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  • Hey, the sauce Michel here.

  • Do you want to see the most illegal thing I own?

  • It's a penny from 2027.

  • That's right.

  • Is a piece of counterfeit U.

  • S currency.

  • Or is it?

  • There are no 2027 pennies today, which means that this is a counterfeit oven original that doesn't exist yet.

  • I mean, sure, if you didn't look at the date, this could pass Israel.

  • But will it not truly be counterfeit until 2027?

  • Well, what we do know is that it's novelty has a life span.

  • It's really cool to show people today.

  • It's a penny from the future, but in 2027 it will become indistinguishable from a common penny, and it will cease to be is interesting.

  • I cannot tell you where I got this, but the point is, I can break the law.

  • I am free, perhaps not free from punishment, but nonetheless, Here we are.

  • I cannot break the laws of physics.

  • Nothing can.

  • Why today I want to look at the lawful behavior of spinning.

  • Let's start with a physics classic as a spinning ice skater pulls their body and closer, they spend faster and faster.

  • It's really cool.

  • But what is accelerating their rotation?

  • What is pushing them around faster and faster?

  • You could try this at home with a chair that spins and some really heavy books in both hands.

  • Now, to get started spinning, I'm gonna have Jake give me a push, But I don't need Jake may not watch this.

  • With him gone, I can nonetheless speed myself up by just pulling the books in.

  • If I move the books out, I slow down somehow pulling the books in, speeds me up around.

  • Now, if you look up why this happens, you'll probably be told that it is because of the conservation of angular Momenta, the conservation of angular momentum.

  • I love demonstrations of it, and this is one of my favorites.

  • This is a Hoberman sphere, a toy that collapses and expands, Doesn't it sort of remind you of me with the books far from my body and then the books close to my body and it behaves in much the same way.

  • I need to give it some angular momentum to start, but once I do, if I bring all of that mass towards the axis of rotation, it speeds up, and then it slows down and then it speeds up and then it slows down.

  • Speeds up, slows down.

  • I love this.

  • Thank you.

  • Conservation of angular momentum.

  • But what are you?

  • Look it up.

  • This is what you will find for a particle in a circular motion around some center of rotation.

  • See, the angular momentum of the particle is defined as the product of the particles mass particles, instantaneous velocity B and the particles distance from the centre of rotation.

  • R m the R.

  • This is angular momentum.

  • If you divided me and the chair and the books, I'm holding into a bunch of tiny little particles and found the envy ours for every one of those particles in some dumb, all up, you would have the angular momentum of the entire system of me, the chair and the books.

  • But notice that this is just a mathematical expression combining three different measures.

  • It's not a physical substance.

  • You could pull out of a particle and holding your hand or put in a jar and study.

  • It's kind of like a lot of no taking like my weight and multiplying it by the number of countries under, then multiplying it by the time however, unlike something like that, this concept is really useful because we have found that in our universe over time it is conserved.

  • If the particle is pulled towards the center of rotation, it's our value will go down.

  • But angular momentum is conserved.

  • So one of these other variables must go up well at low speeds.

  • Masses essentially constant.

  • So the only option is for the velocity of the particle to increase for the particle to spin around faster than it was before.

  • If the R value gets smaller, the velocity must get larger or else a law has been broken.

  • But how do atoms and molecules no follow this law?

  • I mean, is there some kind of physics police force in the universe bullying everything into compliance?

  • How do all the atoms I plan?

  • No to speed up.

  • And why do they always obey our laws like embodied presence is guiding matter around?

  • No, I have with me right now three things a lamb, a nail and a shadow dacha.

  • I actually have four things with me.

  • The fourth is inks astonishing Ruler designed by V sauce.

  • If you're subscribe to the curiosity box.

  • You already have one or it's on its way to you.

  • And if you're not subscribe to the curiosity box, well, you're missing out on the fruits of my mind.

  • I have always wanted a ruler like this, so I made one.

  • And now I and you can have one.

  • It is exactly one light nanosecond long, which means that this is the distance.

  • Light travels in a vacuum during one billionth of a second.

  • If I hold my hand just that far away from I I I am seeing my hand as it waas Ah, billionth of a second in the past.

  • Pretty cool.

  • Now this ruler allows you to measure lengths of things in light PICO seconds sound microseconds, micro ever wrists.

  • That's one millionth of the height of Everest, Beard, Fortnight's decimal inches and, of course, good old centimeters.

  • Now, if you ask me, Hey Mike, why is the shadow of the nail 4.5 centimeters long?

  • Well, I would say who's Mike?

  • But then I would be helpful, and I would answer that the length of the shadow is caused by the height of the nail and the position of the light source.

  • And that's a pretty good explanation because if the nail were taller and or if the light source were lower, the shadow would be longer.

