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Today we will discuss

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what we call
"uniform circular motion."

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What is uniform circular motion?

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An object goes around
in a circle, has radius r

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and the object is here.

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This is the velocity.

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It's a vector, perpendicular.

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And later in time
when the object is here

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the velocity has changed,
but the speed has not changed.

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We introduce T,
what we call the period--

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of course it's in seconds--

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which is the time
to go around once.

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We introduce the frequency, f,
which we call the frequency

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which is the number
of rotations per second.

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And so the units are
either seconds minus one

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or, as most physicists
will call it, "hertz"

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and so frequency is
one divided by T.

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We also introduce
angular velocity, omega

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which we call angular velocity.

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Angular velocity means not
how many meters per second

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but how many radians
per second.

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So since there are two pi
radians in one circumference--

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in one full circle--

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and it takes T seconds
to go around once

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it is immediately obvious

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that omega equals two pi
divided by T.

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This is something that
I would like you to remember.

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Omega equals two pi
divided by T--

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two pi radians
in capital T seconds.

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The speed, v, is, of course,
the circumference two pi r

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divided by the time
to go around once

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but since two pi
divided by T is omega

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you can also write
for this "omega r."

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And this is also something
that I want you to remember.

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These two things
you really want to remember.

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The speed is not changing, but
the velocity vector is changing.

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Therefore there must be
an acceleration.

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That is non-negotiable.

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You can derive
what that acceleration must be

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in terms of magnitude
and in terms of direction.

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It's about a five,
six minutes derivation.

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You'll find it in your book.

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I have decided to give
you the results

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so that you read up on the book

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so that we can more talk
about the physics

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rather than on the derivation.

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This acceleration
that is necessary

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to make the change
in the velocity vector

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is always pointing towards
the center of the circle.

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We call it
"centripetal acceleration."

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Centripetal, pointing
towards the center.

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And here, also pointing
towards the center.

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It's a vector.

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And the magnitude of
the centripetal acceleration

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equals v squared divided by r,
which is this v

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and therefore it's
also omega squared r.

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And so now we have
three equations

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and those are the only three you
really would like to remember.

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We can have a simple example.

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Let's have a vacuum cleaner,
which has a rotor inside

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which scoops the air out or in,
whichever way you look at it.

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And let's assume
that the vacuum cleaner

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these scoops have a radius r
of about ten centimeters

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and that it goes around 600
revolutions per minute, 600 rpm.

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600 rpm would translate
into a frequency, f, of 10 Hz

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so it would translate
into a period

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going around in one-tenth
of a second.

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So omega, angular velocity,
which is two pi divided by T

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is then approximately
63 radians per second

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and the speed, v, equals omega r

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is then roughly 6.3 meters
per second.

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The centripetal acceleration--
and that's really my goal--

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the centripetal acceleration
would be omega squared r

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or if you prefer,
you can take v squared over r.

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You will get the same answer,
of course, and you will find

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that that is about 400 meters
per second squared.

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And that is huge.

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That is 40 times
the acceleration due to gravity.

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It's a phenomenal acceleration,
the simple vacuum cleaner.

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Notice that the acceleration,
the centripetal acceleration

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is linear in r.

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Don't think that it is
inversely proportional with r.

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That's a mistake, because v
itself is a function of r.

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If you were sitting here

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then your velocity
would be lower.

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Since omega is the same
for the entire motion

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you really have to look
at this equation

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and you see that
the centripetal acceleration

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is proportional with r.

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Therefore, if you were...

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if this were a disc
which was rotating

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and you were at
the center of the disc

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the centripetal acceleration
would be zero.

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And as you were to walk out,
further out, it would increase.

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Now, the acceleration
must be caused by something.

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There is no such thing
as a free lunch.

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There is something
that must be responsible

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for the change in this velocity

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and that something
I will call either a pull

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or I will call it a push.

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In our next lecture, when
we deal with Newton's laws

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we will introduce
the word "force."

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Today we will only deal with
the words "pull" and "push."

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So there must be a pull
or a push.

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Imagine that this is
a turntable

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and you are sitting here
on the turntable on a chair.

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It's going around
with angular velocity omega

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and your distance to the center,
let's say, is little r.

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You're sitting on this chair
and you must experience--

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that is non-negotiable--
centripetal acceleration

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A of c, which is omega squared
times r.

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Where do you get it from?

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Well, if your seat is bolted
to the turntable

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then you will feel a push
in your back

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so you're sitting on this thing,
you're going around

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and you will feel that the seat
is pushing you in your back

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and so you feel a push,
and that gives the push out.

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Yeah, I can give this
a red color for now.

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So you feel a push in your back.

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That push, apparently, is
necessary for the acceleration.

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Alternatively, suppose you had
in front of you a stick.

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You're not sitting on a chair.

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You don't get a push
from your back.

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But you hold onto the stick

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and now you can go around
by holding onto the stick.

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Now the stick is pulling on you
in this same direction.

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So now you would say, aha,
someone is pulling on you.

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Whether it is the pull
or whether it is the push

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one of... either one of the two

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is necessary for you
to go around in that circle

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on that turntable
with that constant speed.

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Now, the classic question comes
up, which we often ask to people

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who have
no scientific background.

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If you were to go around
like this

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and something is
either pushing on you

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or is pulling on you
to make this possible

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suppose you took that push
out, all of a sudden.

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The pull is gone.

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(makes whooshing sound )

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What is now the motion
of the person

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who is sitting on the turntable?

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And many non-scientists say,
"Well, it will do like this."

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That's sort of
what your intuition says.

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You go around in a circle,
and all of a sudden

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you no longer have
the pull or the push

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and you go around in a spiral

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and obviously,
that is not the case.

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What will happen is, if you
have, at this moment in time

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a velocity in this direction

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and you take the pull
or the push out

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you will start flying off
in that direction

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and depending upon whether
there is gravity or no gravity

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there may be a change,

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but if this were...
if there were no gravity

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you would just continue
to go along that line

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and you would not make
this crazy spiral motion.

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I have here a disc,
which we will rotate

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and at the end...
the edge of the disc here

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we have a little ball.

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And the ball is attached
to that disc with string.

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So now this is vertical, and
so this is going to go around

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with angular velocity omega.

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And we have a string here

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and the string is attached
to this ball

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and the whole thing is
going around

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and so at one moment in time
this has a velocity, like so.

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And therefore there must be

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non-negotiable
centripetal acceleration

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which in magnitude is
omega squared r

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or, if you want to,
v squared divided by r.

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Now I cut it

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and that's like taking away
the push and the pull.

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The string that you have here

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is providing the pull
on this ball.

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This ball is feeling a pull
from the string

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and that provides it with
the centripetal acceleration.

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Cut the string
and the pull is gone

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and the object will take off.

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And if there were gravity here,
as there is in 26.100

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it would become a parabola
and it would end up here.

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If, however, I cut the ball
exactly when it is here--

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not the ball,
but I cut the string--

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then, of course,
it would fly straight up

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gravity would act on it,
it would come to a halt

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and it would come back.

