# Tagged Questions

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

135 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 ...
230 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 ...
159 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 ...
43 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 ...
130 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 ...
326 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 ...
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 ...
58 views

77 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 ...
59 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 ...
106 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 ...
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 ...
55 views

87 views

### Stand on a black hole

Is there an theoretical possibility that an black hole rotates so fast that the acceleration pushing you out of the black hole is nearly equal to the gravity?
118 views

### Time-reversal procedure for spin

What's the physical reason/explanation for the fact when time is reversed then, in addition to momentum of fermion, spin is also reversed?
190 views

### Conservation of Energy vs Conservation of Momentum in Rotational Dynamics

It is clear to me why angular momentum is always conserved, and how in some cases energy is not necessarily conserved within the system (in those cases where bodies deform, or friction is involved). ...
131 views

### Why is the tilt of Earth in sync with an orbit around the Sun?

Is there any physical reason the changing tilt of Earth (which gives rise to our seasons: Spring, Summer, Autumn and Winter) is in sync with an orbit of the Sun (i.e. one year)? It can't just be ...
102 views

### Resultant center of rotation due to multiple moments

Say, there are multiple moments (M1, M2, M3) acting on a body (of irregular shape) at points P1, P2, P3 respectively. The body is free to rotate about any point. Now, which resultant center (the ...
127 views

### Relativistic rotational squeezing?

I would like to consider a sphere rotating at very high angular speeds, such that the speed in its equator would be relativistic. This is very similar to Ehrenfest paradox situation, except that ...
188 views

### Angular momentum of satellite including momentum wheel

I have consulted textbooks, online sources and professionals (including spacecraft experts, dynamics lectures and mechanical engineers) without a consensus to the answer to this question. I am ...
50 views

### Find the expression of $j_+$ and $j_-$operators [closed]

I have just started to do exercises about quantum mechanics and I have some difficulties. I have a particle with spin $j=1$ and the Hamiltonian is $H=\gamma(j_xj_y+j_y j_x)$ (where $\gamma$ is a ...
34 views

### Advent of our solar system

When the solar system was born why did Sun not consume all the planets by its immense gravity, as the planets were all gases, so it would have been very easy?
37 views

### trace of spherical components of an angular momentum multiplet

My basic mathematical question is whether or not there exist selection rules regarding the traces of the spherical tensor components of some operator acting on some subspace of definite total angular ...
93 views

### Why don't things balance after they stop spinning?

When I spin a penny, I spin it on its "edge" (circumference). So why is it that when the penny inevitably stops spinning, it never comes to rest on its edge, instead falling onto one of its faces? It ...
156 views

### How is angular momentum conserved?

A uniform vertical turntable (mass M and radius R center O) is at rest on the xy plane and is mounted on a frictionless axle, which lies along the vertical z axis. I throw a lump of putty mass m with ...
291 views

### Can we reduce a hurricane's power using wind turbines?

Below is the abstract of an article in Nature: Taming hurricanes with arrays of offshore wind turbines, describing computer simulations that indicate that wind turbines could disrupt a hurricane ...
168 views

### What makes us twist in a somersault?

In a backwards straight somersault you can decide whether you twist early or late. Twisting early means, that you induce the twisting movement before you rotatation hits 180° and twisting late means, ...
6k views

### What stops giant cruise ships toppling over in rough seas?

A week ago, 2 of the most gigantic cruise ships in the world docked near my city. If you have seen one, or been on one, you will know how large they are. They look extremely unsafe to me, although ...
216 views

### Why does earth spin counter-clockwise?

If we observe the earth from the north pole, we can see that the earth is rotating counter clock wise direction. The earth spins due to angular momentum, but why only in counter clock wise. Why ...
664 views

### Total orbital and spin angular momentum for a closed shell

I read one Phys.SE question similar to mine, in Total angular momentum in a full shell but the question was so confusing and vague. The answer, though, was helpful for me to understand a part of my ...
217 views

### How can an infinitesimally small object rotate?

How is it possible for an object like a black hole or electron to spin since they are made up of no other components? If my understanding is correct, an electron is an elementary particle which means ...
52 views

### Why are almost every planet or star rotating? [duplicate]

Is there any simple reason? Why is spinning so common?
153 views

### What variable is the conjugate momentum for angular momentum?

From the definition of conjugate momentum for a generalized coordinate we get that the conjugate for angular momentum should be proportonal to its integral with respect to time. According to my ...
734 views

### How easily can the Earth flip?

The recent media attention to sunspot activity (however warranted) reminds me of a question I had long ago. Given the angular momentum and the slight 'wobble' of the earth, and remembering the ...
49 views

### What will be the affect of Global Warming if Polar Ice melts? [duplicate]

Due to global warming, all the polar ice melts & sea level increases, with increase in humidity. Angular momentum of ice at pole is, very low. Due to shift of water, from pole to equator, it's ...
I have a doubt, I hope you can help me. In the case of a spinning top precessing around the $y$-axis, there's a torque $\vec \tau$ which comes from the weight of the toy. This torque is perpendicular ...
I was going over past PGRE exam questions, and came across this one. The components for the angular momentum operator $\mathbf{L}=(L_x,L_y,L_z)$ satisfy the following commutation relations. \...