 3 Section 54 "Spin" they say: In both classical and quantum mechanics, the law of conservation of angular momentum is a consequence of the isotropy of space with ...
2
votes
1answer
220 views

How can spin be gauge dependent?

Deriving the spin (density) of an electromagnetic wave, I obtained the formula $$\mathbf S = \mathbf E \times \mathbf A$$ But under a gauge transformation $\mathbf A+\nabla f$ this function seems to ...
0
votes
1answer
158 views

Why are galaxies flat since it's an unstable configuration in 3d? [duplicate]

I'll probably have to delete this question because someone's already asked it, but what accounts for the stable 2-d structure of spiral galaxies in three dimensional space (assuming random starting ...
0
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0answers
42 views

Show that $M^{\mu\nu}$ describes the angular momentum of the system

Define $M^{\mu\nu}$ = $\int d^3x(x^\mu T^{0 \nu}-x^{\nu}T^{0 \mu})$ describes the angular momentum of the system. I don't want you to solve it but I'm not really sure what kind of criterion it ...
3
votes
2answers
126 views

What is the meaning of spin of an particle is $1/2$ and $2$ or something? On which factor does these spin no. depend?

I have read a book. The writer had written that if the spin of an particle is $\frac{1}{2}$, then we have to rotate it at $720$ degree. Imagine that there are two balls joined. Then we have to rotate ...
10
votes
2answers
272 views

Why are the higher angular momentum states of a hydrogen atom closer to the nucleus?

I was looking at a plot of hydrogen radial wave functions $r^2|R_{nl}(r)|^2$, and I noticed that for fixed $n$, the states with smaller $l$ were "further out" from the nucleus. This conflicted with ...
0
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1answer
53 views

Why Space Element of Four Momentum Vector is 3 Momentum Vector?

For example, if we look at the relation between space element of 4-velocity and 3-velocity; and space element of 4-force and 3-force $V = v\cdot\gamma(v)$ $F = f\cdot\gamma(v)$ But ...
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votes
1answer
56 views

superposition of states, spin 1/2

Something was wrong... Two particles, their spin are 1/2. The hamiltonian is $H=\gamma s_1 \cdot s_2$ At t=0, the state $|\alpha(0)>$ is such as $s_{1z}|\alpha(0)>=\hbar/2 ...
1
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1answer
144 views

Invariance of law of conservation of angular momentum under a Galilean transformation [closed]

Given a reference frame O' moving at a constant speed $\vec{V}$ in relation to another reference frame O, I want to prove that $\vec{r_{1B}} \times m_1\vec{v_{1B}} + \vec{r_{2B}} \times ...
3
votes
1answer
69 views

How skydivers control their angular momentum?

As the title says, how do skydivers stop spinning from an out of control spin while in freefall? Doesn't conservation of angular momentum doom them to keep spinning, even if they make a small mistake ...
1
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0answers
54 views

Friction of an object falling between two walls

I'm simplifying this problem into 2D for easier understanding. Lets say we have 2 vertical walls separated by distance x. Inside these walls I place an object that is only slightly smaller than x in ...
0
votes
0answers
93 views

How do you determine the symmetry of spatial wave functions?

I have been reading about the ways to determine the ground of state of an atom. There are three Hund's rules in determining which electronic state is a ground state. And the second rule says you need ...
52
votes
4answers
5k views

Do solar systems typically spin in the same direction as their galaxy?

Is the net angular momentum vector of our solar system pointing in roughly the same direction as the Milky Way galaxy's net angular momentum vector? If yes or no, is that common for most stars in the ...
-1
votes
2answers
54 views

Expectation value of $S_x$ [closed]

$$\chi=A\begin{bmatrix} 3i \\ 4 \end{bmatrix}$$ I am asked to evaluate the expectation value of $S_x$. I understand the equation $$\langle S_x \rangle=\frac{\hbar}{50} \begin{pmatrix} -3i & 4 ...
4
votes
1answer
105 views

Total angular momentum of earth

I have problem understanding total angular momentum of earth about center of sun. Consider that earth has an orbital angular velocity of $\omega_0 \hat z$ and a spin angular velocity of $\omega_s \hat ...
1
vote
2answers
258 views

Electron Spin state probability [closed]

Suppose there is a spin 1/2 particle in a state $\chi = {1 \over \sqrt{5}} \begin{bmatrix} 1\\ 2\\ \end{bmatrix} $. To determine the probability of finding the particle in a spin up($\hbar/2$) state, ...
0
votes
1answer
59 views

Possible values for $L_x$

I've a physical system with $l=1$ and I have to calculate the values I can obtain if I measure $L_x$ and their probability. I know that: the values I can obtain are $\ m=0, \pm 1$ $\displaystyle ...
1
vote
1answer
507 views

Is Wikipedia's definition of angular velocity incorrect?

According to Wikipedia, the general formula for the angular velocity of a particle in three dimensions is $$\boldsymbol \omega = \frac{\mathbf r \times \mathbf v}{\left |\mathbf r\right|^2}.$$ But if ...
4
votes
1answer
105 views

Does a Buckyball spin like an electron or like a baseball?

Does a Buckyball spin like an electron or like a baseball? We are often told that an electron does not really spin like a baseball. Only one (or two, if you count up and down) spin states, for ...
8
votes
1answer
260 views

How deep can a whirlpool descend?

My question is based around comparing the physics of a tornado against, what I imagine/assume to be the marine equivalent of a tornado, that is a whirlpool located either at sea, in a tidal region or ...
1
vote
1answer
318 views

Commutation between Dirac hamiltonian and angular momentum

In reading about angular momentum and spin, I came across a derivation showing that the Dirac Hamiltonian does not commute with orbital angular momentum, and hence L is not conserved. What is it about ...
0
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2answers
64 views

Intuitive interpretation of angular momentum in a macroscopic system

My professor defined the angular momentum operators in quantum mechanics as the infinitesimal rotations in the Hilbert space of quantum states. I'm looking for a qualitative, intuitive explanation of ...
1
vote
1answer
126 views

Sequential Stern-Gerlach devices - realizable experiment or teaching aid?

At least one textbook [1] uses sequential Stern-Gerlach devices to introduce to students that the components of angular momentum are incompatible observables. Viz., the $z$-up beam from a SG device ...
3
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5answers
382 views

Eigenspaces of angular momentum operator and its square (Casimir operator)

The casimir operator $\textbf{L}^2$ commutates with the elements $L_i$ of the angular momentum operator $\textbf{L}$: $$ [\textbf{L}^2, L_i] = 0. $$ However, the $L_i$ do not commute among ...
0
votes
2answers
94 views

Why isn't angular velocity the moment of velocity if angular momentum is moment of momentum? [closed]

Angular momentum can be defined as $L$ = $\textbf{r}$ x $m\textbf{v}$. Why is angular velocity $\omega$ then not $\textbf{r}$ x $\textbf{v}$, but instead $v = \omega \times \textbf{r}$?