Laws & Causes

published on July 9, 2020

Hey Vsauce Michael here do you want tosee the most illegal thing I own it's apenny from 2027 that's right it is apiece of counterfeit US currency or isit there are no 2027 pennies today whichmeans that this is a counterfeit of an

Original that doesn't exist yetI mean sure if you didn't look at thedate this could pass is real but will itnot truly be counterfeit until 2027 wellwhat we do know is that it's novel teamhas a lifespan it's really cool to show

People today it's a penny from thefuture but in 2027 it will becomeindistinguishable from a common pennyand it will cease to be as interesting Icannot tell you where I got this but thepoint is I can break the law I am free

Perhaps not free from punishment butnonetheless here we are I cannot breakthe laws of physicsnothing can why today I want to look atthe lawful behavior of spinning let'sstart with a physics classic as a

Spinning ice skater pulls their body incloser they spin faster and faster it'sreally cool but what is acceleratingtheir rotation what is pushing themaround faster and faster you can trythis at home with a chair that spins and

Some really heavy books in both handsnow to get started spinning I'm gonnahave Jake give me a pushI don't need Jake no no watch this withhim gone I can nonetheless speed myselfup by just pulling the books in if I

Move the books out I slow down somehowpulling the books in speeds me up aroundnow if you look up why this happensyou'll probably be told that it isbecause of the conservation of angularmomentum

Oh the conservation of angular momentumI love demonstrations of it and this isone of my favorites this is a Hoberman'ssphere a toy that collapses and expandsdoesn't it sort of remind you of me withthe books far from my body and in the

Books close to my body and it behaves inmuch the same way I need to give it someangular momentum to start but once I doif I bring all of that mass towards theaxis of rotation it speeds up and thenit slows down and then it speeds up and

Then it slows down speeds up slows downI love this thank youconservation of angular momentum butwhat are you well if you look it up thisis what you will find for a particle incircular motion around some center of

Rotation see the angular momentum of theparticle is defined as the product ofthe particles mass the particlesinstantaneous velocity B and theparticles distance from the center ofrotation are M V R this is angular

Momentum if you divided me and the chairand the books I'm holding into a bunchof tiny little particles and found theMV ours for every one of those particlesand summed them all up you would havethe angular momentum of the entire

System of me the chair and the books butnotice that this is just a mathematicalexpression combining three differentmeasures it's not a physical substanceyou could pull out of a particle andhold in your hand or put in a jar and

Study it's kind of like oh I don't knowtaking like my weight and multiplying itby the number of countries on earth andthen multiplying it by the time howeverunlike something like thatthis concept is really useful because we

Have found that in our universe overtime it is conserved if the particle ispulled towards the center of rotationits our value will go down but angularmomentum is conserved so one of theseother variables must go up well at low

Speeds mass is essentially constant sothe only option is for the velocity ofthe particle to increase for theparticle to spin around faster than itwas before if the R value gets smallerthe velocity must get larger or else a

Law has been broken but how do atoms andmolecules know to follow this law I meanis there some kind of physics policeforce in the universebullying everything into compliance howdo all the atoms I pull in know to speed

Up and why do they always obey our lawslike embodied presences guiding matteraround No I have with me right now threethings a lamp a nail and a shadowgotcha I actually have four things withme

The fourth is inks astonishing rulerdesigned by Vsauce if you're subscribedto the Curiosity box you already haveone or it's on its way to you and ifyou're not subscribed to the CuriosityBox well you're missing out on the

Fruits of my mindI have always wanted a ruler like thisso I made one and now I and you can haveone it is exactly one light nanosecondlong which means that this is thedistance light travels in a vacuum

During one billionth of a second if Ihold my hand just that far away from myeye I am seeing my hand as it was abillionth of a second in the past prettycool now this ruler allows you tomeasure lengths of things in light

Picoseconds sound microseconds MicroEverest s' that's one millionth of theheight of Everest beard fortnight'sdecimal inches and of course good-oldcentimeters now if you asked me hey Mikewhy is the shadow of the nail four and a

Half centimeters long well I would saywho's Mike but that I would be helpfuland I would answer that the length ofthe shadow is caused by the height ofthe nail and the position of the lightsource and that's a pretty good

Explanation because if the nail weretaller and or if the light source werelower the shadow would be longer or ifthe nail were shorter and or the lightsource was higher the shadow would besmaller now these three measures the

Nails height the lights position and theshadows length are all relatedmathematically such that if you gave meonly two of them I could figure out thethird always so I could declare thisrelationship to be a law but that does

Not mean that the law causes them to allhave the measure that they do forexample if you ask me hey um why is thenail six centimeters tall what causesthe nail to have that height well if Isaid well the nails height is caused by

The shadows lengthen the lights positionyou'd be likeas if alright I mean sure we can figureout the nails height by knowing aboutthe shadow and the light but that doesnot mean that they are causing the nail

