Lec 05: Uniform Circular Motion | 8.01 Classical Mechanics, Fall 1999 (Walter Lewin)

Lec 05: Uniform Circular Motion | 8.01 Classical Mechanics, Fall 1999 (Walter Lewin)


Today we will discuss what we call
“uniform circular motion.” What is uniform circular motion? An object goes around
in a circle, has radius r and the object is here. This is the velocity. It’s a vector, perpendicular. And later in time
when the object is here the velocity has changed,
but the speed has not changed. We introduce T,
what we call the period– of course it’s in seconds– which is the time
to go around once. We introduce the frequency, f,
which we call the frequency which is the number
of rotations per second. And so the units are
either seconds minus one or, as most physicists
will call it, “hertz” and so frequency is
one divided by T. We also introduce
angular velocity, omega which we call angular velocity. Angular velocity means not
how many meters per second but how many radians
per second. So since there are two pi
radians in one circumference– in one full circle– and it takes T seconds
to go around once it is immediately obvious that omega equals two pi
divided by T. This is something that
I would like you to remember. Omega equals two pi
divided by T– two pi radians
in capital T seconds. The speed, v, is, of course,
the circumference two pi r divided by the time
to go around once but since two pi
divided by T is omega you can also write
for this “omega r.” And this is also something
that I want you to remember. These two things
you really want to remember. The speed is not changing, but
the velocity vector is changing. Therefore there must be
an acceleration. That is non-negotiable. You can derive
what that acceleration must be in terms of magnitude
and in terms of direction. It’s about a five,
six minutes derivation. You’ll find it in your book. I have decided to give
you the results so that you read up on the book so that we can more talk
about the physics rather than on the derivation. This acceleration
that is necessary to make the change
in the velocity vector is always pointing towards
the center of the circle. We call it
“centripetal acceleration.” Centripetal, pointing
towards the center. And here, also pointing
towards the center. It’s a vector. And the magnitude of
the centripetal acceleration equals v squared divided by r,
which is this v and therefore it’s
also omega squared r. And so now we have
three equations and those are the only three you
really would like to remember. We can have a simple example. Let’s have a vacuum cleaner,
which has a rotor inside which scoops the air out or in,
whichever way you look at it. And let’s assume
that the vacuum cleaner these scoops have a radius r
of about ten centimeters and that it goes around 600
revolutions per minute, 600 rpm. 600 rpm would translate
into a frequency, f, of 10 Hz so it would translate
into a period going around in one-tenth
of a second. So omega, angular velocity,
which is two pi divided by T is then approximately
63 radians per second and the speed, v, equals omega r is then roughly 6.3 meters
per second. The centripetal acceleration–
and that’s really my goal– the centripetal acceleration
would be omega squared r or if you prefer,
you can take v squared over r. You will get the same answer,
of course, and you will find that that is about 400 meters
per second squared. And that is huge. That is 40 times
the acceleration due to gravity. It’s a phenomenal acceleration,
the simple vacuum cleaner. Notice that the acceleration,
the centripetal acceleration is linear in r. Don’t think that it is
inversely proportional with r. That’s a mistake, because v
itself is a function of r. If you were sitting here then your velocity
would be lower. Since omega is the same
for the entire motion you really have to look
at this equation and you see that
the centripetal acceleration is proportional with r. Therefore, if you were… if this were a disc
which was rotating and you were at
the center of the disc the centripetal acceleration
would be zero. And as you were to walk out,
further out, it would increase. Now, the acceleration
must be caused by something. There is no such thing
as a free lunch. There is something
that must be responsible for the change in this velocity and that something
I will call either a pull or I will call it a push. In our next lecture, when
we deal with Newton’s laws we will introduce
the word “force.” Today we will only deal with
the words “pull” and “push.” So there must be a pull
or a push. Imagine that this is
a turntable and you are sitting here
on the turntable on a chair. It’s going around
with angular velocity omega and your distance to the center,
let’s say, is little r. You’re sitting on this chair
and you must experience– that is non-negotiable–
centripetal acceleration A of c, which is omega squared
