Frames of Reference (1960)

for we are used to seeing things from a particular point of view that is from a particular frame of reference and things look different to us under different circumstances at the moment things look you look peculiar you're upside down no you're the one that's upside down no you're upside down no I'm not he's the one that's upside down isn't he well let's toss for it all right okay you lose he's the one that's really upside down you better come into my frame of reference now s [Music] my frame of reference was inverted from what it usually is that view of things would be normal for me if I normally walked on my [Music] hands this represents a frame of reference just three rods stuck together so that each is at right angles to the other two now I'm going to move in this direction you see the frame at the same spot on your screen but you know I'm moving this way because you see the wall moving this way behind me but how do you know that I'm not standing still and the wall moving it was the wall that was [Applause] moving now the wall has disappeared and you have no way of telling whether I am moving or not but now you know that I'm moving the point of this is that all motion is relative in both cases I was moving relative to the wall and the wall was moving relative to me all motion is relative but we tend to think of one thing as being fixed and the other thing as being moving we usually think of the earth as fixed and walls are usually fixed to the Earth so perhaps you were surprised the first time when it was the wall that was moving and not Dr Hume a frame of reference fixed to the Earth is the most common frame of reference in which to observe the motion of other things this is the frame of reference that you're used to the frame is fastened to the table the table is bolted to the floor the floor is anchored in the building and the building is firmly attached to the Earth of course the reason for having three rods is that the position of any object such as this ball can be specified using these three reference lines this reference line points in the direction which we call up which is a different direction here than it is in the other side of the earth and these two reference lines specify a plane which we call horizontal or level in this film we're going to look at the motion of objects in this earth frame of reference and in other frames of reference moving in different ways relative to the Earth frame well let's look at a motion this steel ball can be held up by the electromagnet now I'm going to open the switch and you watch the motion of the ball the ball is accelerated straight down by gravity along a line parallel to this vertical reference line [Applause] as you can see the electromagnet is mounted on a cart that can move and I'm going to do exactly the same experiment that Dr Hume did but this time while the cart is moving at a constant velocity the cart is pulled Along by a string which is wound around this phonograph turntable and that pulls it with a constant velocity when the cart passes this line the ball is released as you can see I'm going to start the cart down at the end of the table so that by the time it gets to this point I can be sure it's moving with a constant velocity now I want you to watch right here so that you will see the ball [Applause] falling I think you can see that the ball landed in exactly the same position that it did before when Dr hum did the experiment with the Cart fixed but this time the ball could not have fallen straight down let me show you why the ball was released at that point if it had fallen straight down because the cart moves on and the time that it takes to fall it would have landed back here somewhere but it didn't now I'm going to do the experiment again and this time I'm going to let you watch the motion through a slow motion camera which is fixed here is the cart moves by the ball will fall and you can watch in the slow motion camera I'll show you this again this time there will be a L on the film so that you can see the path I think that you can see that the path of the ball is a parabola but all of this has been in a frame of reference fixed to the Earth how would this motion look in a frame of reference which was moving along with the cart frame of reference like that well so that you can see what it looks like I'm going to fix this slow motion camera so that it moves with the car like this I'm going to do the experiment again and incidentally I'll start it and then I'm going to stand here so that when the ball Falls you will have something which is fixed as a reference point in the moving frame of reference I think you could see that the path of the ball is a vertical straight line it looks exactly the same as it did before when Dr Hume did the experiment with the Cart fixed if we were moving along in this frame of reference and we couldn't see the surroundings then we wouldn't be able to tell by this experiment that we were moving at a constant velocity as a matter of fact we wouldn't be able to tell by any experiment that we were moving at a constant velocity I'm going to do the experiment once more and this time I'm not going to stand here behind the ball as it falls so that you won't have any fixed reference [Applause] frame as far as you're concerned that time the cart wasn't necessarily moving at all that time when you couldn't see the background then I think perhaps it was harder for you to realize that you were in a moving frame of reference the important thing to realize here is that all frames of reference moving at constant velocity with respect to one another are equivalent Dr iy showed you what the motion of the ball that was released from the moving cart looked like in the earth frame of reference and in the cart frame the motion looks simpler from the cart now I want you to watch the motion of this white spot you probably see the spot moving in a circle but this is what its path is actually like in the earth frame of