To have the height that it does to knowwhy the nail is six centimeters tallwe'd have to ask whoever manufactured itor whoever sets nail standards orwhatever the point here is that weshould not confuse relationships laws

With causes explanations that involvethe causal reasons for things are oftenbetter but what is an explanation wellthat's easy to answer explanations helpus understand things but what does itmean to understand does it mean to not

Stand up fully or does it mean to standunderneath and to look at from below ifI can understand something can I alsoover stand something well as it turnsout the under in understand does notmean beneath or below instead it means

Inside to stand surrounded by to be apart ofnow this sense of under is quite commonfor example when you say ah well underthose circumstances you don't mean wellwhen those circumstances are overhead

And I'm under them instead you mean if Ifind myself in those circumstances andthat is how under is used in understandto understand something is to stand inthe midst of it to be part of it and tobe within it and that is helpful to keep

In mind I cannot walk into somethingthat's crumpled up and closed off totruly understand something it needs tobe opened up for meunfolded and that is what an explanationshould do the word explain literally

Means to flatten plain out Xexplain to make flat now if you'llexcuse the analogy if this is a story Iwant to read and it's all crumpled up aphysical law basically just tells me asummary of the story it'll tell me how

The story ends what language andgrammatical rules were used to write itbut an explanation will flatten the pageout and allow me to see the details anactual word and the word that follows itand so on all the way through so let's

Unfold the phenomenon of me speeding upmy rotation when I pull the books in andfind a physical mechanical cause forthat increased rotation I have here twodifferent circular motion paths aroundthe center of rotation which we'll call

C now when a particle is traveling inthis outer ring and is suddenly pulledinit doesn't stop moving around andsuddenly just go right in instead ittakes a bit of a curved path like this

Now this is really interesting becausein order for a particle to be incircular motion it must have two thingsit must have put the particle there itmust have a velocity that is tangentialto the path but it must also have a

Centripetal force a center seeking forcethat always points towards the center ofrotation now notice that these twoarrows are at a right angle to eachother so the centripetal force is notspeeding up or slowing down the particle

It's just changing its directionconstantly tada circular motion howeverwhen the particle is pulled in and itfollows this curved path to this innerorbit its instantaneous velocity is nolonger perpendicular to the centripetal

Force its tangential velocity tangent tothat curve is going to look somethinglike this but notice that now thecentripetal force is no longer at aright angle the force that is changingthat particles Direction is no longer at

A right angle to its velocity instead ifthis is the normal to its velocity thecentripetalis pulling the particle forward ahead inits rotation speeding up its rotationalvelocity so as you can see I speed up

When I pull the books in because when Iaccelerate the books towards myself I'mnot just accelerating them towardsmyself I'm also accelerating them aroundnow likewise if a particle were to bepushed out from an orbit like this into

A larger orbit it's gonna not you knowit's not gonna do this it's not gonna goup time to go here one straight line noit's gonna go like this okay I'll go tothe larger orbit but look now on thisline the particles instantaneous

Velocity is something like this and thecentripetal force is not perpendicularto that line this is let me give that alittle V oh yeah nice labeling all rightso oh wait now you can see it whoops allright so this is the one we're talking

About though this is the one thatmatters all right so the the the normalto that velocity might be like this sonow notice that the centripetal force isactually working against the velocity ofthe particle decelerating it so of

Course it slows down when I move thebooks further out my rotation slows downbecause moving them out is alsodecelerating them now this is why it isharder to pull your arms in when you'respinning than when you're not because

You're not just moving your arms intoyourself you're also accelerating themin the direction of their rotation notonly is the magnitude of angularmomentum conserved so is the directionbut what is the direction of something

Spin what seems easy enough right lookat this what's the direction of its spinclockwise or is it someone standing onthe other side would say that it wastraveling counterclockwise Ohinterestingly this means that if you

Were to ask the face of a clock whichway its hands spun it would saycounterclockwise of course in order tounambiguously differentiate thedirection of rotation we need a toolthat has no axis of symmetry in any of

The three spatial dimensions of ouruniverse and luckily I've got a tooljust like thatin here I've been keeping it fresh andOHbecause a sworn I oh there it is it's my

Right hand a human hand is asymmetricalin the X Y & Z directionswe've got thumb no thumb wristfingertips palm knuckles now because ofthis property if we orient two pairs ofopposite sides in a particular way the

One remaining pair will be locked now myfingers can only really curl in the palmdirection on the palm side so if I havemy fingertips in the direction of awheelspin curled such that an object onthat spinning object travels from my

Wrist around to my fingertips well thenmy thumb will only point in onedirection no matter which side I'm onfrom behind this is now going clockwisebut the right hand rule still puts mythumb backwards

That's very cool we call the directionthat the right-hand thumb is pointingthe direction of the wheels angularmomentum but we could also use the lefthand we'd get opposite directions thanthe right hand gives us but so long as

We all agree to use the same hand wewill always be on the same page but asit turns out of course the right handwas chosen and so determining thedirection of angular momentum andvelocity is called the use of the right