  • Or if the nail were shorter and or the light source was higher, the shadow would be smaller.

  • Now, these three measures the nails height, the lights position and the shadows length are all related mathematically such that if you gave me only two of them, I could figure out the third always.

  • So I could declare this relationship to be a law.

  • But that does not mean that the law causes them to all have the measure that they do.

  • For example, if you ask me Hey, why is the nail six centimeters tall?

  • What causes the nail to have that height?

  • Well, if I said well, the nails height is caused by the shadows.

  • Lengthen the lights position.

  • You'd be like, uh, as if All right.

  • I mean, sure, we can figure out the nails height by knowing about the shadow and the light.

  • But that does not mean that they are causing the nail tohave the height that it does to know why the nail is six centimeters tall.

  • We'd have to ask whoever manufactured it or whoever sent snail standards or whatever.

  • The point here is that we should not confuse relationships, laws with causes, explanations that involved the causal reasons for things are often better.

  • But what is an explanation?

  • Well, that's easy to answer.

  • Explanations help us understand things.

  • But what does it mean?

  • Toe understand?

  • Does it mean to not stand up fully or does it mean to stand underneath and toe?

  • Look at from below?

  • If I can understand something, can I also over stand something?

  • Well, as it turns out, the under and understand does not mean beneath or below.

  • Instead, it means inside to stand surrounded by to be a part of.

  • Now, this sense of under is quite common.

  • For example, when you say, uh, well, under those circumstances, you don't mean well when those circumstances are overhead and I'm under them instead.

  • You mean if I find myself in those circumstances and that is how under is used in understand, to understand something is to stand in the midst of it, to be part of it and to be within it, and that is helpful to keep in mind.

  • I cannot walk into something that's crumpled up and closed off to truly understand something.

  • It needs to be opened up for me unfolded, and that is what an explanation should do.

  • Theo Word explain literally means to flatten plane out.

  • Ex explain to make flat Now if you'll excuse the analogy, If this is a story I want to read and it's all crumpled up, a physical law basically just tells me a summary of the story.

  • It'll tell me how the story ends, what language and grammatical rules were used to write it.

  • But an explanation will flatten the page out and allow me to see the details, an actual word and the word that follows it, and so on, all the way through.

  • So let's unfold the phenomenon of me speeding up my rotation when I pull the books in and find a physical mechanical cause for that increased rotation, I have here two different circular motion paths around the center of rotation, which will call see now when a particle is traveling in this outer ring and it's suddenly pulled in.

  • It doesn't stop moving around and suddenly just go right in.

  • Instead, it takes a bit of a curved path like this.

  • Now this is really interesting, because in order for a particle to be in circular motion, it must have two things.

  • It must have put the particle there.

  • It must have a velocity that is tangential to the path, but it must also have a centripetal force, a center seeking force that always points towards the center of rotation.

  • I noticed that these two arrows are at a right angle to each other, so the centripetal force is not speeding up or slowing down the particle.

  • It's just changing its direction constantly.

  • Tara Circular motion.

  • However, when the particle is pulled in and it follows this curved path to this inner orbit, it's instantaneous.

  • Velocity is no longer perpendicular to the centripetal force.

  • It's, ah, tangential velocity.

  • Tangent to that curve is gonna look something like this.

  • But notice that now the centripetal force is no longer at a right angle.

  • The force that is changing that particles direction is no longer at a right angle to its velocity.

  • Instead, if this is the normal to its velocity, the centripetal force is pulling the particle forward ahead in its rotation, speeding up its rotational velocity So, as you can see, I speed up when I pull the books in.

  • Because when I accelerate the books towards myself, I'm not just accelerating them towards myself.

  • I'm also accelerating them around now.

  • Likewise.

  • If a particle were too be pushed out from an orbit like this into a larger orbit, it's gonna not, you know it's not gonna do this.

  • It's not gonna go.

  • Time to go here.

  • One straight line.

  • No, it's gonna go like this.

  • Okay, I'll go to a larger orbit.

  • But look, now, on this line, the particles instantaneous velocity is something like this.

  • And the centripetal force is not perpendicular to that line.

  • This is me.

  • Give that a little V.

  • Oh, yeah.

  • Nice labeling.

  • All right, so Oh, wait.

  • Now you can see it.

  • Whips.

  • All right, So this is the one we're talking about.

  • This is the one that matters.

  • All right, so the, uh, the normal to that velocity might be like this.

  • So now notice that the centripetal force is actually working against the velocity of the particle decelerating it.

  • So of course, it slows down.

  • When I move the books further out, my rotation slows down because moving them out is also decelerating them now.

  • This is why it is harder to pull your arms in when you're spinning than when you're not.

  • Because you're not just moving your arms into yourself.

  • You're also accelerating them in the direction of their rotation.

  • Not only is the magnitude of angular momentum conserved, so is the direction.