reference this is your normal frame of reference you saw the spot moving in the circle because your eye moved along with the cart you put yourself in the frame of reference of the moving cart so you see it isn't always true that we view motion from the earth frame of reference when the motion is simpler from the moving frame you automatically put yourself in that moving frame now we're going to do another experiment on relative motion to show how to compare the velocity of an object in one frame of reference to its velocity in another frame of reference if I give this dry ice Puck a certain start it moves straight across the table with a speed which is essentially constant because the forces of friction have been made very small this is just the law of inertia an object moves with a constant velocity unless an unbalanced force acts on it now will you give it the same start backwards I'll try if Dr Hume gives it the same start it moves back in this Direction with the same velocity now we are on a car here a car which can move and which really is going to move in this direction and we're going to repeat the experiment all right let's go if we were making measurements here then we would observe the same velocities that is the same experimental results that we did before and so would you because you are observing this experiment through a camera which is fastened to this cart that is you are in the moving frame of reference with us but now we're going to do the experiment again and this time you watch through a camera which is fixed in the earth frame of reference now concentrate on watching the puck don't let your eye follow us and I think you'll see that it'll move faster that way and not so fast this way relative to you and relative to the wall behind here's the cart which was moving along in this Direction with the velocity U we were sitting on the card at a table here I am over on this side and uh Dr Hume was on this side and we were pushing this puck back and forth on the table when I pushed it it went in this Direction with a velocity V and when Dr Hume pushed it it went in this Direction with the same velocity V but this is the velocity relative to the car what about the velocity relative to an observer on the ground in the fixed frame well if it was pushed in this direction its velocity is U plus v if it's in this direction its velocity is U minus V this is all very reasonable there's nothing very hard to understand here the surprising thing about this expression is that it is not accurate in all circumstances at very high speeds and by high speeds I mean speeds close to the velocity of light this expression breaks down at these very high speeds we have to use the ideas about relative motion developed by Albert Einstein in his special theory of relativity however for all the speeds that we are ever likely to run into this expression U plus or minus V is completely adequate so far we've been talking about frame of reference moving at a constant velocity relative to one another now I'm going to do the experiment with the dropping ball again only this time the cart will be accelerated relative to the Earth frame these weights will fall and give the cart a constant acceleration I'll put the ball up and then I will release it the motion is very fast and I want you to watch at the point where the ball is released from the fixed camera ready I don't know whether you saw that or not but the path of the ball was the same as it was before only this time it landed in a different spot this is because the car kept on accelerating in this direction as the ball was falling now I'm going to let you see it again with the slow motion camera fixed onto the cart this time you saw the ball moving off to one side and not following down the vertical reference line as it did in the constant velocity case now suppose you were in this accelerated frame of reference how could you explain this motion gravity is the only force acting on this ball so it should fall straight down but if the law of inertia is to hold there must be a force pushing sideways on the ball in this direction to cause it to deviate from the vertical path but what kind of a force is it it isn't a gravitational or an electric or a nuclear force in fact it isn't a force at all as we know one so we're left to conclude that is since there is no force that could be pushing in this direction on the ball that the law of enertia just does not hold this is a strange frame of reference we call a frame of reference in which the law of inertia holds an inertial frame the law of inertia holds in the earth frame of reference so it is an inertial frame the cart moving at constant velocity relative to the Earth is an inertial frame but the cart which is accelerated is not an inertial frame because the frame of reference that we're used to living in is one in which the law of inertia holds when we go into a non-inertial frame like the frame of the accelerated cart our belief in the law of inertia is so strong that when we see an acceleration of the ball sideways we think there is a force causing it so we make up a fiction that there is a force and sometimes we call this a fictitious Force fictitious forces arise in accelerated frames of reference the frame is accelerated in this direction so you in the frame see an acceleration of the ball W in this direction and you say that there is a force causing it what's happening this time why doesn't the puck move straight across the table as it did before as you can see it doesn't so if we believe in the law of inertia then we must believe that there is an unbalanced force to change the velocity of the puck but this Puck is nearly frictionless so what can be exerting this unbalanced force on it suppose that you watch the motion this time through a camera which is fixed in the earth's frame of reference I think if you concentrate on watching just the puck you can see that it is moving in a straight line and that therefore there is no unbalanced force acting