# angular-momentum

Yes, sure its fun to see a lady spin around like that, but I had one of my friends ask me - “Where do you even use this mate?”

Here’s one application that I know very well off.

## Spin Stabilization

If you have ever seen a rocket launch, you might know that sometimes the rockets are given a spin while launching. This is known as spin stabilization.

Basically, the rotational inertia of the rotating body will stabilize the rocket against any disturbances and help maintain its intended heading.

The same principle is used in rifling of firearms as well. **

## YoYo DeSpin

Okay, now there is the question how to “De-spin” the rocket:

Well, you do what the lady does: stretch out your arms and you will slow down !

The rocket has weights connected to a cable that stretch out and almost immediately the rocket slows down. This maneuver is known as the YoYo DeSpin. ( Damn good name ! )

All thanks to the conservation of angular momentum !

Have a good one !

* Another method to stabilization : 3-axis stabilization

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## Why Does The Proton Spin? Physics Holds A Surprising Answer

“With two up quarks – two identical particles – in the ground state, you’d expect that the Pauli exclusion principle would prevent these two identical particles from occupying the same state, and so one would have to be +½ while the other was -½. Therefore, you’d reason, that third quark (the down quark) would give you a total spin of ½. But then the experiments came, and there was quite a surprise at play: when you smashed high-energy particles into the proton, the three quarks inside (up, up, and down) only contributed about 30% to the proton’s spin.”

You might think that the proton, made up of three spin=½ quarks, has a spin of ½ for that exact reason: you can sum three spin=½ particles together to get ½ out. But that oversimplified interpretation ignores the gluons, the sea quarks, the spin-orbit interactions of the component particles. Most importantly, it ignores the experimental data, which shows that the three valence quarks only contribute about 30% of the proton’s spin. Our model of the proton has gotten more sophisticated over time, as advances in experiment and in Lattice QCD calculations have shown that the majority of the proton’s spin comes from the internal gluons, not from the quarks at all. The rest comes from orbital interactions, with the low-momentum gluons requiring a more sophisticated electron-ion collider to experimentally examine.

After decades of mystery, we’re finally closing in on exactly why a proton spins. Find out the surprising physics behind the simple answer!

Physics Reasoning part 2

There is no torque because angular momentum is conserved, and angular momentum is conserved because the heading said “Conservation of Angular Momentum.”

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Superfluid Helium

It was previously thought that superfluid Helium would flow continuously without losing kinetic energy. Mathematicians at Newcastle University demonstrated that this is only the case on a surface completely smooth down to the scale of nanometers; and no surface is that smooth.

When a regular fluid like water is passing over a surface, friction creates a boundary layer that ‘sticks’ to surfaces. Just like a regular fluid, when superfluid Helium passes over a rough surface there is a boundary layer created. However the cause is very different. As superfluid Helium flows past a rough surface, mini tornados are created which tangle up and stick together creating a slow-moving boundary layer between the free-moving fluid and the surface. This lack of viscosity is one of the key features that define what a superfluid is and now we know why it still loses kinetic energy when passing over a rough surface.

Now we can use this information to help our efforts on applications of superfluids in precision measurement devices such as gyroscopes (I think this was on the Big Bang theory where they make a gyroscope using superfluid Helium that can maintain angular momentum indefinitely because it would flow across a smooth surface without losing kinetic energy) and as coolants.

On the direction of the cross product of vectors

One of my math professors always told me:

Understand the concept and not the definition

A lot of times I have fallen into this pitfall where I seem to completely understand how to methodically do something without actually comprehending what it means.

And only after several years after I first encountered the notion of cross products did I actually understand what they really meant. When I did, it was purely ecstatic!

## Why on earth is the direction of cross product orthogonal ? Like seriously…

I mean this is one of the burning questions regarding the cross product and yet for some reason, textbooks don’t get to the bottom of this. One way to think about this is :

It is modeling a real life scenario!!

The scenario being :

When you try to twist a screw (clockwise screws being the convention) inside a block in the clockwise direction like so, the nail moves down and vice versa.

i.e When you move from the screw from u to v, then the direction of the cross product denotes the direction the screw will move..

That’s why the direction of the cross product is orthogonal. It’s really that simple!

## Another perspective

Now that you get a physical feel for the direction of the cross product, there is another way of looking at the direction too:

Displacement is a vector. Velocity is a vector. Acceleration is a vector. As you might expect, angular displacement, angular velocity, and angular acceleration are all vectors, too.

