00:00:28
for
00:00:37
we are used to seeing things from a
00:00:38
particular point of view that is from a
00:00:41
particular frame of reference and things
00:00:44
look different to us under different
00:00:46
circumstances at the moment things
00:00:57
look you look peculiar
00:01:01
you're upside down no you're the one
00:01:04
that's upside down no you're upside down
00:01:08
no I'm
00:01:09
not he's the one that's upside down
00:01:11
isn't he well let's toss for it all
00:01:17
right
00:01:22
okay you lose he's the one that's really
00:01:25
upside down you better come into my
00:01:27
frame of reference now
00:01:36
[Music]
00:01:40
my frame of reference was inverted from
00:01:43
what it usually
00:01:44
is that view of things would be normal
00:01:47
for me if I normally walked on my
00:01:51
[Music]
00:01:54
hands this represents a frame of
00:01:56
reference just three rods stuck together
00:01:59
so that each is at right angles to the
00:02:01
other two now I'm going to move in this
00:02:06
direction you see the frame at the same
00:02:08
spot on your screen but you know I'm
00:02:10
moving this way because you see the wall
00:02:12
moving this way behind me but how do you
00:02:14
know that I'm not standing still and the
00:02:17
wall
00:02:21
moving it was the wall that was
00:02:24
[Applause]
00:02:27
moving now the wall has disappeared and
00:02:29
you have no way of telling whether I am
00:02:32
moving or not but now you know that I'm
00:02:35
moving the point of this is that all
00:02:37
motion is relative in both cases I was
00:02:41
moving relative to the wall and the wall
00:02:44
was moving relative to
00:02:50
me all motion is relative but we tend to
00:02:53
think of one thing as being fixed and
00:02:56
the other thing as being moving we
00:02:58
usually think of the earth as fixed and
00:03:00
walls are usually fixed to the Earth so
00:03:02
perhaps you were surprised the first
00:03:04
time when it was the wall that was
00:03:05
moving and not Dr Hume a frame of
00:03:09
reference fixed to the Earth is the most
00:03:11
common frame of reference in which to
00:03:13
observe the motion of other
00:03:16
things this is the frame of reference
00:03:18
that you're used to the frame is
00:03:20
fastened to the table the table is
00:03:22
bolted to the floor the floor is
00:03:25
anchored in the building and the
00:03:26
building is firmly attached to the Earth
00:03:29
of course the reason for having three
00:03:31
rods is that the position of any object
00:03:35
such as this ball can be specified using
00:03:38
these three reference lines this
00:03:41
reference line points in the direction
00:03:43
which we call up which is a different
00:03:46
direction here than it is in the other
00:03:47
side of the earth and these two
00:03:50
reference lines specify a plane which we
00:03:53
call horizontal or level in this film
00:03:57
we're going to look at the motion of
00:03:59
objects in this earth frame of reference
00:04:02
and in other frames of reference moving
00:04:04
in different ways relative to the Earth
00:04:07
frame well let's look at a
00:04:10
motion this steel ball can be held up by
00:04:15
the
00:04:16
electromagnet now I'm going to open the
00:04:18
switch and you watch the motion of the
00:04:21
ball the ball is accelerated straight
00:04:23
down by gravity along a line parallel to
00:04:26
this vertical reference line
00:04:31
[Applause]
00:04:34
as you can see the electromagnet is
00:04:36
mounted on a cart that can move and I'm
00:04:38
going to do exactly the same experiment
00:04:40
that Dr Hume did but this time while the
00:04:42
cart is moving at a constant velocity
00:04:45
the cart is pulled Along by a string
00:04:47
which is wound around this phonograph
00:04:49
turntable and that pulls it with a
00:04:51
constant
00:04:56
velocity when the cart passes this line
00:05:00
the
00:05:02
ball is released as you can
00:05:05
see I'm going to start the cart down at
00:05:08
the end of the table so that by the time
00:05:10
it gets to this point I can be sure it's
00:05:12
moving with a constant velocity now I
00:05:14
want you to watch right here so that you
00:05:16
will see the ball
00:05:23
[Applause]
00:05:28
falling
00:05:30
[Applause]
00:05:32
I think you can see that the ball landed
00:05:33
in exactly the same position that it did
00:05:35
before when Dr hum did the experiment
00:05:37
with the Cart fixed but this time the
00:05:40
ball could not have fallen straight down
00:05:42
let me show you
00:05:45
why the ball was