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So it really would then go
along a straight line.

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But you would clearly see, then

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that it's not going to do
what many people think--

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that it would start
to swirl around.

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It would just go...
(makes whooshing sound )

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and comes back.

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Let's look at that.

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We have that here.

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So here is that ball.

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The string is behind here;
you cannot see the string.

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I will rotate it, wait for it
to pick up a little speed

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and the knife, that you can't
see either, is behind here

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and when I push the knife in,
I do it exactly here.

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It cuts the string
and it goes up.

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You ready for this?

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You sure you're ready?

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Three, two, one, zero.

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Wow!

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That was very high.

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So you see,
it's nothing like this.

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It simply continued on in
the direction that it was going.

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It wasn't going into a parabola

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because I was shooting it
straight up.

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The string forms the connection

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between the rotating disc
and the ball

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and therefore,
the pull is responsible

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for the centripetal
acceleration.

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Let's now think about planets.

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Planets go around the sun.

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There's no string, so who
is pushing? Who is pulling?

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Well, it's clear
that it must be gravity.

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It must be the sun that is
pulling on the planets.

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Now, I realize that
the orbits of planets

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are not nicely circular

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so it's not really
a uniform circular motion.

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We will deal with orbits in
great detail in a few weeks--

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circular orbits
and elliptical orbits.

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Let us just assume
for simplicity now

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that the orbits are
roughly circular

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just to get a little bit
of feeling for it.

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And you can look up
now in your book--

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which I did for you--

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even in your preliminary version
you can look up

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what the mean distance
of the planets is to the sun

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and you can look up
what the period is

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the time to go around the sun.

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The time to go around the sun
is not the same for all planets.

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The planets are not attached
to a turntable.

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Anywhere,
any person on a turntable

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would go around
in the same amount of time.

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We know that
that's not true for planets.

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It takes the Earth a year
to go around the sun.

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It takes Jupiter
12 years to go around

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so don't make the mistake
to think

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that omega is the same
for all planets.

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That's not true.

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So I look up the distance--

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the mean distance
to these various planets--

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and you see that here
in millions of kilometers.

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Notice that Mercury is about
100 times closer than Pluto.

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By the way, this is on the Web,
so don't copy this.

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You will find this
on the 801 home page.

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Then I looked up

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how many years it takes
to go around the sun--

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12 years for Jupiter,
one year for the Earth--

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and I looked up
all the other values.

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Then, since I know the periods,
I can calculate omega.

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Omega is two pi divided by T,
so I know omega.

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And then I take omega squared

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times the mean distance
to the sun

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and this is, of course,
the centripetal acceleration.

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So the planets experience
this centripetal acceleration

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in some crazy units, but
who cares about the units here?

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And notice that Mercury, which
is 100 times closer than Pluto

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has a centripetal acceleration

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which is 10,000 times
larger than Pluto.

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100 times closer

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has a 10,000 times larger
centripetal acceleration.

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So what I did was

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I plotted this data,
the centripetal acceleration

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versus the mean distance
to the sun

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and I did that on log paper.

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And what immediately strikes...
is very striking is

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that all these points-- I've
done them for all the planets--

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they fall on a straight line.

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And so what is the slope
of that line?

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Well, I tried various slopes

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and I found that the slope is
very, very close to minus two.

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Here is the slope of minus two,
and I can overlay this

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and notice that the fit is
absolutely stunning.

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Therefore, you cannot escape
the conclusion

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that the
centripetal acceleration

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which is the result of gravity,
falls off as one over R squared.

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We refer to this,
often, in physics

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as the "one over R square" law.

286
00:16:28 --> 00:16:34
And therefore, the effect
of gravity itself

287
00:16:31 --> 00:16:37
must go down with R squared.

288
00:16:35 --> 00:16:41
So if you are
100 times further away

289
00:16:39 --> 00:16:45
like Pluto compared to Mercury

290
00:16:42 --> 00:16:48
then the gravitational...
the centripetal acceleration

291
00:16:47 --> 00:16:53
which is due to gravity
is 10,000 times smaller.

292
00:16:50 --> 00:16:56

293
00:16:53 --> 00:16:59
And we will learn a lot
about gravity in the future.

294
00:16:56 --> 00:17:02
We will just leave it for now.

295
00:16:58 --> 00:17:04
If you took the sun away,
it would be

296
00:17:00 --> 00:17:06
like cutting the string
that provides the pull

297
00:17:04 --> 00:17:10
and in that case
what you would see

298
00:17:07 --> 00:17:13
is that the planets would just
take off along a straight line.

299
00:17:11 --> 00:17:17
They would continue to go.

300
00:17:14 --> 00:17:20
They wouldn't have anything
to pull on them anymore.

301
00:17:18 --> 00:17:24
Now let's look at an object
that we're going to rotate.

302
00:17:25 --> 00:17:31
I have a glass tube
that I want to rotate

303
00:17:29 --> 00:17:35
and in the glass tube,
I have a marble.

304
00:17:35 --> 00:17:41
The glass tube is very smooth.

305
00:17:38 --> 00:17:44
I have here the glass tube.

306
00:17:42 --> 00:17:48
Here's a marble.

307
00:17:46 --> 00:17:52
I'm going to rotate it
in this direction

308
00:17:51 --> 00:17:57
say, with some
angular velocity omega

309
00:17:53 --> 00:17:59
about an axis perpendicular
to the blackboard.

310
00:17:56 --> 00:18:02
So the marble here has
a velocity

311
00:18:02 --> 00:18:08
like so, at this moment in time

312
00:18:04 --> 00:18:10
but it's a very smooth
glass tube

313
00:18:07 --> 00:18:13
and the marble is very smooth.

314
00:18:10 --> 00:18:16
The glass cannot push
on the marble

315
00:18:13 --> 00:18:19
nor can the glass pull
on the marble.

316
00:18:17 --> 00:18:23
Now, the marble gets desperate

317
00:18:18 --> 00:18:24
because the marble needs
a centripetal acceleration

318
00:18:23 --> 00:18:29
in this direction
in order to go around like this.

319
00:18:29 --> 00:18:35
But there is nothing to provide
that centripetal acceleration.

320
00:18:33 --> 00:18:39
So the marble is doing
exactly the same

321
00:18:35 --> 00:18:41
that the planets would do
if you take the sun away.

322
00:18:38 --> 00:18:44
The marble continues to go in
the direction that it was going.

323
00:18:42 --> 00:18:48
So by the time that the tube
is here, the marble is here

324
00:18:50 --> 00:18:56
and by the time
that the tube is here

325
00:18:54 --> 00:19:00
the marble is there.

326
00:18:56 --> 00:19:02
So the marble finds its way to
the edge and that's, of course

327
00:19:00 --> 00:19:06
the basic idea
behind a centrifuge.

328
00:19:07 --> 00:19:13
My grandmother had always...

329
00:19:09 --> 00:19:15
She was a great lady

330
00:19:10 --> 00:19:16
and she had such fantastic
ideas, I remember.