times r. Where do you get it from? Well, if your seat is bolted
to the turntable then you will feel a push
in your back so you’re sitting on this thing,
you’re going around and you will feel that the seat
is pushing you in your back and so you feel a push,
and that gives the push out. Yeah, I can give this
a red color for now. So you feel a push in your back. That push, apparently, is
necessary for the acceleration. Alternatively, suppose you had
in front of you a stick. You’re not sitting on a chair. You don’t get a push
from your back. But you hold onto the stick and now you can go around
by holding onto the stick. Now the stick is pulling on you
in this same direction. So now you would say, aha,
someone is pulling on you. Whether it is the pull
or whether it is the push one of… either one of the two is necessary for you
to go around in that circle on that turntable
with that constant speed. Now, the classic question comes
up, which we often ask to people who have
no scientific background. If you were to go around
like this and something is
either pushing on you or is pulling on you
to make this possible suppose you took that push
out, all of a sudden. The pull is gone. (makes whooshing sound ) What is now the motion
of the person who is sitting on the turntable? And many non-scientists say,
“Well, it will do like this.” That’s sort of
what your intuition says. You go around in a circle,
and all of a sudden you no longer have
the pull or the push and you go around in a spiral and obviously,
that is not the case. What will happen is, if you
have, at this moment in time a velocity in this direction and you take the pull
or the push out you will start flying off
in that direction and depending upon whether
there is gravity or no gravity there may be a change, but if this were…
if there were no gravity you would just continue
to go along that line and you would not make
this crazy spiral motion. I have here a disc,
which we will rotate and at the end…
the edge of the disc here we have a little ball. And the ball is attached
to that disc with string. So now this is vertical, and
so this is going to go around with angular velocity omega. And we have a string here and the string is attached
to this ball and the whole thing is
going around and so at one moment in time
this has a velocity, like so. And therefore there must be non-negotiable
centripetal acceleration which in magnitude is
omega squared r or, if you want to,
v squared divided by r. Now I cut it and that’s like taking away
the push and the pull. The string that you have here is providing the pull
on this ball. This ball is feeling a pull
from the string and that provides it with
the centripetal acceleration. Cut the string
and the pull is gone and the object will take off. And if there were gravity here,
as there is in 26.100 it would become a parabola
and it would end up here. If, however, I cut the ball
exactly when it is here– not the ball,
but I cut the string– then, of course,
it would fly straight up gravity would act on it,
it would come to a halt and it would come back. So it really would then go
along a straight line. But you would clearly see, then that it’s not going to do
what many people think– that it would start
to swirl around. It would just go…
(makes whooshing sound ) and comes back. Let’s look at that. We have that here. So here is that ball. The string is behind here;
you cannot see the string. I will rotate it, wait for it
to pick up a little speed and the knife, that you can’t
see either, is behind here and when I push the knife in,
I do it exactly here. It cuts the string
and it goes up. You ready for this? You sure you’re ready? Three, two, one, zero. Wow! That was very high. So you see,
it’s nothing like this. It simply continued on in
the direction that it was going. It wasn’t going into a parabola because I was shooting it
straight up. The string forms the connection between the rotating disc
and the ball and therefore,
the pull is responsible for the centripetal
acceleration. Let’s now think about planets. Planets go around the sun. There’s no string, so who
is pushing? Who is pulling? Well, it’s clear
that it must be gravity. It must be the sun that is
pulling on the planets. Now, I realize that
the orbits of planets are not nicely circular so it’s not really
a uniform circular motion. We will deal with orbits in
great detail in a few weeks– circular orbits
and elliptical orbits. Let us just assume
for simplicity now that the orbits are
roughly circular just to get a little bit
of feeling for it. And you can look up
now in your book– which I did for you– even in your preliminary version
you can look up what the mean distance
of the planets is to the sun and you can look up
what the period is the time to go around the sun. The time to go around the sun
is not the same for all planets. The planets are not attached
to a turntable. Anywhere,