00:05:48
released at that point if it had fallen
00:05:51
straight down because the cart moves on
00:05:53
and the time that it takes to fall it
00:05:55
would have landed back here somewhere
00:05:57
but it
00:05:58
didn't now I'm going to do the
00:06:00
experiment
00:06:01
again and this time I'm going to let you
00:06:04
watch the motion through a slow motion
00:06:07
camera which is
00:06:10
fixed here is the cart moves by the ball
00:06:15
will fall and you can watch in the slow
00:06:16
motion
00:06:26
camera I'll show you this again this
00:06:28
time there will be a line on the film so
00:06:30
that you can see the
00:06:33
path I think that you can see that the
00:06:35
path of the ball is a
00:06:39
parabola but all of this has been in a
00:06:41
frame of reference fixed to the Earth
00:06:44
how would this motion look in a frame of
00:06:46
reference which was moving along with
00:06:48
the
00:06:50
cart frame of reference like that well
00:06:53
so that you can see what it looks like
00:06:55
I'm going to fix this slow motion camera
00:07:00
so that it moves with the
00:07:05
car like this I'm going to do the
00:07:08
experiment again and incidentally I'll
00:07:10
start it and then I'm going to stand
00:07:11
here so that when the ball Falls you
00:07:14
will have something which is fixed as a
00:07:17
reference
00:07:28
point
00:07:39
in the moving frame of reference I think
00:07:40
you could see that the path of the ball
00:07:42
is a vertical straight line it looks
00:07:45
exactly the same as it did before when
00:07:46
Dr Hume did the experiment with the Cart
00:07:49
fixed if we were moving along in this
00:07:52
frame of reference and we couldn't see
00:07:54
the surroundings then we wouldn't be
00:07:56
able to tell by this experiment that we
00:07:58
were moving at a constant velocity as a
00:08:00
matter of fact we wouldn't be able to
00:08:01
tell by any experiment that we were
00:08:02
moving at a constant velocity I'm going
00:08:05
to do the experiment once more and this
00:08:08
time I'm not going to stand here behind
00:08:10
the ball as it falls so that you won't
00:08:11
have any fixed reference
00:08:15
[Applause]
00:08:28
frame
00:08:30
as far as you're concerned that time the
00:08:33
cart wasn't necessarily moving at all
00:08:35
that time when you couldn't see the
00:08:37
background then I think perhaps it was
00:08:39
harder for you to realize that you were
00:08:41
in a moving frame of reference the
00:08:44
important thing to realize here is that
00:08:46
all frames of reference moving at
00:08:49
constant velocity with respect to one
00:08:51
another are
00:08:52
equivalent Dr iy showed you what the
00:08:55
motion of the ball that was released
00:08:57
from the moving cart looked like like in
00:08:59
the earth frame of reference and in the
00:09:01
cart frame the motion looks simpler from
00:09:04
the cart now I want you to watch the
00:09:07
motion of this white
00:09:13
spot you probably see the spot moving in
00:09:16
a
00:09:24
circle but this is what its path is
00:09:26
actually like in the earth frame of
00:09:29
reference this is your normal frame of
00:09:32
reference you saw the spot moving in the
00:09:35
circle because your eye moved along with
00:09:38
the cart you put yourself in the frame
00:09:41
of reference of the moving cart so you
00:09:44
see it isn't always true that we view
00:09:47
motion from the earth frame of reference
00:09:50
when the motion is simpler from the
00:09:51
moving frame you automatically put
00:09:54
yourself in that moving
00:09:58
frame
00:10:04
now we're going to do another experiment
00:10:06
on relative motion to show how to
00:10:08
compare the velocity of an object in one
00:10:10
frame of reference to its velocity in
00:10:12
another frame of reference if I give
00:10:15
this dry ice Puck a certain start it
00:10:18
moves straight across the table with a
00:10:20
speed which is essentially constant
00:10:22
because the forces of friction have been
00:10:23
made very small this is just the law of
00:10:26
inertia an object moves with a constant
00:10:28
velocity unless an unbalanced force acts
00:10:31
on it now will you give it the same
00:10:32
start backwards I'll
00:10:36
try if Dr Hume gives it the same start
00:10:39
it moves back in this Direction with the
00:10:41
same velocity now we are on a car here a
00:10:44
car which can move and which really is
00:10:45
going to move in this direction and
00:10:47
we're going to repeat the experiment all
00:10:49
right let's
00:10:58
go
