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8.01x - Lect 5 - Circular Motion, Centripetal Forces, Perceived Gravity — Transcript

by Lectures by Walter Lewin. They will make you ♥ Physics. · 6,538 words · 867 segments · language en · Watch on YouTube

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0:01Today we will discuss
0:03what we call "uniform circular motion."
0:14What is uniform circular motion?
0:16An object goes around in a circle, has radius r
0:24and the object is here.
0:28This is the velocity.
0:30It's a vector, perpendicular.
0:34And later in time when the object is here
0:40the velocity has changed, but the speed has not changed.
0:45We introduce T, what we call the period--
0:50of course it's in seconds--
0:52which is the time to go around once.
0:56We introduce the frequency, f, which we call the frequency
1:03which is the number of rotations per second.
1:08And so the units are either seconds minus one
1:12As most physicists will call it, "hertz"
1:15and so frequency is one divided by T.
1:21We also introduce angular velocity, omega
1:28which we call angular velocity.
1:34Angular velocity means not how many meters per second
1:38but how many radians per second.
1:41So since there are two pi radians in one circumference--
1:48in one full circle--
1:49and it takes T seconds to go around once
1:54it is immediately obvious
1:55that omega equals two pi divided by T.
2:00This is something that I would like you to remember.
2:03Omega equals two pi divided by T--
2:10two pi radians in capital T seconds.
2:14The speed, v, is, of course, the circumference two pi r
2:23divided by the time to go around once
2:25but since two pi divided by T is omega
2:28you can also write for this "omega r."
2:31And this is also something that I want you to remember.
2:34These two things you really want to remember.
2:39The speed is not changing, but the velocity vector is changing.
2:44Therefore there must be an acceleration.
2:47That is non-negotiable.
2:51You can derive what that acceleration must be
2:54in terms of magnitude and in terms of direction.
2:56It's about a five, six minutes derivation.
2:59You'll find it in your book.
3:01I have decided to give you the results
3:03so that you read up on the book
3:05so that we can more talk about the physics
3:07rather than on the derivation.
3:10This acceleration that is necessary
3:13to make the change in the velocity vector
3:16is always pointing towards the center of the circle.
3:20We call it "centripetal acceleration."
3:27Centripetal, pointing towards the center.
3:32And here, also pointing towards the center.
3:36It's a vector.
3:38And the magnitude of the centripetal acceleration
3:44equals v squared divided by r, which is this v
3:48and therefore it's also omega squared r.
3:52And so now we have three equations
3:55and those are the only three you really would like to remember.
4:02We can have a simple example.
4:05Eh, let's have a vacuum cleaner, which has a rotor inside
4:11which scoops the air out or in, whichever way you look at it.
4:15And let's assume that the vacuum cleaner
4:17these scoops have a radius r of about ten centimeters
4:21and that it goes around 600 revolutions per minute, 600 rpm.
4:28600 rpm would translate into a frequency, f, of 10 Hz
4:35so it would translate into a period
4:37going around in one-tenth of a second.
4:42So omega, angular velocity, which is two pi divided by T
4:50is then approximately 63 radians per second
4:57and the speed, v, equals omega r
5:02is then roughly 6.3 meters per second.
5:09The centripetal acceleration-- and that's really my goal--
5:13the centripetal acceleration would be omega squared r
5:18or if you prefer, you can take v squared over r.
5:20You will get the same answer, of course, and you will find
5:24that that is about 400 meters per second squared.
5:29And that is huge.
5:30That is 40 times the acceleration due to gravity.
5:33It's a phenomenal acceleration, the simple vacuum cleaner.
5:39Notice that the acceleration, the centripetal acceleration
5:43is linear in r.
5:45Don't think that it is inversely proportional with r.
5:48That's a mistake, because v itself is a function of r.
5:52If you were sitting here
5:54then your velocity would be lower.
5:56Since omega is the same for the entire motion
6:01you really have to look at this equation
6:03and you see that the centripetal acceleration
6:05is proportional with r.
6:07Therefore, if you were...
6:09if this were a disc which was rotating
6:11and you were at the center of the disc
6:13the centripetal acceleration would be zero.
6:16And as you were to walk out, further out, it would increase.
6:21Now, the acceleration must be caused by something.
6:25There is no such thing as a free lunch.
6:28There is something that must be responsible
6:31for the change in this velocity
6:34and that something I will call either a pull
6:37or I will call it a push.
6:39In our next lecture, when we deal with Newton's laws
6:42we will introduce the word "force."
