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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Conservation of angular momentum for a rigid body rotating about a fixed point

Picture a rigid body such as a sledge hammer. Imagine that the base of the handle is attached to a fixed point such that it can rotate but not translate. I give the hammer a good push to get it ...
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1answer
196 views

How much effort would be required to fix the Earth's rotation?

Given that the earth's rotation has been slowing down by very slight amounts over time, forcing us to introduce leap seconds and so forth into our clocks and calendars, I would like to ask if this ...
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2k views

Effect on length of day as the polar ice caps melt

If the polar ice caps of the Earth melt, how will the length of the day be affected?
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262 views

Why doesn't the dark matter halo co-rotate with the luminous disk? What keeps it from falling into the center if not angular momentum?

Why doesn't the dark matter halo co-rotate with the luminous disk? What keeps it from falling into the center if not angular momentum?
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2answers
284 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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997 views

Conservation of angular momentum experiment

I've learned in that in this experiment: ...the skater will start rotating faster when she brings her arms in and there is no net torque acting on her. But what would happen to her angular momentum ...
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1answer
148 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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467 views

Angular momentum of particle rolling around inside of sphere

I have a hemispherical bowl in which I roll a small particle around the edge, starting from the top at point A with a velocity $v_o$. It travels halfway around the sphere and reaches point B, which is ...
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117 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 ...
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286 views

Coupling Coefficients in SO(4)

I have two equations (from two distinct authors) for the decomposition of a coupling coefficient of SO(4) (i.e. Wigner 3j-symbol for SO(4)). In the first: ...
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2answers
278 views

Where does a star's angular momentum go as its spin slows down?

So we know that stars slow down as they age. But total angular momentum must be conserved. Where does that angular momentum go? The dissipation of Earth's tides somehow transfers Earth's angular ...
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Proving angular momentum is conserved for a particle moving in a central force field $\vec F =\phi(r) \vec r$

A problem I am trying to work out is as follows: A particle moves in a force field given by $\vec F =\phi(r) \vec r$. Prove that the angular momentum of the particle about the origin is constant. ...
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Why does the Earth rotate? [duplicate]

Possible Duplicate: Why does every thing spin? So why would the Earth, or any planet for that matter, rotate along an axis? I know of no force which could come into play here, so i assume ...
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Accretion disk physics - Stellar formation

I was going through the Wikipedia page for Accretion disks, and I couldn't comprehend what the meaning of this is: "If matter is to fall inwards it must lose not only gravitational energy but also ...
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3answers
1k views

$\hbar$, the angular momentum and the action

Is there anything interesting to say about the fact that $\hbar$, the angular momentum and the action have the same units or is it a pure coincidence?
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2answers
1k views

How is angular momentum conserved when a spinning top finally stops spinning?

Where does the top's angular momentum get transferred to? Does it very slightly change the angular momentum of the table, and then the angular momentum of the Earth?
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The momentum of a swinging sword

Suppose you are faced with a zombie, and the only way to kill it and save yourself is to chop its head off with your sword. However, you are very weak from illness, and can only afford to strike once. ...
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1answer
267 views

Heat engines and “Angular momentum” engines?

We know that the theory of heat engines is that, if you accept the second law of thermodynamics, $\Delta S > 0$ then you can define temperature using $\frac{1}{T} = \frac{\partial S}{\partial E}$ ...
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Why can't I just think the spin as rotating?

I'm going mad about the problem. I really don't understand why do electron have 1/2 spin number, why they are not actually spinning. I can accept that the electrons have their own magnetic field, ...
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What is the scientific reason for the inclination of earth's rotation axis?

This titled position of the earths axis is known as inclination of the earths axis. The earth's rotation axis makes an angle of about 66.5 degrees with the plane of its orbit around the sun, or about ...
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2answers
282 views

Problem counting spin states

I can't figure out how many different spin states I can create with a four-electron system. I think I can create a spin-zero state, three spin-one states, and five spin-two states. That gives me nine ...
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1answer
693 views

What does it mean for a particle to have spin of 2? [duplicate]

When I first started to study quantum mechanics, my physics text book told that particles have spin of either 1/2 or -1/2. Then I recently read an article saying that gravitons are expected to be ...
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3answers
947 views

confused about ball rolling and rotational energy

I was solving a practice test problem and it was just a conservation of energy problem where a spherical ball is falls from a height h to the ground such that $$mgh = \frac{1}{2}mv^2 + ...
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753 views

Half wave plate and angular momentum

Given: A half wave plate freely floating in space. Circularly polarized light, falling perpendicularly to it. The plate changes polarisation of the beam to the opposite one. Therefore it ...
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595 views

How is Angular Momentum Conserved when Mass is Released?

I am not a physicist (math/comp-sci) but I understand that Angular Momentum is supposed to be conserved. I find this confusing because there seems to be many simple, common cases where a restrained, ...
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1answer
899 views

Matrix representation angular momentum

We are supposed to give a matrix representation of $L\cdot S$ for an electron with $l=1$ and $s=\frac{1}{2}$. I read $L\cdot S$ as $L \otimes S$. Is this correct? Then we would have e.g. for ...
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What is the spin rotation operator for spin > 1/2?