on it e now we're going to stop this rotation so that I can talk to you about what is happening here I don't know about you but I'm dizzy in the earth fixed frame of reference there was no unbalanced force but in the frame of reference rotating in this turntable there was a an unbalanced force because the velocity of this Puck kept changing this was a fix I icious force the rotating frame is a non-inertial or accelerated frame just as the accelerated frame of the cart that Dr Hume showed you was you know that every object which is moving in a circle has an acceleration towards the center of the circle this is the acceleration that has a special name the centripetal acceleration now you hold this Puck for a while hold it steady while the turntable is rotating and I'll get off are you ready I'm ready start the rotation you can see that now the puck is moving in a circle Dr hum is is exerting a force to keep it moving in the circle and you can see this from the fact that the rubber ring is extended he is exerting the cental force and this is the only horizontal force acting on the puck but now let's look at it again from his point of view in the rotating system he is exerting a force towards the center of the table and yet the puck is standing still at least more or less still there is some vibration now he believes in the law of inertia so he he thinks there's an equal force on the puck away from the center of the table so that there is no unbalanced force this outward force on the puck is the fictitious force in this case sometimes it's called the centrifugal force in the fixed reference frame there is no outward force on the puck now suppose that Dr Hume stops exerting a force watch the puck in the fixed frame of reference the puck moves off in a straight line there is now no unbalanced force acting on it now let's look at it again from his point of view in the rotating system when he releases the puck which to him was at rest it moved the force away from the center is now an unbalanced force on the puck to him remember to us the outward force on the puck is fictitious because in our Earth frame of reference it doesn't exist but to Dr Hume in the accelerated frame of reference it's a perfectly real Force I hope by now Dr iy and I have convinced you that a rotating frame of reference is not an inertial frame now you've all been told that the Earth is rotating about its axis and that also it travels in a nearly circular orbit around the sun why then do we find that in a frame of reference attached securely to the Earth that the law of inertia seems to hold why don't we observe fictitious forces the size of the fictitious forces which we have to introduce in a non-inertial frame depends on the acceleration of the frame the smaller the acceleration is the smaller the fictitious forces that we introduce now here is a frame of a reference attached to the equator of the Earth the acceleration of this Frame is really very small because the Earth is spinning about its axis it has an acceleration directly inward of 3 100s of a m/s squared so on a 1 kg mass at the equator there is a fictitious force acting directly upwards of 300s of a Newton but this is masked by gravity which is a force downward of 9.8 Newtons so the net downward force is smaller than that of gravity alone so if if I dropped a mass of 1 kg at the Equator the acceleration would be slightly smaller than that due to gravity alone but not really very much now the acceleration of the Earth in its orbit is even smaller still and produces even smaller effects in our frame of reference now I said that the Earth was rotating about its axis how do we know that this is so well if you take a Time exposure photograph of the Stars they seem to be moving in circles about the pole star but all motion is relative is there any way of telling which is moving the Earth or the Stars the fact that it is the earth which is rotating can be demonstrated by means of a pendulum if I set a pendulum swinging it swings back and forth in a plane now it turns out if this pendulum were at the North Pole of the Earth the plane of Swing would remain fixed relative to the stars but would rotate relative to the earth now I'll have to show you what I mean this pendulum is at the center of this turntable which will represent the earth now I'm going to start the table turning around in this direction I'll put a Black Arrow on so that you'll remember all right start the rotation the pendulum is at the North Pole of the earth and you are looking at its motion as you ordinarily do standing on the earth the plane of Swing rotates in the opposite direction from the rotation of the turntable and at exactly the same rate now now look at it from the fixed camera which will represent the frame of the Stars the turntable the Earth rotates but the plane of the pendulum remains fixed a pendulum used for this purpose is called a Fuko pendulum you saw me start one at the beginning of this film let's look back again now this Fuko pendulum drops sand as it swings I think you can see the faint faint line where the sand Trail began the amplitude of Swing is decreasing the sand Trail isn't as long now but the important thing to see is that the plane of Swing has been rotating during the half hour that we've been talking to you an inertial frame of reference is one in which the law of inertia is valid all frames of reference moving at a con Conant velocity with respect to an inertial frame are also inertial frames we use the Earth as an inertial frame of reference but it is only approximately one it has a small acceleration with respect to the stars for example the frame of reference of the stars is the best we can do when we look for a frame of reference which is for all practical purposes fixed an accelerated frame of reference is not an inertial frame and when we are in an accelerated frame we have to introduce forces which we call fictitious forces in order that the law of inertia and the other laws of physics don't change