  • But what is the direction of something spent?

  • What seems easy enough, right?

  • Look at this.

  • What's the direction of its spin clockwise?

  • Or is it someone standing on the other side would say that it was traveling counterclockwise?

  • Oh, Interestingly, this means that if you were to ask the face of a clock which way it's hand spun, it would say counterclockwise.

  • Of course, in order to unambiguously differentiate the direction of rotation, we need a tool that has no access of symmetry in any of the three spatial dimensions of our universe.

  • And luckily I've got a tool just like that in here.

  • I've been keeping it fresh and because someone I Oh, there it is.

  • It's my right hand.

  • A human hand is asymmetrical in the X Y and Z directions.

  • We've got thumb, no thumb, wrist fingertips, palm knuckles now because of this property, if we orient two pairs of opposites sides in a particular way, the one remaining pair will be locked.

  • My fingers could only really curl in the palm direction on the palm side.

  • So if I have my fingertips in the direction of a wheel, spin curled such that an object on that spinning object travels from my wrist around on my fingertips will then my thumb will only point in one direction, no matter which side I'm on from behind.

  • This is now going clockwise, but the right hand rule still puts my thumb backwards.

  • That's very cool.

  • We call the direction that the right hand thumb is pointing the direction of the wheels angular momentum.

  • But we could also use the left hand.

  • We get opposite directions, then the right hand gives us.

  • But so long as we all agree to use the same hand, we will all always be on the same page.

  • But it turns out, of course, the right hand was chosen, and so determining the direction of angular momentum and velocity is called the use of the right hand rule.

  • Okay, so now that we know how to find the direction of angular momentum.

  • We could explore how that part of it is also conserved.

  • I have here a very special wheels.

  • Whoa!

  • Yeah, it's pretty crazy looking.

  • That's because I wanted it to be really massive, so I wrapped a chain around it.

  • I'm not sure it's really that safe, but oh, man, is the effect good?

  • All right, now let's say that I got you have my right hand free.

  • Let's say that I start spinning the wheel like this.

  • The direction of its angular momentum can be found using the right hand rule.

  • I curl my fingers in the direction of rotation, so that's something on the wheel is going from my wrist to my fingertips on.

  • I look at which way my thumb this point animal's pointing up.

  • Let's call up positive direction.

  • I don't know the magnitude of the angular moment of the wheel right now.

  • It's some number, but let's just call it out.

  • And since it's up, we'll call it positive.

  • I could call it negative.

  • All that matters is that I could differentiate one direction from the opposite.

  • All right, wonderful.

  • So noticed that if I spun the wheel this way I'd have to turn my right hand over to curl my fingers properly.

  • Now my thumb is pointing down, so this would be negative.

  • Let's call the magnitude of this wheel's angular momentum.

  • L positive l Well, if I got the wheels spinning so that it had an angular momentum of positive L If I then turned it upside down, its angular momentum will have changed direction would have swapped from being positive.

  • L too negative.

  • L however, if nothing else is interfering, that can't happen without angular momentum being conserved.

  • So what?

  • Plus negative l is positive.

  • L our original Well, positive to L.

  • A.

  • And that is what we will see happen if I spin this wheel like this such that it has an angular momentum of positive l and then I turn it upside down.

  • Something else will have to have an angular momentum off positive to l So like.

  • Imagine my thumb being twice as long.

  • What is that?

  • Something else.

  • Well, it'll be me in the chair.

  • This is very cool.

  • So let's make sure we know what's about to happen.

  • I'm gonna spend the wheel this way, Then I'm going to turn it upside down.

  • And so I'm going to see myself in the chair, wind up rotating this way.

  • I'll rotate that way.

  • All right, So what I'm gonna do is have Scott step in and give this wheel a nice, healthy spin in that direction.

  • So it has an angular momentum of positive L.

  • I'll take my foot off the ground when he's done so or less isolated system, and I'll turn the wheel upside down and I should go that way.

  • Whoa, angular momentum is conserved.

  • That's pretty cool.

  • But the conservation of angular momentum either its magnitude or or its direction is not why turning the wheel upside down spun me this way.

  • I kicked my empty cup container anyway, what caused me to move?

  • Well, if you do this yourself, you will feel the handles of the wheel literally pushing you putting a torque on your body.

  • And it has everything to do with that concept I have covered in my spinning video and my video undying about Oilers disc.

  • If the wheel isn't spinning and I push it down right here, it'll tilt like that, right?

  • Not very surprising.

  • That's the kind of tilt we would expect But when the wheel is spinning all the piece of matter out here, well, they all have some velocity before I hit them.

  • For example, when a piece of matter on the wheel is out here, it's moving backwards, and when I push it down, it doesn't suddenly stopped moving backwards.

  • The wheel doesn't stop.