6:45Today we will only deal with the words "pull" and "push."
6:50So there must be a pull or a push.
6:54Imagine that this is a turntable
6:58and you are sitting here on the turntable on a chair.
7:03It's going around with angular velocity omega
7:07and your distance to the center, let's say, is little r.
7:12You're sitting on this chair and you must experience--
7:16that is non-negotiable-- centripetal acceleration
7:23A of c, which is omega squared times r.
7:27Where do you get it from?
7:29Well, if your seat is bolted to the turntable
7:34then you will feel a push in your back
7:38so you're sitting on this thing, you're going around
7:40and you will feel that the seat is pushing you in your back
7:44and so you feel a push, and that gives the push.
7:49Yeah, I can give this a red color for now.
7:52So you feel a push in your back.
7:57That push, apparently, is necessary for the acceleration.
8:02Alternatively, suppose you had in front of you a stick.
8:06You're not sitting on a chair.
8:09You don't get a push from your back.
8:10But you hold onto the stick
8:13and now you can go around by holding onto the stick.
8:17Now the stick is pulling on you in this same direction.
8:21So now you would say, aha, someone is pulling on you.
8:24Whether it is the pull or whether it is the push
8:27one of... either one of the two
8:29is necessary for you to go around in that circle
8:34on that turntable with that constant speed.
8:43Now, the classic question comes up, which we often ask to people
8:46who have no scientific background.
8:48If you were to go around like this
8:51and something is either pushing on you
8:53or is pulling on you to make this possible
8:56suppose you took that push out, all of a sudden.
8:59The pull is gone. (makes whooshing sound)
9:01What is now the motion of the person
9:04who is sitting on the turntable?
9:06And many non-scientists say, "Well, it will do like this."
9:11That's sort of what your intuition says.
9:12You go around in a circle, and all of a sudden
9:15you no longer have the pull or the push
9:16and you go around in a spiral
9:18and obviously, that is not the case.
9:22What will happen is, if you have, at this moment in time
9:26a velocity in this direction
9:29and you take the pull or the push out
9:31you will start flying off in that direction
9:35and depending upon whether there is gravity or no gravity
9:38there may be a change,
9:39but if this were... if there were no gravity
9:41you would just continue to go along that line
9:44and you would not make this crazy spiral motion.
9:47I have here a disc, which we will rotate
9:50and at the end... the edge of the disc here
9:53we have a little ball.
9:55And the ball is attached to that disc with string.
10:00So now this is vertical, and so this is going to go around
10:03with angular velocity omega.
10:06And we have a string here
10:08and the string is attached to this ball
10:11and the whole thing is going around
10:14and so at one moment in time this has a velocity, like so.
10:19And therefore there must be
10:20non-negotiable centripetal acceleration
10:24which in magnitude is omega squared r
10:28or, if you want to, v squared divided by r.
10:34Now I cut it
10:37and that's like taking away the push and the pull.
10:40The string that you have here
10:42is providing the pull on this ball.
10:45This ball is feeling a pull from the string
10:49and that provides it with the centripetal acceleration.
10:52Cut the string and the pull is gone
10:56and the object will take off.
11:00And if there were gravity here, as there is in 26.100
11:03it would become a parabola and it would end up here.
11:06If, however, I cut the ball exactly when it is here--
11:10not the ball, but I cut the string--
11:12then, of course, it would fly straight up
11:16gravity would act on it, it would come to a halt
11:19and it would come back.
11:20So it really would then go along a straight line.
11:22But you would clearly see, then
11:24that it's not going to do what many people think--
11:27that it would start to swirl around.
11:29It would just go... (makes whooshing sound)
11:30and comes back.
11:32Let's look at that.
11:33We have that here.
11:34So here is that ball.
11:35The string is behind here; you cannot see the string.
11:39I will rotate it, wait for it to pick up a little speed
11:45and the knife, that you can't see either, is behind here
11:49and when I push the knife in, I do it exactly here.
11:54It cuts the string and it goes up.
11:59You ready for this?
12:01You sure you're ready?
12:03Three, two, one, zero.
12:06Wow!
12:07That was very high.
12:08So you see, it's nothing like this.
12:10It simply continued on in the direction that it was going.
12:14It wasn't going into a parabola
12:16because I was shooting it straight up.
12:22The string forms the connection
12:26between the rotating disc and the ball
12:29and therefore, the pull is responsible
12:32for the centripetal acceleration.
