# 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)”

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.

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

Anyone else watching this for a summer assignment?

Jen Jen….. I ma need ur help later….. go ego

if omega is 2 pi over T, how did it change to 2 pi multiplied by f?

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?

He should get the Nobel Prize for best drawer of dotted lines on a blackboard

Is this the American University course? In Britain, we do this at High School.

What's 26100

the quality of this video is brighter than my future

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

Is this algebra based or Calculus based?

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

is the universe finite or infinite

Sir…u are the best.. Such broad explanation no one can explain

Those students are really blessed aren't they?

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?

Girl in the red jacket at 24:14, i feel you

"In the worst case, it will be a disaster" lmao

He is a Gem..

Which book is being referred to?

MIT and this video quality!!

Has he given every things of circular motion in only this particular lecture. ..?pls reply

Please upload video lectures of wave motion and other lectures of Walter