Frames of Reference: A trippy physics lecture from 1960
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Frames of Reference: A trippy physics lecture from 1960

October 8, 2019


We’re 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 a different circumstance. 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
– Alright – Okay. You lose.
He’s the one that’s really upside-down. You better come into my frame of reference now. – 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 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 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 is 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 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 on 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 refrence 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… – As you can see, the electromagnet
is mounted on a cart that can move. Now 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. I want you to watch right here
so that you will see the ball falling I think you can see that the ball landed
in exactly the same position that it did before when Dr. Hume 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 in the time that it takes to fall, would
have landed back here somewhere but it didn’t. Now I’m going to do the
experiment again but this time I’m going to let you watch the motion through a
slow-motion camera which is fixed… here 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 line 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? A 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 current. 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 car 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 at the fall so that you won’t have any fixed reference 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. Ivey showed you what the motion of the ball that was released from the moving cart looked like in the earth’s 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’s 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 it 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’s frame of reference Now concentrate on watching the puck, don’t let your eye follow us 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 a velocity “u” We were sitting on the cart at a table.
Here I am over on this side and 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 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 it’s velocity is “u” plus “v”… If it’s in this direction it’s 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 So far we’ve been talking about frames 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’s 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 cart 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. But 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 since there is no
force that could be pushing in this direction on the ball, that the law of
inertia 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’s 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 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 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’s fixed frame of reference there was no unbalanced
force but in the frame of reference rotating in this turntable there was
an unbalanced force because the velocity of this puck kept changing. This was a fictitious 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 buck 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. Hume 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 centripetal 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 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. Ivey 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
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 three one hundredths of a meter per second squared. So on a one kilogram mass at the equator, there is a fictitious force acting directly upwards of three one hundredths 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 I dropped a mass
of one kilogram 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’re at 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 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 Foucault pendulum. You saw me start one at the beginning of this film.
Let’s look back again now. This Foucault pendulum drops and as it swings. I think you can see
the 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 constant 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 [Subtitles by Tamur Qutab]

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