Hand rule okay so now that we know howto find the direction of angularmomentum we could explore how that partof it is also conserved I have here avery special wheel oh yeah it's prettycrazy looking that's because I wanted it

To be really massive so I wrapI'm not sure it's really that safe butoh man is the effect good all right nowlet's say that I gotta you have my righthand free let's say that I startspinning the wheel like this the

Direction of its angular momentum can befound using the right-hand rule I curlmy fingers in the direction of rotationso that's something on the wheel isgoing from my wrist to my fingertips andI look at which way my thumb is point it

Was pointing up let's call up thepositive direction I don't know themagnitude of the angular momentum of thewheel right now it's some number butlet's just call it L and since it's upwe'll call it positive I could call it

Negative all that matters is that I candifferentiate one direction from theopposite all right wonderful so noticethat if I spun the wheel this way I'dhave to turn my right hand over to curlmy fingers properly now my thumb is

Pointing down so this would be negativelet's call the magnitude of this wheelsangular momentum L positive L well if Igot the wheel spinning so that it had anangular momentum of positive L if I thenturn it upside down its angular momentum

Will have changed direction it wouldhave swapped from being positive L tonegative L however if nothing else isinterfering that can't happen withoutangular momentum being conserved so whatplus negative L is positive L our

Original well positive 2l and that iswhat we will see happen if I spin thiswheel like this such that it has anangular momentum of positive L and thenI turn it upside down something elsewill have to have an angular momentum of

Positive 2 L so like imagine my thumbbeing twice as long what is thatsomething elsewell it'll be me in the chair is thisvery cool so let's make sure we knowwhat's about to happen I'm gonna spin

The wheel this way then I'm going toturn it upside down and so I'm going tosee myself in the chair wind up rotatingthis way I'll rotate that way all rightso what I'm gonna do is have Scott stepin and give this wheel a nice healthy

Spin in that direction so it has anangular momentum of positive L I'll takemy foot off the ground when he's done soI'm inmore or less isolated system and I'llturn the wheel upside down and I should

Go that way whoaangular momentum is conservedthat's pretty cool but the conservationof angular momentum either its magnitudeor or its direction is not Y turning thewheel upside down spun me this way

Website kicked my empty to cup acontainer anyway what caused me to movewell if you do this yourself you willfeel the handles of the wheel literallypushing you put in a torque on your bodyand it has everything to do with that

Concept I have covered in my spinningvideo and my video ending about Euler'sdisk if the wheel isn't spinning and Ipush it down right hereit'll tilt like that right not verysurprising that's the kind of tilt we

Would expect but when the wheel isspinning all the piece of matter outhere well they all have some velocitybefore I hit them for example when apiece of matter on the wheel is out hereit's moving backwards and when I push it

Down it doesn't suddenly stop movingbackwards the wheel doesn't stop insteadthe pieces I'm pushing are now going togo backwards as they already were anddown so they go backwards and down andthen they come back up and the entire

Wheel is found to tilt this way looktowards me 90 degrees ahead from where Iactually pushed it down a push down herecauses the wheel to move like this apush down here would cause the wheel totilt like this a push up here would

Cause the wheel to tilt like let's see90 degrees ahead in the rotation likethis and this and this is exactly whatI'm doing when I turn the wheel upsidedown so when I put a torque on the wheelto turn it while it's spinning like this

The wheel actually turns this way but Ihave two hands holding it my left handlines up getting pushed backwards and myright hand pulled forwards that puts atorque on my body which causes me beingpushed back here and pulled forward here

It causes me to be turned and so I turnthis way the way that we saw in the demoin theand that is the physical origin of thephenomenon we just witnessed the keypoint here is that nothing you have seen

Happen today happened because of theconservation of angular momentumphysical laws don't cause anything tohappen but plenty of things aredemonstrations of their truth now don'tget me wrong I love physical laws they

Truly do represent a conquering ofmystery when we find a way to projectdefinite numbers onto reality and makepredictions that's amazing but notcoupled with causal mechanical physicalexplanations their generality can come

Across like magicnow magic is fun for sure butcongruences between mathematics andreality oh that's a sweet nectar inmathematics we get to make the rulespick the axioms we can even decide what

Kinds of reasoning are allowed or notand after doing so we get to play aroundand see what happens mathematics is theplane of games science is finding outwhat game you're playing and we stilldon't know what game we have found

Ourselves in but we should keepwondering and never be happy until weget answers that satisfy us stay curiousand as always thanks for watchingI have some pretty exciting news toshare with you as of today for the rest

Of the year every single episode of mindfield all three seasons all 24 episodeswill be free to view all around theworld I am thrilled so go and checkthose out there's a very special wellactually two very special things coming

On this channel this month can't waitfor you to see them in the meantime ifyou need more of me and I always needmore of me check out ding I've doneabout 15 videos this year over thereit's a blast we learn a lot over there

And things often get a little bit weirdyou know what I guess maybe I don't knowcheck it out and find out and as alwaysthanks for watching

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