00:11:02
if we were making measurements here then
00:11:05
we would observe the same velocities
00:11:08
that is the same experimental results
00:11:10
that we did before and so would you
00:11:12
because you are observing this
00:11:13
experiment through a camera which is
00:11:16
fastened to this cart that is you are in
00:11:18
the moving frame of reference with us
00:11:20
but now we're going to do the experiment
00:11:22
again and this time you watch through a
00:11:24
camera which is fixed in the earth frame
00:11:27
of
00:11:27
reference
00:11:30
now concentrate on watching the puck
00:11:32
don't let your eye follow us and I think
00:11:34
you'll see that it'll move faster that
00:11:35
way and not so fast this way relative to
00:11:39
you and relative to the wall
00:11:51
behind here's the cart which was moving
00:11:54
along in this Direction with the
00:11:57
velocity U we were sitting on the card
00:12:01
at a
00:12:01
table here I am over on this
00:12:04
side and uh Dr Hume was on this
00:12:09
side and we were pushing this puck back
00:12:13
and forth on the table when I pushed it
00:12:16
it went in this Direction with a
00:12:18
velocity V and when Dr Hume pushed it it
00:12:21
went in this
00:12:22
Direction with the same velocity V but
00:12:25
this is the velocity relative to the car
00:12:29
what about the velocity relative to an
00:12:31
observer on the ground in the fixed
00:12:34
frame well if it was pushed in this
00:12:36
direction its velocity is U plus
00:12:42
v if it's in this direction its velocity
00:12:44
is U minus
00:12:48
V this is all very reasonable there's
00:12:51
nothing very hard to understand here the
00:12:53
surprising thing about this expression
00:12:56
is that it is not accurate in all
00:12:58
circumstances
00:12:59
at very high speeds and by high speeds I
00:13:02
mean speeds close to the velocity of
00:13:04
light this expression breaks
00:13:08
down at these very high speeds we have
00:13:11
to use the ideas about relative motion
00:13:14
developed by Albert Einstein in his
00:13:16
special theory of relativity however for
00:13:19
all the speeds that we are ever likely
00:13:20
to run into this expression U plus or
00:13:23
minus V is completely adequate so far
00:13:27
we've been talking about frame of
00:13:29
reference moving at a constant velocity
00:13:31
relative to one another now I'm going to
00:13:33
do the experiment with the dropping ball
00:13:35
again only this time the cart will be
00:13:39
accelerated relative to the Earth frame
00:13:43
these weights will fall and give the
00:13:45
cart a constant
00:13:52
acceleration I'll put the ball up and
00:13:55
then I will release it the motion is
00:13:57
very fast and I want you to watch at the
00:14:00
point where the ball is released from
00:14:02
the fixed
00:14:03
camera
00:14:06
ready I don't know whether you saw that
00:14:09
or not but the path of the ball was the
00:14:11
same as it was before only this time it
00:14:13
landed in a different spot this is
00:14:16
because the car kept on accelerating in
00:14:19
this direction as the ball was falling
00:14:22
now I'm going to let you see it again
00:14:24
with the slow motion camera fixed onto
00:14:26
the
00:14:27
cart
00:14:49
this time you saw the ball moving off to
00:14:51
one side and not following down the
00:14:54
vertical reference line as it did in the
00:14:56
constant velocity case
00:14:59
now suppose you were in this accelerated
00:15:01
frame of reference how could you explain
00:15:03
this
00:15:07
motion gravity is the only force acting
00:15:11
on this ball so it should fall straight
00:15:14
down but if the law of inertia is to
00:15:17
hold there must be a force pushing
00:15:20
sideways on the ball in this direction
00:15:22
to cause it to deviate from the vertical
00:15:25
path but what kind of a force is it it
00:15:28
it isn't a gravitational or an electric
00:15:31
or a nuclear force in fact it isn't a
00:15:34
force at all as we know one so we're
00:15:37
left to conclude that is since there is
00:15:39
no force that could be pushing in this
00:15:41
direction on the ball that the law of
00:15:44
inertia just does not hold this is a
00:15:47
strange frame of reference we call a
00:15:51
frame of reference in which the law of
00:15:53
inertia holes an inertial frame the law
00:15:57
of inertia holes in the earth frame of
00:15:59
reference so it is an inertial
00:16:02
frame the cart moving at constant
00:16:06
velocity relative to the Earth is an
00:16:08
inertial frame but the cart which is