12:35Let's now think about planets.
12:39Planets go around the sun.
12:42There's no string, so who is pushing? Who is pulling?
12:48Well, it's clear that it must be gravity.
12:51It must be the sun that is pulling on the planets.
12:57Now, I realize that the orbits of planets
13:00are not nicely circular
13:01so it's not really a uniform circular motion.
13:04We will deal with orbits in great detail in a few weeks--
13:07circular orbits and elliptical orbits.
13:10Let us just assume for simplicity now
13:13that the orbits are roughly circular
13:17just to get a little bit of feeling for it.
13:20And you can look up now in your book--
13:23which I did for you--
13:24even in your preliminary version you can look up
13:27what the mean distance of the planets is to the sun
13:33and you can look up what the period is
13:35the time to go around the sun.
13:38The time to go around the sun is not the same for all planets.
13:42The planets are not attached to a turntable.
13:45Anywhere, any person on a turntable
13:47would go around in the same amount of time.
13:49We know that that's not true for planets.
13:51It takes the Earth a year to go around the sun.
13:55It takes Jupiter 12 years to go around
13:57so don't make the mistake to think
13:59that omega is the same for all planets.
14:01That's not true.
14:04So I look up the distance--
14:08the mean distance to these various planets--
14:12and you see that here in millions of kilometers.
14:16Notice that Mercury is about 100 times closer than Pluto.
14:20By the way, this is on the Web, so don't copy this.
14:23You will find this on the 801 home page.
14:25Then I looked up
14:27how many years it takes to go around the sun--
14:2912 years for Jupiter, one year for the Earth--
14:32and I looked up all the other values.
14:34Then, since I know the periods, I can calculate omega.
14:37Omega is two pi divided by T, so I know omega.
14:42And then I take omega squared
14:44times the mean distance to the sun
14:46and this is, of course, the centripetal acceleration.
14:50So the planets experience this centripetal acceleration
14:53in some crazy units, but who cares about the units here?
14:57And notice that Mercury, which is 100 times closer than Pluto
15:02has a centripetal acceleration
15:06which is 10,000 times larger than Pluto.
15:11100 times closer
15:12has a 10,000 times larger centripetal acceleration.
15:17So what I did was
15:18I plotted this data, the centripetal acceleration
15:21versus the mean distance to the sun
15:24and I did that on log paper.
15:27And what immediately strikes... is very striking is
15:35that all these points-- I've done them for all the planets--
15:38they fall on a straight line.
15:40And so what is the slope of that line?
15:44Well, I tried various slopes
15:47and I found that the slope is very, very close to minus two.
15:55Here is the slope of minus two, and I can overlay this
16:03and notice that the fit is absolutely stunning.
16:08Therefore, you cannot escape the conclusion
16:13that the centripetal acceleration
16:15which is the result of gravity, falls off as one over R squared.
16:22We refer to this, often, in physics
16:25as the "one over R square" law.
16:27And therefore, the effect of gravity itself
16:31must go down with R squared.
16:35So if you are 100 times further away
16:39like Pluto compared to Mercury
16:42then the gravitational... the centripetal acceleration
16:46which is due to gravity is 10,000 times smaller.
16:53And we will learn a lot about gravity in the future.
16:56We will just leave it for now.
16:57If you took the sun away, it would be
17:00like cutting the string that provides the pull
17:04and in that case what you would see
17:07is that the planets would just take off along a straight line.
17:11They would continue to go.
17:13They wouldn't have anything to pull on them anymore.
17:18Now let's look at an object that we're going to rotate.
17:25I have a glass tube that I want to rotate
17:28and in the glass tube, I have a marble.
17:35The glass tube is very smooth.
17:38I have here the glass tube.
17:42Here's a marble.
17:46I'm going to rotate it in this direction
17:51say, with some angular velocity omega
17:53about an axis perpendicular to the blackboard.
17:56So the marble here has a velocity
18:02like so, at this moment in time
18:04but it's a very smooth glass tube
18:07and the marble is very smooth.
18:10The glass cannot push on the marble
18:13nor can the glass pull on the marble.
18:17Now, the marble gets desperate
18:18because the marble needs a centripetal acceleration
18:23in this direction in order to go around like this.
18:28But there is nothing to provide that centripetal acceleration.
18:32So the marble is doing exactly the same
18:35that the planets would do if you take the sun away.
18:38The marble continues to go in the direction that it was going.
18:42So by the time that the tube is here, the marble is here
18:50and by the time that the tube is here
18:54the marble is there.