any person on a turntable would go around
in the same amount of time. We know that
that’s not true for planets. It takes the Earth a year
to go around the sun. It takes Jupiter
12 years to go around so don’t make the mistake
to think that omega is the same
for all planets. That’s not true. So I look up the distance– the mean distance
to these various planets– and you see that here
in millions of kilometers. Notice that Mercury is about
100 times closer than Pluto. By the way, this is on the Web,
so don’t copy this. You will find this
on the 801 home page. Then I looked up how many years it takes
to go around the sun– 12 years for Jupiter,
one year for the Earth– and I looked up
all the other values. Then, since I know the periods,
I can calculate omega. Omega is two pi divided by T,
so I know omega. And then I take omega squared times the mean distance
to the sun and this is, of course,
the centripetal acceleration. So the planets experience
this centripetal acceleration in some crazy units, but
who cares about the units here? And notice that Mercury, which
is 100 times closer than Pluto has a centripetal acceleration which is 10,000 times
larger than Pluto. 100 times closer has a 10,000 times larger
centripetal acceleration. So what I did was I plotted this data,
the centripetal acceleration versus the mean distance
to the sun and I did that on log paper. And what immediately strikes…
is very striking is that all these points– I’ve
done them for all the planets– they fall on a straight line. And so what is the slope
of that line? Well, I tried various slopes and I found that the slope is
very, very close to minus two. Here is the slope of minus two,
and I can overlay this and notice that the fit is
absolutely stunning. Therefore, you cannot escape
the conclusion that the
centripetal acceleration which is the result of gravity,
falls off as one over R squared. We refer to this,
often, in physics as the “one over R square” law. And therefore, the effect
of gravity itself must go down with R squared. So if you are
100 times further away like Pluto compared to Mercury then the gravitational…
the centripetal acceleration which is due to gravity
is 10,000 times smaller. And we will learn a lot
about gravity in the future. We will just leave it for now. If you took the sun away,
it would be like cutting the string
that provides the pull and in that case
what you would see is that the planets would just
take off along a straight line. They would continue to go. They wouldn’t have anything
to pull on them anymore. Now let’s look at an object
that we’re going to rotate. I have a glass tube
that I want to rotate and in the glass tube,
I have a marble. The glass tube is very smooth. I have here the glass tube. Here’s a marble. I’m going to rotate it
in this direction say, with some
angular velocity omega about an axis perpendicular
to the blackboard. So the marble here has
a velocity like so, at this moment in time but it’s a very smooth
glass tube and the marble is very smooth. The glass cannot push
on the marble nor can the glass pull
on the marble. Now, the marble gets desperate because the marble needs
a centripetal acceleration in this direction
in order to go around like this. But there is nothing to provide
that centripetal acceleration. So the marble is doing
exactly the same that the planets would do
if you take the sun away. The marble continues to go in
the direction that it was going. So by the time that the tube
is here, the marble is here and by the time
that the tube is here the marble is there. So the marble finds its way to
the edge and that’s, of course the basic idea
behind a centrifuge. My grandmother had always… She was a great lady and she had such fantastic
ideas, I remember. And when she made lettuce we had no good way
of drying the lettuce and I would take the lettuce
and go like this… paper towel. She had a method of her own. She took a colander
and, of course, first of all we would wash the lettuce,
that goes without saying. I would wash it once. My grandmother would wash it
three times but that’s what you have
grandmothers for. So there comes the lettuce. We were also very fond of
spinach, so add some spinach. We would wash it…
there goes the spinach. Then she would take
something to cover it up– maybe some Saran wrap,
or something else– put it over it and put a rubber
band around it to hold it. And now what she’s going to do,
she’s going to swing it around. And now the water is
like these marbles. The water will work its way
to the edge but there are holes,
so the water will come out. Isn’t she clever? Okay, I’ll give you
a demonstration. Be careful or you may get some water
on your lecture notes. But I want to show you the basic idea behind it
is very interesting. She would go out… she would do
this outside, by the way. But I have no choice,
so I will do it here. So there we go. (class laughs ) You see?
