Laws & Causes

[Music] hey Vsauce Michael here do you want to see the most illegal thing I own it's a penny from 2027 that's right it is a piece of counterfeit US currency or is it there are no 2027 pennies today which means that this is a counterfeit of an original that doesn't exist yet I mean sure if you didn't look at the date this could pass is real but will it not truly be counterfeit until 2027 well what we do know is that it's novel team has a lifespan 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 as 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 in closer they spin faster and faster it's really cool but what is accelerating their rotation what is pushing them around faster and faster you can 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 I don't need Jake no no 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 momentum oh the conservation of angular momentum I love demonstrations of it and this is one of my favorites this is a Hoberman's sphere a toy that collapses and expands doesn't it sort of remind you of me with the books far from my body and in 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 well if you look it up this is what you will find for a particle in circular motion around some center of rotation see the angular momentum of the particle is defined as the product of the particles mass the particles instantaneous velocity B and the particles distance from the center of rotation are M V 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 MV ours for every one of those particles and summed them 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 hold in your hand or put in a jar and study it's kind of like oh I don't know taking like my weight and multiplying it by the number of countries on earth and 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 its our value will go down but angular momentum is conserved so one of these other variables must go up well at low speeds mass is 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 know to 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 pull in know to speed up and why do they always obey our laws like embodied presences guiding matter around No I have with me right now three things a lamp a nail and a shadow gotcha I actually have four things with me the fourth is inks astonishing ruler designed by Vsauce if you're subscribed to the Curiosity box you already have one or it's on its way to you and if you're not subscribed 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 my eye I am seeing my hand as it was a billionth of a second in the past pretty cool now this ruler allows you to measure lengths of things in light picoseconds sound microseconds Micro Everest s' that's one millionth of the height of Everest beard fortnight's decimal inches and of course good-old centimeters now if you asked me hey Mike why is the shadow of the nail four and a half centimeters long well I would say who's Mike but that 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 um 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 as if alright 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 to have the height that it does to know why the nail is six centimeters tall we'd have to ask whoever manufactured it or whoever sets nail standards or whatever the point here is that we should not confuse relationships laws with causes explanations that involve 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 to understand does it mean to not stand up fully or does it mean to stand underneath and to look at from below if I can understand something can I also over stand something well as it turns out the under in 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 ah 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 the word explain literally means to flatten plain out X 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 we'll call C now when a particle is traveling in this outer ring and is 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 now notice 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 tada circular motion however when the particle is pulled in and it follows this curved path to this inner orbit its instantaneous velocity is no longer perpendicular to the centripetal force its tangential velocity tangent to that curve is going to 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 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 to 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 up time to go here one straight line no it's gonna go like this okay I'll go to the 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 let me give that a little V oh yeah nice labeling all right so oh wait now you can see it whoops all right so this is the one we're talking about though this is the one that matters all right so the the 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 spin 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 its hands spun it would say counterclockwise of course in order to unambiguously differentiate the direction of rotation we need a tool that has no axis 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 OH because a sworn I oh there it is it's my right hand a human hand is asymmetrical in the X Y & Z directions we've got thumb no thumb wrist fingertips palm knuckles now because of this property if we orient two pairs of opposite sides in a particular way the one remaining pair will be locked now my fingers can only really curl in the palm direction on the palm side so if I have my fingertips in the direction of a wheelspin curled such that an object on that spinning object travels from my wrist around to my fingertips well 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'd get opposite directions than the right hand gives us but so long as we all agree to use the same hand we will always be on the same page but as 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 wheel oh yeah it's pretty crazy looking that's because I wanted it to be really massive so I wrap I'm not sure it's really that safe but oh man is the effect good all right now let's say that I gotta 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 and I look at which way my thumb is point it was pointing up let's call up the positive direction I don't know the magnitude of the angular momentum of the wheel right now it's some number but let's just call it L and since it's up we'll call it positive I could call it negative all that matters is that I can differentiate one direction from the opposite all right wonderful so notice 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 wheels angular momentum L positive L well if I got the wheel spinning so that it had an angular momentum of positive L if I then turn it upside down its angular momentum will have changed direction it would have swapped from being positive L to 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 2l 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 of positive 2 L so like imagine my thumb being twice as long what is that something else well it'll be me in the chair is this very cool so let's make sure we know what's about to happen I'm gonna spin 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 I'm in more 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 Y turning the wheel upside down spun me this way website kicked my empty to cup a container anyway what caused me to move well if you do this yourself you will feel the handles of the wheel literally pushing you put in a torque on your body and it has everything to do with that concept I have covered in my spinning video and my video ending about Euler's disk 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 stop moving backwards the wheel doesn't stop instead the pieces I'm pushing are now going to go backwards as they already were and down so they go backwards and down and then they come back up and the entire wheel is found to tilt this way look towards me 90 degrees ahead from where I actually pushed it down a push down here causes the wheel to move like this a push down here would cause the wheel to tilt like this a push up here would cause the wheel to tilt like let's see 90 degrees ahead in the rotation like this and this and this is exactly what I'm doing when I turn the wheel upside down so when I put a torque on the wheel to turn it while it's spinning like this the wheel actually turns this way but I have two hands holding it my left hand lines up getting pushed backwards and my right hand pulled forwards that puts a torque on my body which causes me being pushed back here and pulled forward here it causes me to be turned and so I turn this way the way that we saw in the demo in the and that is the physical origin of the phenomenon we just witnessed the key point here is that nothing you have seen happen today happened because of the conservation of angular momentum physical laws don't cause anything to happen but plenty of things are demonstrations of their truth now don't get me wrong I love physical laws they truly do represent a conquering of mystery when we find a way to project definite numbers onto reality and make predictions that's amazing but not coupled with causal mechanical physical explanations their generality can come across like magic now magic is fun for sure but congruences between mathematics and reality oh that's a sweet nectar in mathematics we get to make the rules pick the axioms we can even decide what kinds of reasoning are allowed or not and after doing so we get to play around and see what happens mathematics is the plane of games science is finding out what game you're playing and we still don't know what game we have found ourselves in but we should keep wondering and never be happy until we get answers that satisfy us stay curious and as always thanks for watching [Music] I have some pretty exciting news to share with you as of today for the rest of the year every single episode of mind field all three seasons all 24 episodes will be free to view all around the world I am thrilled so go and check those out there's a very special well actually two very special things coming on this channel this month can't wait for you to see them in the meantime if you need more of me and I always need more of me check out ding I've done about 15 videos this year over there it's a blast we learn a lot over there and things often get a little bit weird you know what I guess maybe I don't know check it out and find out and as always thanks for watching

Channel: Vsauce

Views: 3,600,212

Rating: 4.9713602 out of 5

Keywords: angular momentum, spin, conservation, physics, law, math, science, ice skater, books, spinning

Id: _WHRWLnVm_M

Length: 22min 21sec (1341 seconds)

Published: Tue Oct 01 2019

Reddit Comments

[u/killjoy_x]

THE LEGEND IS BACK! AND THE BEARD HAS GROWN!

[u/Snakeoil27]

🦀🦀🦀 MINDFIELD IS NOW FREE🦀🦀🦀

[u/running_toilet_bowl]

LOOK AT THE DESCRIPTION

[u/wildgoosespeeder]

Wait a minute. This is real?

✅ Vsauce

✅ 4 hours ago

DEAR GOD

[u/drewbltz]

HOLY SHIT

[u/LordPylar]

HES BACK MY GOD HE DID IT

[u/rezuke]

It's about time!

[u/jdutt524]

Its been 84 years...

[u/AidanLambComposer]

Looks like HL3 just came out!