18:56So the marble finds its way to the edge and that's, of course
19:01the basic idea behind a centrifuge.
19:06My grandmother had always...
19:09She was a great lady
19:10and she had such fantastic ideas, I remember.
19:13And when she made lettuce
19:17we had no good way of drying the lettuce
19:20and I would take the lettuce and go like this... paper towel.
19:26She had a method of her own.
19:29She took a colander and, of course, first of all
19:34we would wash the lettuce, that goes without saying.
19:37I would wash it once.
19:38My grandmother would wash it three times
19:40but that's what you have grandmothers for.
19:43So there comes the lettuce.
19:47We were also very fond of spinach, so add some spinach.
19:53We would wash it... there goes the spinach.
19:58Then she would take something to cover it up--
20:01maybe some Saran wrap, or something else--
20:06put it over it and put a rubber band around it to hold it.
20:14And now what she's going to do, she's going to swing it around.
20:17And now the water is like these marbles.
20:22The water will work its way to the edge
20:24but there are holes, so the water will come out.
20:28Isn't she clever?
20:30Okay, I'll give you a demonstration.
20:33Be careful
20:35or you may get some water on your lecture notes.
20:39But I want to show you
20:40the basic idea behind it is very interesting.
20:42She would go out... she would do this outside, by the way.
20:45But I have no choice, so I will do it here.
20:47So there we go.
20:52(class laughs)
20:54You see? This is the way you dry...
20:59(class laughs)
21:00Oh, I lost my magnetic strawberry--
21:03that's a detail in the process.
21:05So you end up with...
21:09you end up with dry and clean and nice lettuce.
21:15This is 801 at work
21:18and this is clearly an early version of a centrifuge.
21:23Now, my grandmother's method, very tragically
21:27has been replaced lately
21:29with something that you can buy at Crate and Barrel.
21:33We have it here.
21:35Um, it is very boring.
21:39It's very decadent.
21:41Put the salad in here
21:42and all you do is you rotate and it dries.
21:47It's a centrifuge.
21:48This is actually a high-tech version
21:51of the much more sophisticated invention of my grandmother.
21:55And it's nowhere nearly as exciting.
22:00The days of romance are really over
22:04but that's the way it goes.
22:07I'm now going to make a connection
22:11between rotation on the one hand
22:14and centripetal acceleration on the other.
22:20I'm going to make a connection
22:22between centripetal acceleration and perceived gravity.
22:29The way that you perceive gravity.
22:33I'm going to put you in various positions
22:35and then ask you what is the direction of gravity.
22:39I'm going to create artificial gravity for you.
22:43And let's first do it as follows.
22:45I first hang you on a string.
22:50There you are, like this.
22:56And I ask you, do you feel a push or a pull?
23:00And you say, "Yeah, I feel a pull."
23:04And you feel a pull in this direction.
23:09So now I ask you
23:10"Ah, in what direction do you perceive gravity?"
23:18and you think I'm crazy.
23:20You're right in that case, but nevertheless you say
23:23"Gravity is in this direction."
23:26The other direction is the pull.
23:28Okay, so far, so good.
23:31So now I'm going to put you just standing on the floor
23:36and I say to you, "Do you feel a push or a pull?"
23:40And you say, "Yeah, I feel a push.
23:43I feel a push from the floor up."
23:47So I say, "In what direction do you perceive gravity?"
23:51You say, "Well, come on, don't be boring.
23:54Gravity is in this direction."
23:57Notice in both cases you tell me
24:01that gravity is always in the opposite direction
24:04of either your pull or your push.
24:08Okay, now I'm going to be a little rough on you.
24:14Now I'm going to swing you around on a string
24:17just as if you were an apple
24:20and I'm going to do this with you.
24:22And you're at the end of the apple.
24:24You are the apple, not at the end.
24:26You're at the end of the string.
24:27You are the apple.
24:29So there you are.
24:31Here... poor you.
24:36(class laughs)
24:40And I say, "Do you feel a push or a pull?"
24:43And you say, "Yeah, I do, I feel a pull."
24:46Fine, in what direction?
24:48"I feel a pull in this direction."
24:52Okay, so now I say to you
24:56"In what direction do you perceive gravity?"
24:59And you say, "Well, in the opposite direction as pull."
25:02So now you perceive gravity in this direction
25:07which is very real for you.
25:10Now, in this particular case
25:12since the direction changes all the time--
25:16since I swirl you around--
25:18you will, of course, get dizzy like hell, but that's a detail.