This is the way you dry… Oh, I lost
my magnetic strawberry– that’s a detail in the process. So you end up with… you end up with dry
and clean and nice lettuce. This is 801 at work and this is clearly an early
version of a centrifuge. Now, my grandmother’s method,
very tragically has been replaced lately with something that you can buy
at Crate and Barrel. We have it here. Um, it is very boring. It’s very decadent. Put the salad in here and all you do is
you rotate and it dries. It’s a centrifuge. This is actually
a high-tech version of the much more sophisticated
invention of my grandmother. And it’s nowhere
nearly as exciting. The days of romance are
really over but that’s the way it goes. I’m now going to make
a connection between rotation on the one hand and centripetal acceleration
on the other. I’m going to make a connection between centripetal acceleration
and perceived gravity. The way that
you perceive gravity. I’m going to put you
in various positions and then ask you what is
the direction of gravity. I’m going to create
artificial gravity for you. And let’s first do it
as follows. I first hang you on a string. There you are, like this. And I ask you, do you feel
a push or a pull? And you say,
“Yeah, I feel a pull.” And you feel a pull
in this direction. So now I ask you “Ah, in what direction
do you perceive gravity?” and you think I’m crazy. You’re right in that case,
but nevertheless you say “Gravity is
in this direction.” The other direction is the pull. Okay, so far, so good. So now I’m going to put you
just standing on the floor and I say to you,
“Do you feel a push or a pull?” And you say,
“Yeah, I feel a push. I feel a push
from the floor up.” So I say, “In what direction
do you perceive gravity?” You say, “Well, come on,
don’t be boring. Gravity is in this direction.” Notice in both cases you tell me that gravity is always
in the opposite direction of either your pull
or your push. Okay, now I’m going to be
a little rough on you. Now I’m going to swing you
around on a string just as if you were an apple and I’m going to do this
with you. And you’re at the end
of the apple. You are the apple,
not at the end. You’re at the end of the string. You are the apple. So there you are. Here… poor you. (class laughs ) And I say, “Do you feel
a push or a pull?” And you say, “Yeah, I do,
I feel a pull.” Fine, in what direction? “I feel a pull
in this direction.” Okay, so now I say to you “In what direction
do you perceive gravity?” And you say, “Well, in the
opposite direction as pull.” So now you perceive gravity
in this direction which is very real for you. Now, in this particular case since the direction changes
all the time– since I swirl you around– you will, of course, get dizzy
like hell, but that’s a detail. You will perceive gravity in
this direction when you’re here and when you’re here you will perceive gravity
in that direction. So you perceive gravity in the direction
which is opposing the pull and the faster I rotate you,
the stronger will be the pull and therefore the stronger
will be your perceived gravity. A carpenter would use
a plumb line and the carpenter would just
hold the plumb line like this. The pull is in this direction
and so the carpenter says “Okay, perceived gravity is
in that direction.” The carpenter happens to be
right in this case. Gravityis in this direction,
but it’s the same idea. The plumb line is being used to
find the direction of gravity. Think of this
as being a plumb line to find… used to find the direction
of gravity. Now you’re in outer space. You’re going to play
Captain Kirk and you’re in a space station
and there is no gravity. So we’re going to make
some gravity for you. We’re going to create
some artificial gravity. So let this be
your space station; it’s a big wheel,
a radius of about 100 meters and we’ll make it
very fancy for you. We’ll make some corridors
around, like here. We’ll make it
a very interesting space station like so… and like so. And this is rotating around
with angular velocity omega. You’re here– there you are. You go around. Therefore, non-negotiable you’re going around
with a certain velocity v. This v equals omega r and therefore, you require
centripetal acceleration towards the center–
that is non-negotiable. Where do you get it from? Well, the floor– this is your
floor– is pushing on you. Simple as that, just like
the floor is pushing on me now. This floor is pushing. There’s nothing wrong with that;
I don’t fall over. And so I say to you, “In what direction
do you perceive gravity?” And you say, “This is
the direction of gravity” which is as real for you
as it can be. Someone else is standing here. What do you think that person
will think if I ask that person “What is the direction
of gravity?” Exactly, radially outwards, opposing the push
from the floor. So we could now calculate how fast we have to rotate
this space ship to mimic the gravitational
acceleration on Earth– which is 9.8 meters
per second squared. Let’s call that 10,
just to round it off a little. So we want the people
who walk around in this corridor to have an acceleration omega
squared R which is about 10 so omega squared is about 0.1 so omega is
about 0.3 radians per second. And so the period to go around
is about two pi divided by omega and that is about 20 seconds. And the tangential speed– that
value for v, which is omega R– would then be 0.3 times 100 would be
about 30 meters per second just to give you an idea
for these numbers which are by no means