331
00:19:13 --> 00:19:19
And when she made lettuce

332
00:19:17 --> 00:19:23
we had no good way
of drying the lettuce

333
00:19:20 --> 00:19:26
and I would take the lettuce
and go like this... paper towel.

334
00:19:26 --> 00:19:32
She had a method of her own.

335
00:19:29 --> 00:19:35
She took a colander
and, of course, first of all

336
00:19:34 --> 00:19:40
we would wash the lettuce,
that goes without saying.

337
00:19:37 --> 00:19:43
I would wash it once.

338
00:19:39 --> 00:19:45
My grandmother would wash it
three times

339
00:19:41 --> 00:19:47
but that's what you have
grandmothers for.

340
00:19:43 --> 00:19:49
So there comes the lettuce.

341
00:19:47 --> 00:19:53
We were also very fond of
spinach, so add some spinach.

342
00:19:53 --> 00:19:59
We would wash it...
there goes the spinach.

343
00:19:58 --> 00:20:04
Then she would take
something to cover it up--

344
00:20:01 --> 00:20:07
maybe some Saran wrap,
or something else--

345
00:20:06 --> 00:20:12
put it over it and put a rubber
band around it to hold it.

346
00:20:14 --> 00:20:20
And now what she's going to do,
she's going to swing it around.

347
00:20:17 --> 00:20:23
And now the water is
like these marbles.

348
00:20:22 --> 00:20:28
The water will work its way
to the edge

349
00:20:25 --> 00:20:31
but there are holes,
so the water will come out.

350
00:20:28 --> 00:20:34
Isn't she clever?

351
00:20:30 --> 00:20:36
Okay, I'll give you
a demonstration.

352
00:20:33 --> 00:20:39
Be careful

353
00:20:34 --> 00:20:40
or you may get some water
on your lecture notes.

354
00:20:39 --> 00:20:45
But I want to show you

355
00:20:40 --> 00:20:46
the basic idea behind it
is very interesting.

356
00:20:43 --> 00:20:49
She would go out... she would do
this outside, by the way.

357
00:20:45 --> 00:20:51
But I have no choice,
so I will do it here.

358
00:20:48 --> 00:20:54
So there we go.

359
00:20:50 --> 00:20:56
(class laughs )

360
00:20:54 --> 00:21:00
You see?
This is the way you dry...

361
00:20:57 --> 00:21:03

362
00:21:01 --> 00:21:07
Oh, I lost
my magnetic strawberry--

363
00:21:04 --> 00:21:10
that's a detail in the process.

364
00:21:06 --> 00:21:12
So you end up with...

365
00:21:09 --> 00:21:15
you end up with dry
and clean and nice lettuce.

366
00:21:16 --> 00:21:22
This is 801 at work

367
00:21:18 --> 00:21:24
and this is clearly an early
version of a centrifuge.

368
00:21:23 --> 00:21:29
Now, my grandmother's method,
very tragically

369
00:21:27 --> 00:21:33
has been replaced lately

370
00:21:29 --> 00:21:35
with something that you can buy
at Crate and Barrel.

371
00:21:33 --> 00:21:39
We have it here.

372
00:21:36 --> 00:21:42
Um, it is very boring.

373
00:21:39 --> 00:21:45
It's very decadent.

374
00:21:41 --> 00:21:47
Put the salad in here

375
00:21:42 --> 00:21:48
and all you do is
you rotate and it dries.

376
00:21:47 --> 00:21:53
It's a centrifuge.

377
00:21:48 --> 00:21:54
This is actually
a high-tech version

378
00:21:51 --> 00:21:57
of the much more sophisticated
invention of my grandmother.

379
00:21:55 --> 00:22:01
And it's nowhere
nearly as exciting.

380
00:22:00 --> 00:22:06
The days of romance are
really over

381
00:22:04 --> 00:22:10
but that's the way it goes.

382
00:22:07 --> 00:22:13
I'm now going to make
a connection

383
00:22:11 --> 00:22:17
between rotation on the one hand

384
00:22:14 --> 00:22:20
and centripetal acceleration
on the other.

385
00:22:19 --> 00:22:25
I'm going to make a connection

386
00:22:23 --> 00:22:29
between centripetal acceleration
and perceived gravity.

387
00:22:28 --> 00:22:34
The way that
you perceive gravity.

388
00:22:33 --> 00:22:39
I'm going to put you
in various positions

389
00:22:35 --> 00:22:41
and then ask you what is
the direction of gravity.

390
00:22:39 --> 00:22:45
I'm going to create
artificial gravity for you.

391
00:22:43 --> 00:22:49
And let's first do it
as follows.

392
00:22:45 --> 00:22:51
I first hang you on a string.

393
00:22:49 --> 00:22:55

394
00:22:51 --> 00:22:57
There you are, like this.

395
00:22:56 --> 00:23:02
And I ask you, do you feel
a push or a pull?

396
00:23:00 --> 00:23:06
And you say,
"Yeah, I feel a pull."

397
00:23:05 --> 00:23:11
And you feel a pull
in this direction.

398
00:23:10 --> 00:23:16
So now I ask you

399
00:23:11 --> 00:23:17
"Ah, in what direction
do you perceive gravity?"

400
00:23:18 --> 00:23:24
and you think I'm crazy.

401
00:23:20 --> 00:23:26
You're right in that case,
but nevertheless you say

402
00:23:23 --> 00:23:29
"Gravity is
in this direction."

403
00:23:26 --> 00:23:32
The other direction is the pull.

404
00:23:28 --> 00:23:34
Okay, so far, so good.

405
00:23:31 --> 00:23:37
So now I'm going to put you
just standing on the floor

406
00:23:36 --> 00:23:42
and I say to you,
"Do you feel a push or a pull?"

407
00:23:40 --> 00:23:46
And you say,
"Yeah, I feel a push.

408
00:23:43 --> 00:23:49
I feel a push
from the floor up."

409
00:23:47 --> 00:23:53
So I say, "In what direction
do you perceive gravity?"

410
00:23:52 --> 00:23:58
You say, "Well, come on,
don't be boring.

411
00:23:54 --> 00:24:00
Gravity is in this direction."

412
00:23:57 --> 00:24:03
Notice in both cases you tell me

413
00:24:01 --> 00:24:07
that gravity is always
in the opposite direction

414
00:24:04 --> 00:24:10
of either your pull
or your push.

415
00:24:08 --> 00:24:14
Okay, now I'm going to be
a little rough on you.

416
00:24:14 --> 00:24:20
Now I'm going to swing you
around on a string

417
00:24:18 --> 00:24:24
just as if you were an apple

418
00:24:20 --> 00:24:26
and I'm going to do this
with you.

419
00:24:22 --> 00:24:28
And you're at the end
of the apple.

420
00:24:24 --> 00:24:30
You are the apple,
not at the end.

421
00:24:26 --> 00:24:32
You're at the end of the string.

422
00:24:27 --> 00:24:33
You are the apple.

423
00:24:29 --> 00:24:35
So there you are.

424
00:24:32 --> 00:24:38
Here... poor you.