25:21You will perceive gravity in this direction when you're here
25:25and when you're here
25:26you will perceive gravity in that direction.
25:30So you perceive gravity
25:32in the direction which is opposing the pull
25:35and the faster I rotate you, the stronger will be the pull
25:40and therefore the stronger will be your perceived gravity.
25:47A carpenter would use a plumb line
25:52and the carpenter would just hold the plumb line like this.
25:55The pull is in this direction and so the carpenter says
25:59"Okay, perceived gravity is in that direction."
26:01The carpenter happens to be right in this case.
26:04Gravityis in this direction, but it's the same idea.
26:07The plumb line is being used to find the direction of gravity.
26:11Think of this as being a plumb line to find...
26:16used to find the direction of gravity.
26:22Now you're in outer space.
26:26You're going to play Captain Kirk
26:28and you're in a space station and there is no gravity.
26:34So we're going to make some gravity for you.
26:37We're going to create some artificial gravity.
26:40So let this be your space station;
26:44it's a big wheel, a radius of about 100 meters
26:51and we'll make it very fancy for you.
26:54We'll make some corridors around, like here.
27:03We'll make it a very interesting space station
27:06like so... and like so.
27:12And this is rotating around with angular velocity omega.
27:19You're here-- there you are.
27:25You go around.
27:26Therefore, non-negotiable
27:30you're going around with a certain velocity v.
27:35This v equals omega r
27:37and therefore, you require centripetal acceleration
27:41towards the center-- that is non-negotiable.
27:44Where do you get it from?
27:46Well, the floor-- this is your floor-- is pushing on you.
27:51Simple as that, just like the floor is pushing on me now.
27:54This floor is pushing.
27:55There's nothing wrong with that; I don't fall over.
27:59And so I say to you,
28:01"In what direction do you perceive gravity?"
28:03And you say, "This is the direction of gravity"
28:08which is as real for you as it can be.
28:11Someone else is standing here.
28:17What do you think that person will think if I ask that person
28:21"What is the direction of gravity?"
28:24Exactly, radially outwards,
28:27opposing the push from the floor.
28:33So we could now calculate
28:35how fast we have to rotate this space ship
28:39to mimic the gravitational acceleration on Earth--
28:42which is 9.8 meters per second squared.
28:44Let's call that 10, just to round it off a little.
28:48So we want the people who walk around in this corridor
28:51to have an acceleration omega squared R which is about 10
28:58so omega squared is about 0.1
29:03so omega is about 0.3 radians per second.
29:11And so the period to go around is about two pi divided by omega
29:19and that is about 20 seconds.
29:23And the tangential speed-- that value for v, which is omega R--
29:30would then be 0.3 times 100
29:33would be about 30 meters per second
29:35just to give you an idea for these numbers
29:38which are by no means so ridiculous.
29:42What is interesting, that the perceived gravity--
29:47and therefore the centripetal acceleration--
29:51is zero here.
29:54There is nothing; there is no gravity there.
29:57And so that may be a good place
29:59for you to have your sleeping quarters.
30:02Now comes an interesting question.
30:05You can walk around here without any problem.
30:09Could you walk into these spokes?
30:14So when you were here, could you then walk
30:19towards your sleeping quarters?
30:21When you were standing here and I first ask you
30:24"In what direction is gravity?"
30:25And you will say, "Well, gravity is in this direction."
30:29Can you now walk to your sleeping quarters?
30:32And what's the answer?
30:34You cannot.
30:35You cannot walk up against gravity.
30:38It would be like asking you to walk to the ceiling.
30:41How do you do that?
30:41An elevator or a staircase, that's fine
30:45because then you get the push from the stairs
30:46when you step on the stairs.
30:48So you could have the staircase here
30:50and that's the way this person could go here.
30:53But you cannot simply walk here
30:55because gravity is always in this direction.
30:59Now let's suppose you are at your sleeping quarters
31:02and you wake up in the morning and you decide to go back
31:06either in this direction or this direction
31:08or this direction or that direction-- it doesn't matter.
31:12Could you do that, just by... just going into this corridor
31:18and slowly, carefully starting moving?
31:21What would happen?
31:23Yeah?
31:24STUDENT: You would fly out.
31:25LEWIN: You would fly out.
31:26It would be suicide, because the moment that you are here
31:30already, you have maybe
31:32not a very large gravitational experience
31:36but already it's beginning to grow on you.