so ridiculous. What is interesting,
that the perceived gravity– and therefore
the centripetal acceleration– is zero here. There is nothing;
there is no gravity there. And so that may be a good place for you to have
your sleeping quarters. Now comes
an interesting question. You can walk around here
without any problem. Could you walk
into these spokes? So when you were here,
could you then walk towards your sleeping quarters? When you were standing here
and I first ask you “In what direction is gravity?” And you will say, “Well,
gravity is in this direction.” Can you now walk
to your sleeping quarters? And what’s the answer? You cannot. You cannot walk
up against gravity. It would be like asking you
to walk to the ceiling. How do you do that? An elevator or a staircase,
that’s fine because then you get
the push from the stairs when you step on the stairs. So you could have
the staircase here and that’s the way
this person could go here. But you cannot simply walk here because gravity is always
in this direction. Now let’s suppose you are
at your sleeping quarters and you wake up in the morning
and you decide to go back either in this direction
or this direction or this direction or that
direction– it doesn’t matter. Could you do that, just by…
just going into this corridor and slowly, carefully
starting moving? What would happen? Yeah? STUDENT:
You would fly out. LEWIN:
You would fly out. It would be suicide, because
the moment that you are here already, you have maybe not a very large
gravitational experience but already it’s beginning
to grow on you. The farther out you are,
the stronger it will be. By the time you’re here, it’s
10 meters per second squared. Remember? We had 10 meters
per second squared because we wanted
to mimic the Earth and so you literally crash. It’s like falling into a shaft,
jumping into a shaft. It’s not quite the same because you start off
with no pull on you. The moment you start going,
however the situation gets out of hand
and indeed you will slam. So you can use
the same elevator. You can use the same staircase. There’s nothing wrong with that. Suppose I have a liquid which has very, very fine,
small particles in it– extremely small,
so small and so light that they will not sink
to the bottom. So you will always see
some colored milky-type liquid. And here is that tube
which has these fine particles. And the tube is sitting there and the line of the liquid
is obviously like this. Why? Well, that’s obvious. Because gravity is
in this direction. And so the surface of the liquid is always perpendicular
to gravity. You see here
two glasses with water. The surface is
perpendicular to gravity. Now I’m going to rotate this
about this axis– it’s going around like this– and I’m going to rotate it
with an angular velocity omega and this is at a distance, R. Therefore, there is now
a centripetal acceleration in this direction,
and so the particles now say “Aha! Gravity is
in this direction.” The side of the glass
and the liquid is pushing in this direction to provide
this centripetal acceleration. So if you ask them,
“Where is gravity?” they will say
“Gravity is there.” And this gravitational effect
can be so much stronger than this one
that you can forget this one– you will see that in a minute. You can completely forget
this one. And so the liquid will say “I’m going to be
perpendicular to gravity.” And so the liquid will go
like this, clunk. While it rotates around the liquid in this tilted tube
will be vertical. But not only that,
the particles that are here experience now way stronger
gravity than they did before so I have made them heavier. They are no longer
light particles. They are heavy particles,
and what do heavy particles do? They have no problems
in making it to the side. The reason
why the light particles couldn’t fall in the first place
has to do with the fact that the molecules
of the liquid due to their temperature,
have a chaotic motion. We call that
the “thermal agitation.” And these molecules
would interact with these very small
and light particles and so the light particles would
never make it to the bottom. The thermal agitation now
of the liquid is the same– the temperature doesn’t change– but the particles have become
way, way heavier and so the particles now go
in the direction of gravity which is here. And what you will see,
if these particles are white you will see
white precipitation there and the liquid
will become clear. And that is something that I would like
to demonstrate to you. But before I do that, I want
to give you some numbers. Here we have a household, simple,
nothing-special centrifuge that is used in any laboratory. The centrifuge that we have
has an rpm which is 3600 rpm. So 3600 rpm translates
into a frequency of 60 Hz. So it goes around once
in one-sixtieth of a second. Omega is two pi times f is therefore
roughly 360 radians per second. 360 radians per second. If we assume
that the radius is… maybe it’s 10, 15 centimeters. Whatever, let’s take a radius
of 15 centimeters. And we can calculate now what the centripetal
acceleration is. And the centripetal acceleration
a of c which is omega squared R is then roughly about 20
meters per second squared. 20,000 meters
per second squared. And that is 2,000 times
the gravitational acceleration. It means that these particles
experience gravity which is 2,000 times stronger
than if I don’t rotate them. And so they will go
to the side here. But the glass itself is