But which way do they point ?

Let’s take a rolling tire. The velocity vector of every point in the tire is pointed in every other direction.

BUT every point on a rolling tire has to have the same angular velocity – Magnitude and Direction.

How can we possibly assign a direction to the angular velocity ?

Well, the only way to ensure that the direction of the angular velocity is the same for every point is to make the direction of the angular velocity perpendicular to the plane of the tire.

Problem solved!

2

angular momentum

A set of tops illustrating moments of inertia. Still an idea in evolution with a ways to go, but one of my favorite sculpture ideas I’ve had so far.

10

## Ask Ethan: What’s The Difference Between A Fermion And A Boson?

“Could you explain the difference between fermions and bosons? What differs from an integer spin and a half-integer spin?”

On the surface, it shouldn’t appear to make all that much difference to the Universe whether a particle has a spin in half-integer intervals (±1/2, ±3/2, ±5/2) or in integer intervals (0, ±1, ±2). The former is what defines fermions, while the latter defines bosons. This hardly seems like an important distinction, since intrinsic angular momentum is such a nebulous property to our intuitions, unlike, say, mass or electric charge. Yet this simple, minor difference carries with it two incredible consequences: one for the existence of distinct particles for antimatter and one for the Pauli exclusion principle, that are required for matter as we know it to be. Without these differences, and without these rules, it’s simply a matter of fact that the atoms, molecules and living things we see today wouldn’t be possible to create.

What’s the difference between fermions and bosons? A little difference goes a long way! Find out on this edition of Ask Ethan. (And thanks to the anonymous tumblr question that inspired it!)

A result of my brief obsession with cat physics and angular momentum.

I like to print out PDFs of all my textbooks, comb bind them, and then go on a walk and study them at the same time and bleed all over them with gel pens.

5

Where does cosmic rotation come from?

“Before our Universe was filled with matter, radiation, neutrinos, dark matter or any of the particles that we currently find in it, it was in a rapidly expanding state, where the only energy found in our spacetime was the energy intrinsic to space itself. This was the period of cosmic inflation that gave rise to the Big Bang that we identify with the birth of what we call our Universe. During this time, as far as we can tell, there were quantum fluctuations produced, but they couldn’t interact with one another, as the expansion of space was too rapid to permit interactions mediated “only” at the speed-of-light. As far as we can tell, the expansion was the same everywhere and in all directions, with no particular preferred axis of any type.”

And yet, everything in the Universe today revolves and rotates. Where did this cosmic “spin” come from? Your excellent questions answered on this week’s Ask Ethan!

Angular momentum - it makes the world go round!

From I Fucking Love Science on Facebook

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This is an Euler’s Disk. It’s a physics toy that demonstrates angular momentum, potential energy, and kinetic energy.

Could you explain what "spin" is?

In quantum mechanics, ‘spin’ is a pretty abstract concept. When a ball spins, it creates angular momentum. Particles appear to have angular momentum, but since they are treated just as points, we can’t say they are ‘spinning’ like a ball. To just add to the weirdness, you can never ‘speed up’ or ‘slow down’ the quantum spin of a particle, it will always stay at some fixed value.

Because charged objects create a magnetic field when they spin, so do charged particles. I think this concept is easier to understand if you imagine particles as tiny bar magnets, since that is what quantum spin essentially means. That way you don’t have to imagine something with no volume actually ‘spinning’.

3

A new study (published in PLOS Biology) investigated how bats make sharp turns in the air, particularly when they have to grab the ceiling. It turns out aerodynamics have very little to do with it - it’s all about inertia. Just as a figure skater clutches his arms to his chest to increase his speed, bats pull in their wings to help them make turns.

You can read all about it (and see more video) in this piece by my friend Nsikan Akpan over at PBS Newshour.

here's a space question, space papi: is there square planets? are spheres the only possible shape? does everything in space look like a ball

thats スペース パピ for the vaporwave fans.

So everything is a sphere or a disc. The spheres are smaller things like planets and stars, and galaxies are the big spheres.

Imagine you have a big clump of gas and all the particles attract each other. The only shape they’ll form is a sphere, because with a sphere every point is being pulled by this attraction with the same force. This is the same reason balloons become more spherical the more you blow into them.

For bigger things like a galaxy, everything is moving much faster around the centre. If galaxies were super small they’d probably be spherical, but because of the speed everything moves at, it flattens out like a pizza dough being tossed. This is a result of angular momentum which likes to flatten stuff out.