31:39The farther out you are, the stronger it will be.
31:42By the time you're here, it's 10 meters per second squared.
31:45Remember? We had 10 meters per second squared
31:47because we wanted to mimic the Earth
31:50and so you literally crash.
31:52It's like falling into a shaft, jumping into a shaft.
31:56It's not quite the same
31:57because you start off with no pull on you.
32:00The moment you start going, however
32:02the situation gets out of hand and indeed you will slam.
32:06So you can use the same elevator.
32:08You can use the same staircase.
32:09There's nothing wrong with that.
32:12Suppose I have a liquid
32:15which has very, very fine, small particles in it--
32:21extremely small, so small and so light
32:27that they will not sink to the bottom.
32:31So you will always see some colored milky-type liquid.
32:37And here is that tube which has these fine particles.
32:45And the tube is sitting there
32:47and the line of the liquid is obviously like this.
32:50Why? Well, that's obvious.
32:52Because gravity is in this direction.
32:57And so the surface of the liquid
32:58is always perpendicular to gravity.
33:00You see here two glasses with water.
33:03The surface is perpendicular to gravity.
33:06Now I'm going to rotate this about this axis--
33:12it's going around like this--
33:14and I'm going to rotate it with an angular velocity omega
33:19and this is at a distance, R.
33:21Therefore, there is now a centripetal acceleration
33:27in this direction, and so the particles now say
33:31"Aha! Gravity is in this direction."
33:36The side of the glass and the liquid is pushing
33:40in this direction to provide this centripetal acceleration.
33:44So if you ask them, "Where is gravity?"
33:46they will say "Gravity is there."
33:48And this gravitational effect can be so much stronger
33:53than this one that you can forget this one--
33:55you will see that in a minute.
33:56You can completely forget this one.
33:58And so the liquid will say
34:00"I'm going to be perpendicular to gravity."
34:03And so the liquid will go like this, clunk.
34:07While it rotates around
34:09the liquid in this tilted tube will be vertical.
34:13But not only that, the particles that are here
34:19experience now way stronger gravity than they did before
34:24so I have made them heavier.
34:25They are no longer light particles.
34:27They are heavy particles, and what do heavy particles do?
34:31They have no problems in making it to the side.
34:34The reason why the light particles
34:36couldn't fall in the first place has to do with the fact
34:40that the molecules of the liquid
34:42due to their temperature, have a chaotic motion.
34:45We call that the "thermal agitation."
34:47And these molecules would interact
34:49with these very small and light particles
34:52and so the light particles would never make it to the bottom.
34:55The thermal agitation now of the liquid is the same--
34:58the temperature doesn't change--
35:00but the particles have become way, way heavier
35:03and so the particles now go in the direction of gravity
35:08which is here.
35:09And what you will see, if these particles are white
35:12you will see white precipitation there
35:15and the liquid will become clear.
35:19And that is something
35:21that I would like to demonstrate to you.
35:22But before I do that, I want to give you some numbers.
35:25Here we have
35:26a household, simple, nothing-special centrifuge
35:31that is used in any laboratory.
35:34The centrifuge that we have has an rpm which is 3600 rpm.
35:45So 3600 rpm translates into a frequency of 60 Hz.
35:52So it goes around once in one-sixtieth of a second.
35:57Omega is two pi times f
36:02is therefore roughly 360 radians per second.
36:08360 radians per second.
36:12If we assume that the radius is...
36:15maybe it's 10, 15 centimeters.
36:17Whatever, let's take a radius of 15 centimeters.
36:22And we can calculate now
36:23what the centripetal acceleration is.
36:26And the centripetal acceleration a of c which is omega squared R
36:32is then roughly about 20 meters per second squared.
36:3820,000 meters per second squared.
36:44And that is 2,000 times the gravitational acceleration.
36:51It means that these particles experience gravity
36:55which is 2,000 times stronger than if I don't rotate them.
37:01And so they will go to the side here.
37:05But the glass itself is also 2,000 times heavier
37:09and therefore the glass can easily break
37:11so when you design a centrifuge like that
37:13you have to really think that through very carefully--
37:17that the pieces that are in there don't fly apart.
37:24I have here water in which I have dissolved some table salt--
37:29the same table salt that you use in the kitchen
37:32when you prepare your food, table salt in here.
37:37Here I have water in which I dissolved some silver nitrate.
37:44It's nasty stuff, I warn you for it, you have to be very careful
37:49because if you get the stuff on your hands
37:52it burns through your hands very quickly
37:54without your realizing it
37:55and you end up with a very black spot.