425
00:24:35 --> 00:24:41
(class laughs )

426
00:24:40 --> 00:24:46
And I say, "Do you feel
a push or a pull?"

427
00:24:43 --> 00:24:49
And you say, "Yeah, I do,
I feel a pull."

428
00:24:47 --> 00:24:53
Fine, in what direction?

429
00:24:49 --> 00:24:55
"I feel a pull
in this direction."

430
00:24:52 --> 00:24:58
Okay, so now I say to you

431
00:24:56 --> 00:25:02
"In what direction
do you perceive gravity?"

432
00:24:59 --> 00:25:05
And you say, "Well, in the
opposite direction as pull."

433
00:25:02 --> 00:25:08
So now you perceive gravity
in this direction

434
00:25:07 --> 00:25:13
which is very real for you.

435
00:25:10 --> 00:25:16
Now, in this particular case

436
00:25:13 --> 00:25:19
since the direction changes
all the time--

437
00:25:16 --> 00:25:22
since I swirl you around--

438
00:25:18 --> 00:25:24
you will, of course, get dizzy
like hell, but that's a detail.

439
00:25:21 --> 00:25:27
You will perceive gravity in
this direction when you're here

440
00:25:25 --> 00:25:31
and when you're here

441
00:25:26 --> 00:25:32
you will perceive gravity
in that direction.

442
00:25:30 --> 00:25:36
So you perceive gravity

443
00:25:32 --> 00:25:38
in the direction
which is opposing the pull

444
00:25:35 --> 00:25:41
and the faster I rotate you,
the stronger will be the pull

445
00:25:40 --> 00:25:46
and therefore the stronger
will be your perceived gravity.

446
00:25:46 --> 00:25:52
A carpenter would use
a plumb line

447
00:25:51 --> 00:25:57
and the carpenter would just
hold the plumb line like this.

448
00:25:55 --> 00:26:01
The pull is in this direction
and so the carpenter says

449
00:25:59 --> 00:26:05
"Okay, perceived gravity is
in that direction."

450
00:26:02 --> 00:26:08
The carpenter happens to be
right in this case.

451
00:26:04 --> 00:26:10
Gravityis in this direction,
but it's the same idea.

452
00:26:07 --> 00:26:13
The plumb line is being used to
find the direction of gravity.

453
00:26:12 --> 00:26:18
Think of this
as being a plumb line to find...

454
00:26:16 --> 00:26:22
used to find the direction
of gravity.

455
00:26:22 --> 00:26:28
Now you're in outer space.

456
00:26:26 --> 00:26:32
You're going to play
Captain Kirk

457
00:26:28 --> 00:26:34
and you're in a space station
and there is no gravity.

458
00:26:34 --> 00:26:40
So we're going to make
some gravity for you.

459
00:26:37 --> 00:26:43
We're going to create
some artificial gravity.

460
00:26:40 --> 00:26:46
So let this be
your space station; 

461
00:26:44 --> 00:26:50
it's a big wheel,
a radius of about 100 meters

462
00:26:51 --> 00:26:57
and we'll make it
very fancy for you.

463
00:26:54 --> 00:27:00
We'll make some corridors
around, like here.

464
00:26:59 --> 00:27:05

465
00:27:03 --> 00:27:09
We'll make it
a very interesting space station

466
00:27:06 --> 00:27:12
like so... and like so.

467
00:27:12 --> 00:27:18
And this is rotating around
with angular velocity omega.

468
00:27:19 --> 00:27:25
You're here-- there you are.

469
00:27:22 --> 00:27:28

470
00:27:25 --> 00:27:31
You go around.

471
00:27:27 --> 00:27:33
Therefore, non-negotiable

472
00:27:30 --> 00:27:36
you're going around
with a certain velocity v.

473
00:27:35 --> 00:27:41
This v equals omega r

474
00:27:37 --> 00:27:43
and therefore, you require
centripetal acceleration

475
00:27:41 --> 00:27:47
towards the center--
that is non-negotiable.

476
00:27:45 --> 00:27:51
Where do you get it from?

477
00:27:46 --> 00:27:52
Well, the floor-- this is your
floor-- is pushing on you.

478
00:27:51 --> 00:27:57
Simple as that, just like
the floor is pushing on me now.

479
00:27:54 --> 00:28:00
This floor is pushing.

480
00:27:56 --> 00:28:02
There's nothing wrong with that;
I don't fall over.

481
00:27:59 --> 00:28:05
And so I say to you,

482
00:28:01 --> 00:28:07
"In what direction
do you perceive gravity?"

483
00:28:04 --> 00:28:10
And you say, "This is
the direction of gravity"

484
00:28:08 --> 00:28:14
which is as real for you
as it can be.

485
00:28:11 --> 00:28:17
Someone else is standing here.

486
00:28:18 --> 00:28:24
What do you think that person
will think if I ask that person

487
00:28:21 --> 00:28:27
"What is the direction
of gravity?"

488
00:28:24 --> 00:28:30
Exactly, radially outwards,

489
00:28:27 --> 00:28:33
opposing the push
from the floor.

490
00:28:32 --> 00:28:38
So we could now calculate

491
00:28:35 --> 00:28:41
how fast we have to rotate
this space ship

492
00:28:39 --> 00:28:45
to mimic the gravitational
acceleration on Earth--

493
00:28:43 --> 00:28:49
which is 9.8 meters
per second squared.

494
00:28:45 --> 00:28:51
Let's call that 10,
just to round it off a little.

495
00:28:48 --> 00:28:54
So we want the people
who walk around in this corridor

496
00:28:51 --> 00:28:57
to have an acceleration omega
squared R which is about 10

497
00:28:59 --> 00:29:05
so omega squared is about 0.1

498
00:29:03 --> 00:29:09
so omega is
about 0.3 radians per second.

499
00:29:11 --> 00:29:17
And so the period to go around
is about two pi divided by omega

500
00:29:19 --> 00:29:25
and that is about 20 seconds.

501
00:29:23 --> 00:29:29
And the tangential speed-- that
value for v, which is omega R--

502
00:29:30 --> 00:29:36
would then be 0.3 times 100

503
00:29:33 --> 00:29:39
would be
about 30 meters per second

504
00:29:36 --> 00:29:42
just to give you an idea
for these numbers

505
00:29:38 --> 00:29:44
which are by no means
so ridiculous.

506
00:29:43 --> 00:29:49
What is interesting,
that the perceived gravity--

507
00:29:47 --> 00:29:53
and therefore
the centripetal acceleration--

508
00:29:51 --> 00:29:57
is zero here.

509
00:29:54 --> 00:30:00
There is nothing; 
there is no gravity there.

510
00:29:57 --> 00:30:03
And so that may be a good place

511
00:30:00 --> 00:30:06
for you to have
your sleeping quarters.

512
00:30:03 --> 00:30:09
Now comes
an interesting question.

513
00:30:05 --> 00:30:11
You can walk around here
without any problem.

514
00:30:08 --> 00:30:14

515
00:30:11 --> 00:30:17
Could you walk
into these spokes?