I like this question, hope that explains it enough for you :)

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Figure Skating Elements: Upright and Layback Spins

There are four main categories of spins in figure skating: upright spins, layback spins, camel spins, and sit spins. This post will cover upright and layback spins. Upright spins are defined as spins with at least one extended leg on the ice and the body in a more-or-less upright position. Laybacks are scored as a separate element from upright spins; they appear as LSp on protocols while general upright spins appear as USp.

There are many, many, many variations on spin positions in skating; in fact, coming up with interesting positions and combinations is one way to get higher levels on spins. (A common criticism of the judging system is that it encourages weird or ugly spin positions in the name of difficulty and gaining points.) It’s impossible to account for all of the variations out there, so I’ve only gifed some common positions and famous variations.

On Wind Power

So, this thing sometimes happens where a prominent person makes a public claim that wind is a finite resource, and therefore that we shouldn’t make wind turbines because they will stop all of the airflow.  Then everybody points at them at laughs, and the clip gets passed around as a Weak Man argument against renewable energy, etcetera etcetera.  But climate systems are pretty complicated, and people might be making fun of the “we’ll run out of wind” claim without necessarily understanding why it’s wrong.  And it turns out to be wrong in a fairly interesting way.  After all, there’s a certain amount of logic to it- you can’t get energy from nothing!  We’ve got to be depleting something, right?

Asyouknowbob, wind is a rebalancing of atmospheric pressure differences on large scales, from high pressure to low.  To the first order, these are caused mainly by thermal gradients (north-south) and coriolis forces (east-west)- basically, sunlight hits the equator head-on, and the poles at an oblique angle, so the energy density of any given patch of land will be higher at the equator.  The thermal expansion increases pressure at the equator relative to the poles, and convection takes care of the rest, with the direction of Earth’s rotation setting the counter/clockwise direction of the convection cells (if the Earth spun the other way, England would be frozen and Quebec would be temperate).  The presence of liquid water bodies, dark forests, and reflective snow or sand can influence this a bit, as can the atmospheric composition, but honestly the order of magnitude is mostly just set by the spherical geometry of the Earth and its distance from the sun.

A windmill can leach energy from a given gust of wind, sure. But that doesn’t mean the pressure difference across two different geographic regions has suddenly been equalized. Instead, it just makes wind a less efficient conveyor of heat and mass, as if air had a higher viscosity wherever windmills are common. In fact, with pressure imbalances being corrected more slowly, that creates an opportunity for atmospheric imbalances to grow *more* severe.  So the immediate lee side of a wind farm might be dead air, but elsewhere, where people live and work, average wind speeds might well increase!  Think about what happens to the flow rate of water coming out of a garden hose, if you cover half the opening with your thumb.

So you can see that broadly, wind power is actually a kind of once-removed solar power, with some of the same advantages and disadvantages.  They do, of course, have other consequences.  Higher atmospheric “viscosity” means that our wind turbines are causing a warmer equator, and cooler poles.  Inland areas are more arid, coastal areas are more prone to monsoons, and with extreme windmill proliferation California might even start having seasons.  In general, oceans and large lakes store heat very well, which is why coastal areas are less seasonal, and our windmills insulate those oceans further and prevent them from moderating nearby land areas.

However, it’s not only solar power.  See, if we increase the “viscosity” of the atmosphere by sticking a bunch of windmills into it, then it’s more tightly tied to the motion of the rocky planet underneath it.  From the perspective of our angular momentum as a rotating planet, it makes the Earth “heavier” in a sense, harder to move.  Thus, we see that unlike pure solar panels, wind turbines draw from a second, non-renewable source of power.  The real problem with windmills isn’t that they use up all the wind somehow- if anything, they increase the speed of the wind you can expect to feel. The real problem with them is that they deplete the Earth’s finite store of angular momentum, slowing down the rotation of the Earth. If unrestrained windmill propagation is allowed to continue, the day and night will get longer and longer, until eventually the spinning stops completely and the Earth becomes tidelocked.  One hemisphere will be trapped in eternal daylight, baked to a desert, while the frozen night on the other side makes life all but impossible.  In the narrow band of twilight at the boundary of these two hemispheres, where the last remnants of humanity scratch out a desperate living, the thermal gradient between the dark and light sides of our world will produce some very strong winds.   They’ll be steady and unidirectional from the day side to the night side, making wind an ideal power source for our dystopian cities.