00:16:11
accelerated is not an inertial frame
00:16:15
because the frame of reference that
00:16:16
we're used to living in is one in which
00:16:19
the law of inertia holds when we go into
00:16:22
a non-inertial frame like the frame of
00:16:25
the accelerated cart our belief in the
00:16:28
law of inertia is so strong that when we
00:16:31
see an acceleration of the ball sideways
00:16:35
we think there is a force causing it so
00:16:38
we make up a fiction that there is a
00:16:40
force and sometimes we call this a
00:16:43
fictitious Force fictitious forces arise
00:16:47
in accelerated frames of
00:16:50
reference the frame is accelerated in
00:16:53
this direction so you in the frame see
00:16:57
an acceleration of the B ball in this
00:16:59
direction and you say that there is a
00:17:01
force causing
00:17:11
it what's happening this time why
00:17:14
doesn't the puck move straight across
00:17:16
the table as it did
00:17:25
before as you can see it doesn't
00:17:30
so if we believe in the law of inertia
00:17:33
then we must believe that there is an
00:17:35
unbalanced force to change the velocity
00:17:37
of the puck but this Puck is nearly
00:17:40
frictionless so what can be exerting
00:17:42
this unbalanced force on
00:17:44
it suppose that you watch the motion
00:17:47
this time through a camera which is
00:17:49
fixed in the earth's frame of
00:17:57
reference
00:18:18
I think if you concentrate on watching
00:18:20
just the puck you can see that it is
00:18:22
moving in a straight line and that
00:18:25
therefore there is no unbalanced force
00:18:27
acting on it
00:18:57
e
00:18:59
now we're going to stop this rotation so
00:19:01
that I can talk to you about what is
00:19:02
happening
00:19:05
here I don't know about you but I'm
00:19:10
dizzy in the earth fixed frame of
00:19:13
reference there was no unbalanced force
00:19:16
but in the frame of reference rotating
00:19:18
in this turntable there was a an
00:19:21
unbalanced force because the velocity of
00:19:25
this Puck kept changing this was a
00:19:28
fictitious Force the rotating frame is a
00:19:31
non-inertial or accelerated frame just
00:19:34
as the accelerated frame of the cart
00:19:38
that Dr Hume showed you
00:19:40
was you know that every object which is
00:19:43
moving in a circle has an acceleration
00:19:46
towards the center of the circle this is
00:19:48
the acceleration that has a special name
00:19:50
the centripetal
00:19:52
acceleration now you hold this Puck for
00:19:54
a while hold it steady while the
00:19:57
turntable is rotating and I'll get
00:20:04
off are you
00:20:06
ready I'm ready start the
00:20:23
rotation you can see that now the puck
00:20:25
is moving in a circle Dr hum is exerting
00:20:28
a force to keep it moving in the circle
00:20:30
and you can see this from the fact that
00:20:32
the rubber ring is extended he is
00:20:35
exerting the cental force and this is
00:20:37
the only horizontal force acting on the
00:20:40
puck but now let's look at it again from
00:20:43
his point of view in the rotating system
00:20:46
he is exerting a force towards the
00:20:48
center of the table and yet the puck is
00:20:50
standing still at least more or less
00:20:53
still there is some
00:20:54
vibration now he believes in the law of
00:20:56
inertia so he thinks there's an equal
00:20:59
force on the puck away from the center
00:21:01
of the table so that there is no
00:21:03
unbalanced force this outward force on
00:21:06
the puck is the fictitious force in this
00:21:08
case sometimes it's called the
00:21:10
centrifugal force in the fixed reference
00:21:13
frame there is no outward force on the
00:21:16
puck now suppose that Dr Hume stops
00:21:19
exerting a force watch the
00:21:22
puck in the fixed frame of reference the
00:21:24
puck moves off in a straight line there
00:21:27
is now no
00:21:28
unbalanced force acting on it now let's
00:21:31
look at it again from his point of view
00:21:33
in the rotating system when he releases
00:21:36
the puck which to him was at rest it
00:21:39
moved the force away from the center is
00:21:42
now an unbalanced force on the puck to
00:21:44
him remember to us the outward force on
00:21:48
the puck is fictitious because in our
00:21:52
Earth frame of reference it doesn't
00:21:54
exist but to Dr Hume in the accelerated
00:21:57
frame of reference it's a perfectly real
00:21:59
Force I hope by now Dr Ivy and I have
00:22:02
convinced you that a rotating frame of
00:22:04
reference is not an inertial frame now
00:22:08