516
00:30:14 --> 00:30:20
So when you were here,
could you then walk

517
00:30:19 --> 00:30:25
towards your sleeping quarters?

518
00:30:21 --> 00:30:27
When you were standing here
and I first ask you

519
00:30:24 --> 00:30:30
"In what direction is gravity?"

520
00:30:26 --> 00:30:32
And you will say, "Well,
gravity is in this direction."

521
00:30:29 --> 00:30:35
Can you now walk
to your sleeping quarters?

522
00:30:32 --> 00:30:38
And what's the answer?

523
00:30:34 --> 00:30:40
You cannot.

524
00:30:35 --> 00:30:41
You cannot walk
up against gravity.

525
00:30:38 --> 00:30:44
It would be like asking you
to walk to the ceiling.

526
00:30:41 --> 00:30:47
How do you do that?

527
00:30:42 --> 00:30:48
An elevator or a staircase,
that's fine

528
00:30:44 --> 00:30:50
because then you get
the push from the stairs

529
00:30:47 --> 00:30:53
when you step on the stairs.

530
00:30:48 --> 00:30:54
So you could have
the staircase here

531
00:30:50 --> 00:30:56
and that's the way
this person could go here.

532
00:30:53 --> 00:30:59
But you cannot simply walk here

533
00:30:55 --> 00:31:01
because gravity is always
in this direction.

534
00:30:59 --> 00:31:05
Now let's suppose you are
at your sleeping quarters

535
00:31:02 --> 00:31:08
and you wake up in the morning
and you decide to go back

536
00:31:06 --> 00:31:12
either in this direction
or this direction

537
00:31:08 --> 00:31:14
or this direction or that
direction-- it doesn't matter.

538
00:31:11 --> 00:31:17
Could you do that, just by...
just going into this corridor

539
00:31:18 --> 00:31:24
and slowly, carefully
starting moving?

540
00:31:21 --> 00:31:27
What would happen?

541
00:31:22 --> 00:31:28
Yeah?

542
00:31:24 --> 00:31:30
STUDENT:
You would fly out.

543
00:31:25 --> 00:31:31
LEWIN:
You would fly out.

544
00:31:27 --> 00:31:33
It would be suicide, because
the moment that you are here

545
00:31:30 --> 00:31:36
already, you have maybe

546
00:31:32 --> 00:31:38
not a very large
gravitational experience

547
00:31:37 --> 00:31:43
but already it's beginning
to grow on you.

548
00:31:39 --> 00:31:45
The farther out you are,
the stronger it will be.

549
00:31:42 --> 00:31:48
By the time you're here, it's
10 meters per second squared.

550
00:31:45 --> 00:31:51
Remember? We had 10 meters
per second squared

551
00:31:48 --> 00:31:54
because we wanted
to mimic the Earth

552
00:31:51 --> 00:31:57
and so you literally crash.

553
00:31:52 --> 00:31:58
It's like falling into a shaft,
jumping into a shaft.

554
00:31:56 --> 00:32:02
It's not quite the same

555
00:31:57 --> 00:32:03
because you start off
with no pull on you.

556
00:32:00 --> 00:32:06
The moment you start going,
however

557
00:32:02 --> 00:32:08
the situation gets out of hand
and indeed you will slam.

558
00:32:06 --> 00:32:12
So you can use
the same elevator.

559
00:32:08 --> 00:32:14
You can use the same staircase.

560
00:32:10 --> 00:32:16
There's nothing wrong with that.

561
00:32:12 --> 00:32:18
Suppose I have a liquid

562
00:32:15 --> 00:32:21
which has very, very fine,
small particles in it--

563
00:32:20 --> 00:32:26
extremely small,
so small and so light

564
00:32:26 --> 00:32:32
that they will not sink
to the bottom.

565
00:32:30 --> 00:32:36
So you will always see
some colored milky-type liquid.

566
00:32:37 --> 00:32:43
And here is that tube
which has these fine particles.

567
00:32:45 --> 00:32:51
And the tube is sitting there

568
00:32:47 --> 00:32:53
and the line of the liquid
is obviously like this.

569
00:32:50 --> 00:32:56
Why? Well, that's obvious.

570
00:32:53 --> 00:32:59
Because gravity is
in this direction.

571
00:32:57 --> 00:33:03
And so the surface of the liquid

572
00:32:59 --> 00:33:05
is always perpendicular
to gravity.

573
00:33:01 --> 00:33:07
You see here
two glasses with water.

574
00:33:04 --> 00:33:10
The surface is
perpendicular to gravity.

575
00:33:06 --> 00:33:12
Now I'm going to rotate this
about this axis--

576
00:33:12 --> 00:33:18
it's going around like this--

577
00:33:14 --> 00:33:20
and I'm going to rotate it
with an angular velocity omega

578
00:33:19 --> 00:33:25
and this is at a distance, R.

579
00:33:21 --> 00:33:27
Therefore, there is now
a centripetal acceleration

580
00:33:27 --> 00:33:33
in this direction,
and so the particles now say

581
00:33:32 --> 00:33:38
"Aha! Gravity is
in this direction."

582
00:33:36 --> 00:33:42
The side of the glass
and the liquid is pushing

583
00:33:40 --> 00:33:46
in this direction to provide
this centripetal acceleration.

584
00:33:44 --> 00:33:50
So if you ask them,
"Where is gravity?"

585
00:33:46 --> 00:33:52
they will say
"Gravity is there."

586
00:33:48 --> 00:33:54
And this gravitational effect
can be so much stronger

587
00:33:52 --> 00:33:58
than this one
that you can forget this one--

588
00:33:54 --> 00:34:00
you will see that in a minute.

589
00:33:56 --> 00:34:02
You can completely forget
this one.

590
00:33:58 --> 00:34:04
And so the liquid will say

591
00:34:00 --> 00:34:06
"I'm going to be
perpendicular to gravity."

592
00:34:03 --> 00:34:09
And so the liquid will go
like this, clunk.

593
00:34:07 --> 00:34:13
While it rotates around

594
00:34:10 --> 00:34:16
the liquid in this tilted tube
will be vertical.

595
00:34:13 --> 00:34:19
But not only that,
the particles that are here

596
00:34:19 --> 00:34:25
experience now way stronger
gravity than they did before

597
00:34:24 --> 00:34:30
so I have made them heavier.

598
00:34:26 --> 00:34:32
They are no longer
light particles.

599
00:34:27 --> 00:34:33
They are heavy particles,
and what do heavy particles do?

600
00:34:31 --> 00:34:37
They have no problems
in making it to the side.

601
00:34:34 --> 00:34:40
The reason
why the light particles

602
00:34:36 --> 00:34:42
couldn't fall in the first place
has to do with the fact

603
00:34:40 --> 00:34:46
that the molecules
of the liquid

604
00:34:42 --> 00:34:48
due to their temperature,
have a chaotic motion.

605
00:34:46 --> 00:34:52
We call that
the "thermal agitation."

