[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