you've all been told that the Earth is
00:22:10
rotating about its axis and that also it
00:22:13
travels in a nearly circular orbit
00:22:16
around the
00:22:17
sun why then do we find that in a frame
00:22:20
of reference attached securely to the
00:22:22
Earth that the law of inertia seems to
00:22:25
hold why don't we observe fictitious
00:22:28
forces the size of the fictitious forces
00:22:31
which we have to introduce in a
00:22:33
non-inertial frame depends on the
00:22:36
acceleration of the frame the smaller
00:22:39
the acceleration is the smaller the
00:22:42
fictitious forces that we
00:22:44
introduce now here is a frame of
00:22:47
reference attached to the equator of the
00:22:50
Earth the acceleration of this Frame is
00:22:53
really very small because the Earth is
00:22:55
spinning about its axis it it has an
00:22:58
acceleration directly inward of 3 100s
00:23:02
of a m/s squared so on a 1 kg mass at
00:23:09
the equator there is a fictitious force
00:23:11
acting directly upwards of 300s of a
00:23:15
Newton but this is masked by gravity
00:23:18
which is a force downward of 9.8 Newtons
00:23:23
so the net downward force is smaller
00:23:25
than that of gravity alone so if I
00:23:28
dropped a mass of 1 kg at the Equator
00:23:32
the acceleration would be slightly
00:23:34
smaller than that due to gravity alone
00:23:38
but not really very much now the
00:23:42
acceleration of the Earth in its orbit
00:23:45
is even smaller still and produces even
00:23:48
smaller effects in our frame of
00:23:51
reference now I said that the Earth was
00:23:53
rotating about its axis how do we know
00:23:57
that this is so well if you take a Time
00:24:00
exposure photograph of the Stars they
00:24:02
seem to be moving in circles about the
00:24:05
pole star but all motion is relative is
00:24:09
there any way of telling which is moving
00:24:11
the Earth or the Stars the fact that it
00:24:14
is the earth which is rotating can be
00:24:16
demonstrated by means of a
00:24:18
pendulum if I set a pendulum swinging it
00:24:22
swings back and forth in a plane now it
00:24:25
turns out if this pendulum were at the
00:24:27
North Pole of the Earth the plane of
00:24:29
Swing would remain fixed relative to the
00:24:32
stars but would rotate relative to the
00:24:36
earth now I'll have to show you what I
00:24:42
mean this pendulum is at the center of
00:24:45
this turntable which will represent the
00:24:50
earth now I'm going to start the table
00:24:53
turning around in this direction I'll
00:24:55
put a Black Arrow on so that you'll
00:25:02
remember all right start the
00:25:08
rotation the pendulum is at the North
00:25:11
Pole of the earth and you are looking at
00:25:13
its motion as you ordinarily do standing
00:25:16
on the
00:25:17
earth the plane of Swing rotates in the
00:25:20
opposite direction from the rotation of
00:25:22
the turntable and at exactly the same
00:25:26
rate now look at it from the fixed
00:25:29
camera which will represent the frame of
00:25:31
the
00:25:33
Stars the turntable the Earth rotates
00:25:37
but the plane of the pendulum remains
00:25:39
fixed a pendulum used for this purpose
00:25:42
is called a Fuko pendulum you saw me
00:25:45
start one at the beginning of this film
00:25:48
let's look back again
00:25:51
now this Fuko pendulum drops sand as it
00:25:55
swings I think you can see the faint
00:25:58
line where the sand Trail began the
00:26:01
amplitude of Swing is decreasing the
00:26:04
sand Trail isn't as long now but the
00:26:07
important thing to see is that the plane
00:26:10
of Swing has been rotating during the
00:26:13
half hour that we've been talking to
00:26:19
you an inertial frame of reference is
00:26:22
one in which the law of inertia is valid
00:26:25
all frames of reference moving at a
00:26:27
constant velocity with respect to an
00:26:29
inertial frame are also inertial frames
00:26:33
we use the Earth as an inertial frame of
00:26:35
reference but it is only approximately
00:26:37
one it has a small acceleration with
00:26:40
respect to the stars for example the
00:26:42
frame of reference of the stars is the
00:26:45
best we can do when we look for a frame
00:26:47
of reference which is for all practical
00:26:49
purposes fixed an accelerated frame of
00:26:52
reference is not an inertial frame and
00:26:55
when we are in an accelerated frame we
00:26:58
have to introduce forces which we call
00:27:00
fictitious forces in order that the law
00:27:03
of inertia and the other laws of physics
00:27:05
don't
00:27:24
change