606
00:34:47 --> 00:34:53
And these molecules
would interact

607
00:34:49 --> 00:34:55
with these very small
and light particles

608
00:34:52 --> 00:34:58
and so the light particles would
never make it to the bottom.

609
00:34:55 --> 00:35:01
The thermal agitation now
of the liquid is the same--

610
00:34:58 --> 00:35:04
the temperature doesn't change--

611
00:35:00 --> 00:35:06
but the particles have become
way, way heavier

612
00:35:03 --> 00:35:09
and so the particles now go
in the direction of gravity

613
00:35:07 --> 00:35:13
which is here.

614
00:35:09 --> 00:35:15
And what you will see,
if these particles are white

615
00:35:12 --> 00:35:18
you will see
white precipitation there

616
00:35:15 --> 00:35:21
and the liquid
will become clear.

617
00:35:19 --> 00:35:25
And that is something

618
00:35:21 --> 00:35:27
that I would like
to demonstrate to you.

619
00:35:22 --> 00:35:28
But before I do that, I want
to give you some numbers.

620
00:35:26 --> 00:35:32
Here we have

621
00:35:27 --> 00:35:33
a household, simple,
nothing-special centrifuge

622
00:35:31 --> 00:35:37
that is used in any laboratory.

623
00:35:34 --> 00:35:40
The centrifuge that we have
has an rpm which is 3600 rpm.

624
00:35:45 --> 00:35:51
So 3600 rpm translates
into a frequency of 60 Hz.

625
00:35:52 --> 00:35:58
So it goes around once
in one-sixtieth of a second.

626
00:35:57 --> 00:36:03
Omega is two pi times f

627
00:36:02 --> 00:36:08
is therefore
roughly 360 radians per second.

628
00:36:08 --> 00:36:14
360 radians per second.

629
00:36:11 --> 00:36:17

630
00:36:13 --> 00:36:19
If we assume
that the radius is...

631
00:36:15 --> 00:36:21
maybe it's 10, 15 centimeters.

632
00:36:17 --> 00:36:23
Whatever, let's take a radius
of 15 centimeters.

633
00:36:21 --> 00:36:27
And we can calculate now

634
00:36:23 --> 00:36:29
what the centripetal
acceleration is.

635
00:36:26 --> 00:36:32
And the centripetal acceleration
a of c which is omega squared R

636
00:36:32 --> 00:36:38
is then roughly about 20
meters per second squared.

637
00:36:38 --> 00:36:44
20,000 meters
per second squared.

638
00:36:44 --> 00:36:50
And that is 2,000 times
the gravitational acceleration.

639
00:36:51 --> 00:36:57
It means that these particles
experience gravity

640
00:36:55 --> 00:37:01
which is 2,000 times stronger
than if I don't rotate them.

641
00:37:01 --> 00:37:07
And so they will go
to the side here.

642
00:37:05 --> 00:37:11
But the glass itself is
also 2,000 times heavier

643
00:37:09 --> 00:37:15
and therefore the glass
can easily break

644
00:37:11 --> 00:37:17
so when you design
a centrifuge like that

645
00:37:14 --> 00:37:20
you have to really think
that through very carefully--

646
00:37:17 --> 00:37:23
that the pieces that are
in there don't fly apart.

647
00:37:21 --> 00:37:27

648
00:37:24 --> 00:37:30
I have here water in which I
have dissolved some table salt--

649
00:37:29 --> 00:37:35
the same table salt
that you use in the kitchen

650
00:37:31 --> 00:37:37
when you prepare your food,
table salt in here.

651
00:37:37 --> 00:37:43
Here I have water in which I
dissolved some silver nitrate.

652
00:37:44 --> 00:37:50
It's nasty stuff, I warn you for
it, you have to be very careful

653
00:37:49 --> 00:37:55
because if you get
the stuff on your hands

654
00:37:52 --> 00:37:58
it burns through your hands
very quickly

655
00:37:54 --> 00:38:00
without your realizing it

656
00:37:55 --> 00:38:01
and you end up
with a very black spot.

657
00:37:58 --> 00:38:04
It really eats away,
burns out your skin.

658
00:38:01 --> 00:38:07
People put it on warts

659
00:38:02 --> 00:38:08
and then the warts,
they think, fall off.

660
00:38:04 --> 00:38:10
They probably do after a while

661
00:38:06 --> 00:38:12
but your finger
may also fall off.

662
00:38:08 --> 00:38:14
So I have here silver nitrate

663
00:38:10 --> 00:38:16
and there I have sodium chloride
and I mix the two.

664
00:38:20 --> 00:38:26
So I get table salt-- sodium
chloride-- plus silver nitrate

665
00:38:26 --> 00:38:32
gives sodium nitrate
plus silver chloride

666
00:38:34 --> 00:38:40
and this, very small white
particles, and you will see

667
00:38:39 --> 00:38:45
that the liquid turns
milky instantaneously.

668
00:38:43 --> 00:38:49
It almost becomes like,
like yogurt, as you will see.

669
00:38:47 --> 00:38:53
And so I want
to show that to you.

670
00:38:51 --> 00:38:57
I have here these two glasses.

671
00:38:53 --> 00:38:59
This is the table salt and
this is the silver nitrate.

672
00:38:58 --> 00:39:04
I'm going to mix them.

673
00:39:01 --> 00:39:07

674
00:39:04 --> 00:39:10
I hope you can see this.

675
00:39:06 --> 00:39:12
Here are the two glasses,
and when I mix them...

676
00:39:10 --> 00:39:16
(whistles )

677
00:39:12 --> 00:39:18
instantaneously you get milk.

678
00:39:15 --> 00:39:21
(class laughs )

679
00:39:18 --> 00:39:24
Yeah.

680
00:39:20 --> 00:39:26
I'm not asking you to taste it
but look at it, right?

681
00:39:25 --> 00:39:31
Just milk.

682
00:39:26 --> 00:39:32
You can leave this for hours
and hours and hours

683
00:39:29 --> 00:39:35
and it will just stay like that.

684
00:39:31 --> 00:39:37
Very small particles
of silver chloride are in here.

685
00:39:36 --> 00:39:42
So now we are going to put this
in the centrifuge.

686
00:39:41 --> 00:39:47
I have to put it
in a very small tube.

687
00:39:45 --> 00:39:51
I'll show you this small tube.

688
00:39:48 --> 00:39:54
There's no way that I can pour
that in without making a mess.

689
00:39:51 --> 00:39:57
Here's this small tube

690
00:39:53 --> 00:39:59
and so what I will do is I will
first put it in a small beaker

691
00:40:00 --> 00:40:06
and then from this small beaker

692
00:40:04 --> 00:40:10
I will transfer it, some of it,
to this tube.

693
00:40:09 --> 00:40:15
When you put this
in a centrifuge

694
00:40:10 --> 00:40:16
your force on this glass
is so high

695
00:40:15 --> 00:40:21
that you must always make sure

696
00:40:16 --> 00:40:22
that you balance it
with another tube

697
00:40:18 --> 00:40:24
that you fill with water
on the other side.