37:58It really eats away, burns out your skin.
38:00People put it on warts
38:02and then the warts, they think, fall off.
38:04They probably do after a while
38:05but your finger may also fall off.
38:08So I have here silver nitrate
38:10and there I have sodium chloride and I mix the two.
38:20So I get table salt-- sodium chloride-- plus silver nitrate
38:27gives sodium nitrate plus silver chloride
38:34and this, very small white particles, and you will see
38:39that the liquid turns milky instantaneously.
38:43It almost becomes like, like yogurt, as you will see.
38:47And so I want to show that to you.
38:51I have here these two glasses.
38:53This is the table salt and this is the silver nitrate.
38:59I'm going to mix them.
39:04I hope you can see this.
39:06Here are the two glasses, and when I mix them...
39:11(whistles)
39:12instantaneously you get milk.
39:15(class laughs)
39:18Yeah.
39:20I'm not asking you to taste it but look at it, right?
39:25Just milk.
39:26You can leave this for hours and hours and hours
39:29and it will just stay like that.
39:31Very small particles of silver chloride are in here.
39:36So now we are going to put this in the centrifuge.
39:41I have to put it in a very small tube.
39:45I'll show you this small tube.
39:47There's no way that I can pour that in without making a mess.
39:51Here's this small tube
39:53and so what I will do is I will first put it in a small beaker
40:00and then from this small beaker
40:02I will transfer it, some of it, to this tube.
40:08When you put this in a centrifuge
40:11your force on this glass is so high
40:14that you must always make sure
40:16that you balance it with another tube
40:18that you fill with water on the other side.
40:20Otherwise the thing begins to shake like crazy.
40:23It's like your centrifuge when you dry your towels.
40:28If they are not equally distributed
40:31it begins to make very obscene sounds and starts to move.
40:34(class laughs)
40:35And the same thing will happen here.
40:37So you just have to take my word for it
40:39that we have put on the other side
40:41just some water to balance it out.
40:44So here is now the yogurt
40:47and on the other side is plain water
40:49and we will just let it sit there for a while
40:52and we will return to that shortly.
40:58I mentioned already your centrifuge for your clothes.
41:01That is the way that you can dry your clothes.
41:04That is the same way that my grandmother dried the lettuce.
41:07The water will go to the circumference.
41:12A household centrifuge for your clothes
41:14would easily rotate 1,200 revolutions per minute
41:18have a radius maybe of 15 centimeters
41:21which would give you a centripetal acceleration
41:23of 200 times g, 200 times the gravitational acceleration.
41:29So your clothes experience gravity
41:32which is 200 times stronger
41:35and therefore your clothes are 200 times heavier
41:37and therefore your clothes can tear apart
41:40and we have all seen that.
41:41We have all put in stuff in a centrifuge
41:44and when you take it out you're disappointed because it's torn.
41:47That's because of the tremendous gravity
41:50that you have exposed them to.
41:52Many times when I take my shirts out, half my buttons are gone.
41:57That's because the force-- I shouldn't use that word...
42:00the gravitational effect on the buttons is enormous
42:04and they just get ripped off.
42:08Now I want to revisit the situation
42:11that you are on the end of my string
42:16and I'm going to swirl you around.
42:20Earlier, I swirled you around like this
42:24and you didn't like it
42:25and I don't blame you because you got dizzy.
42:28Now I'm going to rotate you like this.
42:30You may like that better.
42:33Maybe not.
42:34(chuckles)
42:36And so, whether you like it or not
42:40I'm going to twirl you around and here you are.
42:48This is the circle.
42:49There's a string-- you're here.
42:53Here's the string and there you are.
42:59You have a certain velocity.
43:02Your velocity is in this direction
43:07and there is a certain distance to the center, R.
43:13And so you need a certain centripetal acceleration
43:18to go around in that curve.
43:22So you need a centripetal acceleration
43:25a of c-- which is...
43:27You can take the v squared divided by r
43:30if you like that.
43:31This is the magnitude of that v.
43:34Now follow me very closely.
43:39Just imagine that this number happens to be exactly 9.8.
43:47I can always do that.
43:52Where is this person going to get the push or the pull from
43:59for this centripetal acceleration?
44:02Does the string have to pull on it?
44:04No, because there's always gravity and gravity gives you
44:08an acceleration of 9.8 meters per second squared.