For spin $\frac{1}{2}$, the spin rotation operator $R_\alpha(\textbf{n})=\exp(-i\frac{\alpha}{2}\vec{\sigma}\cdot\textbf{n})$ has a simple form: ...
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How is angular momentum measured in experiments/in practice? [duplicate]

Possible Duplicate: How does one experimentally determine chirality, helicity and spin? How do you find spin of a particle from experimental data? We read about and study angular momentum ...
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Relation between total orbital angular momentum and symmetry of the wavefunction

My question essentially revolves around multi-electron atoms and spectroscopic terms. I understand the idea that the total wavefunction for Fermions should be antisymmetric. Consider as an example, ...
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4answers
838 views

Where does the electron get its high magnetic moment from?

I have always found the concept of spin a little weird. I had read somewhere that for the charge or size of electrons, their magnetic field is very high. In order to produce such fields, they must be ...
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4answers
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What causes matter to initially rotate/spin/orbit?

What causes matter to initially rotate/spin/orbit? All I can find is the statement that in space particles of dust/gas/matter contract into a spinning disk due to gravity (to form stars, solar ...
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3answers
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Can the spin of a photon change during its “life”?

Or is the spin set in one of two possible states at its moment of creation and does not change for the rest of the duration of its "life"?
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1answer
129 views

Visualizing irreps of SU(N)

What physical system can one use as an example while considering irreps of SU(N)? What is the correspondence between the system and the irreps?
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2answers
786 views

Why must the angular part of the Schrodinger Equation be an eigenfunction of L^2?

I was reading about the solution to the Schrodinger Equation in spherical coordinates with a radially symmetric potential, $V(r)$, and the book split the wavefunction into two parts: an angular part ...
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What maintains quark spin alignments in baryons?

What maintains quark spin alignments in baryons? The $uud$ proton and $udd$ neutron are both spin 1/2, implying that two of their spin 1/2 quarks are always parallel and the other is always opposed. ...
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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 ...
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1answer
938 views

Is all angular momentum quantized?

Angular momentum is definitely quantized in elementary particles and electrons in atoms. Molecules also have characteristic rotation spectra. Is it true that all angular momentum is quantized, ...
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1answer
598 views

Why is the value of spin +/- 1/2?

I understand how spin is defined in analogy with orbital angular momentum. But why must electron spin have magnetic quantum numbers $m_s=\pm \frac{1}{2}$ ? Sure, it has to have two values in ...
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1answer
974 views

Angular momentum and EM wave

Is there any sense in saying that circularly polarized EM waves have angular momentum?
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1answer
194 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
413 views

Ground state of Spherical symmetric potential always have $\ell=0$?

I was given a problem where I have a spherically symmetric potential (the exact form is not relevant to this question, I think - but anyway is it 0 for $r\in[a,b]$ and $\infty$ everywhere else) and I ...
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1answer
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How does Delta baryon decay conserve angular momentum?

I'm a chemist so bear with me: I understand the Delta baryons $\Delta^{+}$ and $\Delta^{0}$ to be in some sense spin (and isospin) quartet states of the proton and neutron. These can decay straight ...
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1answer
268 views

Effect of rotation on turbulence threshold for Reynolds number?

If the significance of the Reynolds number is: Then what is the effect of angular momentum on the transition from laminar to turbulent as in a convective vortex? Waterspouts, in particular, seem ...
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1answer
585 views

Simultaneously commuting set

How does one determine the members of an simultaneously commuting set (of operators)? For example, I have read that for orbital angular momentum, the set is {$H,L^2,L_z$}. How does one know that these ...
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1answer
411 views

How to get rotational speed after disk-disk collision with friction?

Assume two circular disks A and B collide. They have both initial linear momentum and angular momentum. If their surface has no friction, their angular velocity does not change after collision, so I ...
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1answer
2k views

Elastic collision of rotating bodies

How would you explain in detail elastic collision of two rotating bodies to someone with basic understanding of classical mechanics? I'm writing simple physics engine, but now only simulating ...
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1answer
672 views

Intuitive understanding of the irreps like Wigner-D matrix?

Wikipedia defines Wigner D-matrix as an irreducible representation of groups SU(2) and SO(3). What is a good way to visualize this representation? Is there any physical system which can be kept in ...
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2answers
425 views

How do objects change their axis of rotation?

If I hold a pencil at its end and spin it, throwing it upwards, it will spin about its end, but will soon start spinning around its center. How is this? I would draw the following torque diagram for ...
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1answer
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Angular momentum operator in terms of ladder operators

I wanted to show that the angular momentum of the particle state with zero momentum $| \vec{0} \rangle$ is $0$, that is to say the intrinsic spin of a scalar field is $0$ using a mode expansion. ...
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How do you combine two rigid bodies into one?

With respect to some fixed frame of reference, given the inertial tensors, positions, orientations, and angular and linear velocities of two rigid bodies, how do you combine them to make a single ...