698
00:40:20 --> 00:40:26
Otherwise the thing begins
to shake like crazy.

699
00:40:23 --> 00:40:29
It's like your centrifuge
when you dry your towels.

700
00:40:28 --> 00:40:34
If they are
not equally distributed

701
00:40:31 --> 00:40:37
it begins to make very obscene
sounds and starts to move.

702
00:40:34 --> 00:40:40
(class laughs )

703
00:40:36 --> 00:40:42
And the same thing
will happen here.

704
00:40:37 --> 00:40:43
So you just have
to take my word for it

705
00:40:39 --> 00:40:45
that we have put
on the other side

706
00:40:41 --> 00:40:47
just some water
to balance it out.

707
00:40:44 --> 00:40:50
So here is now the yogurt

708
00:40:47 --> 00:40:53
and on the other side
is plain water

709
00:40:49 --> 00:40:55
and we will just let it sit
there for a while

710
00:40:52 --> 00:40:58
and we will return
to that shortly.

711
00:40:55 --> 00:41:01

712
00:40:58 --> 00:41:04
I mentioned already your
centrifuge for your clothes.

713
00:41:01 --> 00:41:07
That is the way
that you can dry your clothes.

714
00:41:04 --> 00:41:10
That is the same way that my
grandmother dried the lettuce.

715
00:41:07 --> 00:41:13
The water will go
to the circumference.

716
00:41:11 --> 00:41:17
A household centrifuge
for your clothes

717
00:41:14 --> 00:41:20
would easily rotate
1,200 revolutions per minute

718
00:41:18 --> 00:41:24
have a radius
maybe of 15 centimeters

719
00:41:20 --> 00:41:26
which would give you
a centripetal acceleration

720
00:41:23 --> 00:41:29
of 200 times g, 200 times
the gravitational acceleration.

721
00:41:29 --> 00:41:35
So your clothes
experience gravity

722
00:41:32 --> 00:41:38
which is 200 times stronger

723
00:41:34 --> 00:41:40
and therefore your clothes
are 200 times heavier

724
00:41:37 --> 00:41:43
and therefore your clothes
can tear apart

725
00:41:40 --> 00:41:46
and we have all seen that.

726
00:41:42 --> 00:41:48
We have all put in stuff
in a centrifuge

727
00:41:44 --> 00:41:50
and when you take it out you're
disappointed because it's torn.

728
00:41:47 --> 00:41:53
That's because
of the tremendous gravity

729
00:41:50 --> 00:41:56
that you have exposed them to.

730
00:41:53 --> 00:41:59
Many times when I take my shirts
out, half my buttons are gone.

731
00:41:57 --> 00:42:03
That's because the force--
I shouldn't use that word...

732
00:42:00 --> 00:42:06
the gravitational effect
on the buttons is enormous

733
00:42:04 --> 00:42:10
and they just get ripped off.

734
00:42:08 --> 00:42:14
Now I want to revisit
the situation

735
00:42:11 --> 00:42:17
that you are
on the end of my string

736
00:42:15 --> 00:42:21
and I'm going to swirl
you around.

737
00:42:18 --> 00:42:24
Earlier, I swirled you
around like this

738
00:42:22 --> 00:42:28
and you didn't like it

739
00:42:26 --> 00:42:32
and I don't blame you
because you got dizzy.

740
00:42:28 --> 00:42:34
Now I'm going to rotate
you like this.

741
00:42:31 --> 00:42:37
You may like that better.

742
00:42:32 --> 00:42:38
Maybe not.

743
00:42:34 --> 00:42:40
(chuckles )

744
00:42:36 --> 00:42:42
And so, whether
you like it or not

745
00:42:39 --> 00:42:45
I'm going to twirl you around
and here you are.

746
00:42:48 --> 00:42:54
This is the circle.

747
00:42:50 --> 00:42:56
There's a string-- you're here.

748
00:42:53 --> 00:42:59
Here's the string
and there you are.

749
00:42:56 --> 00:43:02
You have a certain velocity.

750
00:42:59 --> 00:43:05
Your velocity is
in this direction

751
00:43:05 --> 00:43:11
and there is a certain distance
to the center, R.

752
00:43:11 --> 00:43:17
And so you need a certain
centripetal acceleration

753
00:43:16 --> 00:43:22
to go around in that curve.

754
00:43:20 --> 00:43:26
So you need
a centripetal acceleration

755
00:43:22 --> 00:43:28
a of c-- which is...

756
00:43:25 --> 00:43:31
you can take the v squared
divided by r, if you like that.

757
00:43:28 --> 00:43:34
This is the magnitude of that v.

758
00:43:31 --> 00:43:37
Now follow me very closely.

759
00:43:36 --> 00:43:42
Just imagine that this number
happens to be exactly 9.8.

760
00:43:44 --> 00:43:50
I can always do that.

761
00:43:46 --> 00:43:52

762
00:43:50 --> 00:43:56
Where is this person going to
get the push or the pull from

763
00:43:56 --> 00:44:02
for this centripetal
acceleration?

764
00:44:00 --> 00:44:06
Does the string have
to pull on it?

765
00:44:02 --> 00:44:08
No, because there's always
gravity and gravity gives you

766
00:44:05 --> 00:44:11
an acceleration of 9.8 meters
per second squared.

767
00:44:09 --> 00:44:15
So the string says, "Tough luck,
I don't have to do anything.

768
00:44:15 --> 00:44:21
"Gravity provides me with the
9.8 meters per second squared

769
00:44:22 --> 00:44:28
that I required."

770
00:44:25 --> 00:44:31
Now I'm going to swing you
faster, so the v will go up

771
00:44:31 --> 00:44:37
and so the centripetal
acceleration will go up.

772
00:44:34 --> 00:44:40
The string will say

773
00:44:37 --> 00:44:43
"Aha! I'm going to pull
now on this person

774
00:44:42 --> 00:44:48
"because the gravitational
acceleration alone

775
00:44:44 --> 00:44:50
is not enough--
I need some extra pull."

776
00:44:47 --> 00:44:53
So the string is going
to tighten and pull on you.

777
00:44:50 --> 00:44:56
And I say, "Hello, there,
in what direction is gravity?"

778
00:44:54 --> 00:45:00
And you say, "Gravity is
in this direction."

779
00:44:58 --> 00:45:04
Why? Because you feel
the string is pulling on you

780
00:45:01 --> 00:45:07
in this direction,
so you experience gravity there.

781
00:45:06 --> 00:45:12
Now comes the question,
how real is this?

782
00:45:10 --> 00:45:16
This is very, very real.

783
00:45:15 --> 00:45:21
It is so real

784
00:45:17 --> 00:45:23
that if I took a bucket
of water instead of you...

785
00:45:24 --> 00:45:30
and here is the bucket of water.

786
00:45:31 --> 00:45:37
I attached to the bucket a rope.

787
00:45:33 --> 00:45:39
I swing it around,
and I swing it around

788
00:45:38 --> 00:45:44
such that
the centripetal acceleration

789
00:45:41 --> 00:45:47
is substantially larger than 9.8

790
00:45:44 --> 00:45:50
so the string is definitely
going to pull

791
00:45:51 --> 00:45:57
so if you were the water, and I
asked you, "Where is gravity?"