44:12So the string says, "Tough luck, I don't have to do anything.
44:18"Gravity provides me with the 9.8 meters per second squared
44:25that I required."
44:27Now I'm going to swing you faster, so the v will go up
44:34and so the centripical acceleration will go up.
44:38The string will say
44:39"Aha! I'm going to pull now on this person
44:44"because the gravitational acceleration alone
44:46is not enough-- I need some extra pull."
44:49So the string is going to tighten and pull on you.
44:53And I say, "Hello, there, in what direction is gravity?"
44:57And you say, "Gravity is in this direction."
45:01Why? Because you feel the string is pulling on you
45:04in this direction, so you experience gravity there.
45:09Now comes the question, how real is this?
45:13This is very, very real.
45:18It is so real
45:20that if I took a bucket of water instead of you...
45:27and here is the bucket of water.
45:33I attached to the bucket a rope.
45:37I swing it around, and I swing it around
45:41such that the centripetal acceleration
45:44is substantially larger than 9.8
45:47so the string is definitely going to pull
45:53so if you were the water, and I asked you, "Where is gravity?"
45:57you would say the gravitational direction is in this direction
46:01and so the water will say,
46:02"Okay, fine, then this will be my surface
46:05and I want to go in this direction."
46:07But the water can't go in that direction
46:09so it will just stay there.
46:12So I could swing this thing around if I do it fast enough--
46:17so fast that the acceleration at this point here
46:22must be larger than 9.8--
46:24the water will stay up while the bucket is upside down.
46:29How fast should I rotate it?
46:32Well, let's put in some simple numbers.
46:35I have here this bucket
46:39and let's say that this is about one meter.
46:42Let's round some numbers off.
46:44So R is about one meter.
46:48And I want v squared over R
46:52I want that to be larger than 9.8-- let's just call it 10.
46:59So that means v has to be larger
47:02than about 3.2 meters per second.
47:05The time to go around
47:09is two pi R divided by this velocity
47:13so this time to go around, then, has to be six...
47:16has to be less than two seconds.
47:20So if I swing this around in less than two seconds
47:22I will be okay.
47:23Now, I realize that the speed when I move this thing around
47:28is not constant everywhere.
47:30That's very difficult to do that, because of gravity.
47:32But it's close enough to get an idea.
47:35So if I rotate this faster than in two seconds
47:40when the bucket is upside-down
47:43if physics works, the water should not fall out.
47:49So let us fill this with water.
48:00There we go.
48:10I'm always nervous about this.
48:12Um, let's first look at the centrifuge.
48:16We have to see whether the centrifuge has done its job.
48:25So let's look at what this tube...
48:29I think it was tube number four.
48:31Oh, yeah! Very clear is now the liquid
48:35and you see the white stuff here on the side.
48:38It's not too easy for you to see, really.
48:40I put my hand under here.
48:42Maybe some of you can see some white stuff
48:44but it's no longer milk-- really a clear liquid.
48:49Here you see some white stuff here
48:51but it's also on the side.
48:52You can actually see it here.
48:57You see the white stuff
48:59because this was the direction of gravity
49:00so it ended up here and there's some here.
49:02It is completely clear.
49:05You see the white stuff?
49:08So that's the way that you can separate the silver chloride.
49:16So now we come to this daredevil, daredevil experiment.
49:23And we're going to see
49:26whether we can fool the water and make the water think
49:29that gravity is not in this direction but in this direction.
49:33Now, you're doing the right thing, there.
49:35(class laughs)
49:36I don't blame you at all.
49:38(Lewin chuckling)
49:41Okay...
49:45There we go!
49:47You see the water is completely fooled
49:49and notice that I go around
49:51substantually faster than in two seconds.
49:54And the water, when it's up there
49:55just thinks that gravity is towards the ceiling.
49:59Physics works.
50:00Now, who is going to do this for me, too?
50:02(class laughs)
50:03Please, someone should try this.
50:06You think you can do it?
50:09Come on, try it.
50:11In the worst case, it will be a disaster.
50:14(class laughs)
50:17Okay, get some feel for it, but before you do it
50:19make sure that I'm out of the way.
50:22But first swing it a little and don't hold it too close to you
50:26because I don't want you to get hurt.
50:28Larger swing, larger, larger.
50:31Now you get some feel for it.
50:32Go for it, now!
50:35Yeah, faster!
50:36(class laughs)
50:40That was very good.
50:41(class laughs and applauds)
50:42See you Friday.
50:44(applause)

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