also 2,000 times heavier and therefore the glass
can easily break so when you design
a centrifuge like that you have to really think
that through very carefully– that the pieces that are
in there don’t fly apart. I have here water in which I
have dissolved some table salt– the same table salt
that you use in the kitchen when you prepare your food,
table salt in here. Here I have water in which I
dissolved some silver nitrate. It’s nasty stuff, I warn you for
it, you have to be very careful because if you get
the stuff on your hands it burns through your hands
very quickly without your realizing it and you end up
with a very black spot. It really eats away,
burns out your skin. People put it on warts and then the warts,
they think, fall off. They probably do after a while but your finger
may also fall off. So I have here silver nitrate and there I have sodium chloride
and I mix the two. So I get table salt– sodium
chloride– plus silver nitrate gives sodium nitrate
plus silver chloride and this, very small white
particles, and you will see that the liquid turns
milky instantaneously. It almost becomes like,
like yogurt, as you will see. And so I want
to show that to you. I have here these two glasses. This is the table salt and
this is the silver nitrate. I’m going to mix them. I hope you can see this. Here are the two glasses,
and when I mix them… (whistles ) instantaneously you get milk. (class laughs ) Yeah. I’m not asking you to taste it
but look at it, right? Just milk. You can leave this for hours
and hours and hours and it will just stay like that. Very small particles
of silver chloride are in here. So now we are going to put this
in the centrifuge. I have to put it
in a very small tube. I’ll show you this small tube. There’s no way that I can pour
that in without making a mess. Here’s this small tube and so what I will do is I will
first put it in a small beaker and then from this small beaker I will transfer it, some of it,
to this tube. When you put this
in a centrifuge your force on this glass
is so high that you must always make sure that you balance it
with another tube that you fill with water
on the other side. Otherwise the thing begins
to shake like crazy. It’s like your centrifuge
when you dry your towels. If they are
not equally distributed it begins to make very obscene
sounds and starts to move. (class laughs ) And the same thing
will happen here. So you just have
to take my word for it that we have put
on the other side just some water
to balance it out. So here is now the yogurt and on the other side
is plain water and we will just let it sit
there for a while and we will return
to that shortly. I mentioned already your
centrifuge for your clothes. That is the way
that you can dry your clothes. That is the same way that my
grandmother dried the lettuce. The water will go
to the circumference. A household centrifuge
for your clothes would easily rotate
1,200 revolutions per minute have a radius
maybe of 15 centimeters which would give you
a centripetal acceleration of 200 times g, 200 times
the gravitational acceleration. So your clothes
experience gravity which is 200 times stronger and therefore your clothes
are 200 times heavier and therefore your clothes
can tear apart and we have all seen that. We have all put in stuff
in a centrifuge and when you take it out you’re
disappointed because it’s torn. That’s because
of the tremendous gravity that you have exposed them to. Many times when I take my shirts
out, half my buttons are gone. That’s because the force–
I shouldn’t use that word… the gravitational effect
on the buttons is enormous and they just get ripped off. Now I want to revisit
the situation that you are
on the end of my string and I’m going to swirl
you around. Earlier, I swirled you
around like this and you didn’t like it and I don’t blame you
because you got dizzy. Now I’m going to rotate
you like this. You may like that better. Maybe not. (chuckles ) And so, whether
you like it or not I’m going to twirl you around
and here you are. This is the circle. There’s a string– you’re here. Here’s the string
and there you are. You have a certain velocity. Your velocity is
in this direction and there is a certain distance
to the center, R. And so you need a certain
centripetal acceleration to go around in that curve. So you need
a centripetal acceleration a of c– which is… you can take the v squared
divided by r, if you like that. This is the magnitude of that v. Now follow me very closely. Just imagine that this number
happens to be exactly 9.8. I can always do that. Where is this person going to
get the push or the pull from for this centripetal
acceleration? Does the string have
to pull on it? No, because there’s always
gravity and gravity gives you an acceleration of 9.8 meters
per second squared. So the string says, “Tough luck,
I don’t have to do anything. “Gravity provides me with the
9.8 meters per second squared that I required.” Now I’m going to swing you
faster, so the v will go up and so the centripetal
acceleration will go up. The string will say “Aha! I’m going to pull
now on this person “because the gravitational
acceleration alone is not enough–
I need some extra pull.” So the string is going
to tighten and pull on you. And I say, “Hello, there,
in what direction is gravity?” And you say, “Gravity is
in this direction.” Why? Because you feel
the string is pulling on you in this direction,
so you experience gravity there. Now comes the question,