792
00:45:55 --> 00:46:01
you would say the gravitational
direction is in this direction

793
00:45:57 --> 00:46:03
and so the water will say,

794
00:45:59 --> 00:46:05
"Okay, fine,
then this will be my surface

795
00:46:02 --> 00:46:08
and I want to go
in this direction."

796
00:46:05 --> 00:46:11
But the water can't go
in that direction

797
00:46:07 --> 00:46:13
so it will just stay there.

798
00:46:09 --> 00:46:15
So I could swing this thing
around if I do it fast enough--

799
00:46:14 --> 00:46:20
so fast that the acceleration
at this point here

800
00:46:19 --> 00:46:25
must be larger than 9.8--

801
00:46:21 --> 00:46:27
the water will stay up
while the bucket is upside down.

802
00:46:27 --> 00:46:33
How fast should I rotate it?

803
00:46:30 --> 00:46:36
Well, let's put
in some simple numbers.

804
00:46:33 --> 00:46:39
I have here this bucket

805
00:46:36 --> 00:46:42
and let's say that this is
about one meter.

806
00:46:39 --> 00:46:45
Let's round some numbers off.

807
00:46:41 --> 00:46:47
So R is about one meter.

808
00:46:46 --> 00:46:52
And I want v squared over R

809
00:46:49 --> 00:46:55
I want that to be larger than
9.8-- let's just call it 10.

810
00:46:56 --> 00:47:02
So that means v
has to be larger

811
00:46:59 --> 00:47:05
than about 3.2 meters
per second.

812
00:47:03 --> 00:47:09
The time to go around

813
00:47:05 --> 00:47:11
is two pi R divided
by this velocity

814
00:47:10 --> 00:47:16
so this time to go around, then,
has to be six...

815
00:47:14 --> 00:47:20
has to be less than two seconds.

816
00:47:17 --> 00:47:23
So if I swing this around
in less than two seconds

817
00:47:19 --> 00:47:25
I will be okay.

818
00:47:20 --> 00:47:26
Now, I realize that the speed
when I move this thing around

819
00:47:25 --> 00:47:31
is not constant everywhere.

820
00:47:27 --> 00:47:33
That's very difficult
to do that, because of gravity.

821
00:47:30 --> 00:47:36
But it's close enough
to get an idea.

822
00:47:33 --> 00:47:39
So if I rotate this faster
than in two seconds

823
00:47:38 --> 00:47:44
when the bucket is upside-down

824
00:47:40 --> 00:47:46
if physics works, the water
should not fall out.

825
00:47:46 --> 00:47:52
So let us fill this with water.

826
00:47:49 --> 00:47:55

827
00:47:58 --> 00:48:04
There we go.

828
00:47:59 --> 00:48:05

829
00:48:08 --> 00:48:14
I'm always nervous about this.

830
00:48:10 --> 00:48:16
Um, let's first look
at the centrifuge.

831
00:48:12 --> 00:48:18
We have to see whether
the centrifuge has done its job.

832
00:48:18 --> 00:48:24

833
00:48:23 --> 00:48:29
So let's look
at what this tube...

834
00:48:26 --> 00:48:32
I think it was tube number four.

835
00:48:29 --> 00:48:35
Oh, yeah!
Very clear is now the liquid

836
00:48:32 --> 00:48:38
and you see the white stuff
here on the side.

837
00:48:35 --> 00:48:41
It's not too easy for you
to see, really.

838
00:48:38 --> 00:48:44
I put my hand under here.
 

839
00:48:39 --> 00:48:45
Maybe some of you can see
some white stuff

840
00:48:42 --> 00:48:48
but it's no longer milk--
really a clear liquid.

841
00:48:46 --> 00:48:52
Here you see
some white stuff here

842
00:48:48 --> 00:48:54
but it's also on the side.

843
00:48:49 --> 00:48:55
You can actually see it here.

844
00:48:54 --> 00:49:00
You see the white stuff

845
00:48:56 --> 00:49:02
because this was
the direction of gravity

846
00:48:58 --> 00:49:04
so it ended up here
and there's some here.

847
00:49:00 --> 00:49:06
It is completely clear.

848
00:49:02 --> 00:49:08
You see the white stuff?

849
00:49:05 --> 00:49:11
So that's the way that you can
separate the silver chloride.

850
00:49:13 --> 00:49:19
So now we come to this
daredevil, daredevil experiment.

851
00:49:20 --> 00:49:26
And we're going to see

852
00:49:23 --> 00:49:29
whether we can fool the water
and make the water think

853
00:49:27 --> 00:49:33
that gravity is not in this
direction but in this direction.

854
00:49:31 --> 00:49:37
Now, you're doing
the right thing, there.

855
00:49:32 --> 00:49:38
(class laughs )

856
00:49:34 --> 00:49:40
I don't blame you at all.

857
00:49:36 --> 00:49:42
(Lewin chuckling )

858
00:49:38 --> 00:49:44
Okay...

859
00:49:41 --> 00:49:47
There we go!

860
00:49:44 --> 00:49:50
You see the water
is completely fooled

861
00:49:46 --> 00:49:52
and notice that I go around

862
00:49:48 --> 00:49:54
substantially faster
than in two seconds.

863
00:49:51 --> 00:49:57
And the water,
when it's up there

864
00:49:52 --> 00:49:58
just thinks that gravity is
towards the ceiling.

865
00:49:56 --> 00:50:02
Physics works.

866
00:49:57 --> 00:50:03
Now, who is going to do
this for me, too?

867
00:49:59 --> 00:50:05
(class laughs )

868
00:50:00 --> 00:50:06
Please, someone should try this.

869
00:50:03 --> 00:50:09
You think you can do it?

870
00:50:06 --> 00:50:12
Come on, try it.

871
00:50:08 --> 00:50:14
In the worst case,
it will be a disaster.

872
00:50:11 --> 00:50:17
(class laughs )

873
00:50:14 --> 00:50:20
Okay, get some feel for it,
but before you do it

874
00:50:16 --> 00:50:22
make sure
that I'm out of the way.

875
00:50:19 --> 00:50:25
But first swing it a little and
don't hold it too close to you

876
00:50:23 --> 00:50:29
because I don't want you
to get hurt.

877
00:50:25 --> 00:50:31
Larger swing, larger, larger.

878
00:50:28 --> 00:50:34
Now you get some feel for it.

879
00:50:29 --> 00:50:35
Go for it, now!

880
00:50:32 --> 00:50:38
Yeah, faster!

881
00:50:33 --> 00:50:39
(class laughs )

882
00:50:37 --> 00:50:43
That was very good.

883
00:50:38 --> 00:50:44
(class laughs and applauds )

884
00:50:40 --> 00:50:46
See you Friday.

885
00:50:41 --> 00:50:47
(applause )

886
00:50:42 --> 00:50:48

887
00:50:47 --> 00:50:53.000