how real is this? This is very, very real. It is so real that if I took a bucket
of water instead of you… and here is the bucket of water. I attached to the bucket a rope. I swing it around,
and I swing it around such that
the centripetal acceleration is substantially larger than 9.8 so the string is definitely
going to pull so if you were the water, and I
asked you, “Where is gravity?” you would say the gravitational
direction is in this direction and so the water will say, “Okay, fine,
then this will be my surface and I want to go
in this direction.” But the water can’t go
in that direction so it will just stay there. So I could swing this thing
around if I do it fast enough– so fast that the acceleration
at this point here must be larger than 9.8– the water will stay up
while the bucket is upside down. How fast should I rotate it? Well, let’s put
in some simple numbers. I have here this bucket and let’s say that this is
about one meter. Let’s round some numbers off. So R is about one meter. And I want v squared over R I want that to be larger than
9.8– let’s just call it 10. So that means v
has to be larger than about 3.2 meters
per second. The time to go around is two pi R divided
by this velocity so this time to go around, then,
has to be six… has to be less than two seconds. So if I swing this around
in less than two seconds I will be okay. Now, I realize that the speed
when I move this thing around is not constant everywhere. That’s very difficult
to do that, because of gravity. But it’s close enough
to get an idea. So if I rotate this faster
than in two seconds when the bucket is upside-down if physics works, the water
should not fall out. So let us fill this with water. There we go. I’m always nervous about this. Um, let’s first look
at the centrifuge. We have to see whether
the centrifuge has done its job. So let’s look
at what this tube… I think it was tube number four. Oh, yeah!
Very clear is now the liquid and you see the white stuff
here on the side. It’s not too easy for you
to see, really. I put my hand under here.
Maybe some of you can see
some white stuff but it’s no longer milk–
really a clear liquid. Here you see
some white stuff here but it’s also on the side. You can actually see it here. You see the white stuff because this was
the direction of gravity so it ended up here
and there’s some here. It is completely clear. You see the white stuff? So that’s the way that you can
separate the silver chloride. So now we come to this
daredevil, daredevil experiment. And we’re going to see whether we can fool the water
and make the water think that gravity is not in this
direction but in this direction. Now, you’re doing
the right thing, there. (class laughs ) I don’t blame you at all. (Lewin chuckling ) Okay… There we go! You see the water
is completely fooled and notice that I go around substantially faster
than in two seconds. And the water,
when it’s up there just thinks that gravity is
towards the ceiling. Physics works. Now, who is going to do
this for me, too? (class laughs ) Please, someone should try this. You think you can do it? Come on, try it. In the worst case,
it will be a disaster. (class laughs ) Okay, get some feel for it,
but before you do it make sure
that I’m out of the way. But first swing it a little and
don’t hold it too close to you because I don’t want you
to get hurt. Larger swing, larger, larger. Now you get some feel for it. Go for it, now! Yeah, faster! (class laughs ) That was very good. (class laughs and applauds ) See you Friday. (applause )

24 Replies to “Lec 05: Uniform Circular Motion | 8.01 Classical Mechanics, Fall 1999 (Walter Lewin)”

  1. in the spaceship problem, consider a person jumps and tries to reach his sleeping port. The instant after the jump has been made, the person loses contact with the surface of the ship. He no longer should perceive gravity because there is no centripetal force now acting on him.Why? 'cause C.F, in this case is the result of the contact of the man with the walls of the ship. Once the jump's been made; no contact and hence no C.F. and hence no perceived gravity. So, from Newton's 1st law the man continues to move up with the prevailing acceleration that was accounted the moment he jumped with some force ma>mg. But as he moves towards the sleeping port,the ship has moved some angle theta=(wt). He should then collide with the quadrant walls of the ship. 

  2. @FortheAllureofPhysics, perceived gravity is in this lecture Lec 05 not in Lec 07, please make the correction.

  3. He said that centripetal acceleration is proportional to r (radius). But if mercury is the closest to the sun (meaning has the smallest radius in its supposedly circular orbit), why does it have the greatest centripetal acceleration? If mercury were to get closer to the sun and decrease its orbit's radius, shouldn't the centripetal acceleration also decrease if both values are directly proportional?

  4. in case of perceived gravity while why we are at the top most point why would we feel gravity(that is in upward direction) against the pull ..?plss explain

  5. Prof Lewin can you upload the assignments please, like you did with the Electricity and magnetism lectures

  6. Thanks for this great lecture but I'm really confused because we define gravity cauuses by mass, and how in rotational motion gravity is radillay outward? What causes this gravity to exist?

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