1
00:00:00,000 --> 00:00:00,640


2
00:00:00,640 --> 00:00:04,730
Let's continue with our study
of the planet Lubricon VI.

3
00:00:04,730 --> 00:00:07,470
Now the one thing I did not
tell you in the last video

4
00:00:07,470 --> 00:00:14,250
is that Lubricon VI is
not rotating at all.

5
00:00:14,250 --> 00:00:15,900
And because it's
not rotating, it

6
00:00:15,900 --> 00:00:18,190
can really not have an equator.

7
00:00:18,190 --> 00:00:21,110
So when we talked about in
the path of this frozen sock,

8
00:00:21,110 --> 00:00:23,310
instead of saying it's
traveling across an equator,

9
00:00:23,310 --> 00:00:25,990
I should say it's traveling
along a great circle.

10
00:00:25,990 --> 00:00:27,730
If you assume that
earth is a sphere--

11
00:00:27,730 --> 00:00:29,771
and it's not a perfect
sphere-- but if you assume

12
00:00:29,771 --> 00:00:32,340
it's a sphere, our equator
would be a perfect sphere.

13
00:00:32,340 --> 00:00:35,431
But in order to have an equator,
you need to have some rotation.

14
00:00:35,431 --> 00:00:36,930
This right over
here, we'll just say

15
00:00:36,930 --> 00:00:40,040
it's traveling along the
largest possible circle

16
00:00:40,040 --> 00:00:41,230
that it can travel along.

17
00:00:41,230 --> 00:00:44,480
It's traveling along one of the
great circles of this sphere,

18
00:00:44,480 --> 00:00:46,740
this block of sock
right over there.

19
00:00:46,740 --> 00:00:48,590
And now that we know
it's not rotating,

20
00:00:48,590 --> 00:00:50,430
I want to enter another
thought experiment.

21
00:00:50,430 --> 00:00:54,850
Because this little frozen block
of sock is not the only thing

22
00:00:54,850 --> 00:00:58,230
that's on the surface
of Lubricon VI.

23
00:00:58,230 --> 00:01:01,010
Over here-- we were
viewing it at a distance--

24
00:01:01,010 --> 00:01:03,220
but right over there,
if we were to zoom in,

25
00:01:03,220 --> 00:01:08,870
you would see sitting on
the surface of Lubricon VI--

26
00:01:08,870 --> 00:01:12,390
so once again, that's the
surface-- is a frozen banana.

27
00:01:12,390 --> 00:01:16,750
So this right over
here is a block of ice.

28
00:01:16,750 --> 00:01:19,710
And in that block of
ice we have a banana.

29
00:01:19,710 --> 00:01:21,750
It's a frozen banana.

30
00:01:21,750 --> 00:01:25,600
So that's my best attempt
at drawing our banana.

31
00:01:25,600 --> 00:01:29,370
And this relative to the
surface of Lubricon VI

32
00:01:29,370 --> 00:01:32,030
is absolutely stationary.

33
00:01:32,030 --> 00:01:36,800
It has absolutely no tangential
velocity like this block had

34
00:01:36,800 --> 00:01:39,500
and will continue to
have for all eternity.

35
00:01:39,500 --> 00:01:42,900
This has absolutely no
tangential velocity.

36
00:01:42,900 --> 00:01:44,650
And so my question
for you, if we

37
00:01:44,650 --> 00:01:48,680
think about what are the
forces acting on this?

38
00:01:48,680 --> 00:01:51,020
Well, we have the
force of gravity

39
00:01:51,020 --> 00:01:53,590
towards the center
of Lubricon VI.

40
00:01:53,590 --> 00:01:55,350
So we have the force of gravity.

41
00:01:55,350 --> 00:01:57,270
And I'm drawing all the
forces from the center

42
00:01:57,270 --> 00:01:59,570
of mass of this block of banana.

43
00:01:59,570 --> 00:02:01,940
So once again, let me
draw that same color.

44
00:02:01,940 --> 00:02:04,910
We have the force of gravity
acting radially inward.

45
00:02:04,910 --> 00:02:10,080


46
00:02:10,080 --> 00:02:12,650
And then we know that
this banana is not

47
00:02:12,650 --> 00:02:14,900
plummeting straight into
the center of the Earth.

48
00:02:14,900 --> 00:02:19,830
There must be some other force
that is keeping it stationary.

49
00:02:19,830 --> 00:02:21,940
And that force is the
force of the surface

50
00:02:21,940 --> 00:02:26,480
of Lubricon VI on the banana or
on this block that's keeping it

51
00:02:26,480 --> 00:02:29,410
from plunging towards
the center of the planet.

52
00:02:29,410 --> 00:02:31,540
So that, in this case,
is the normal force.

53
00:02:31,540 --> 00:02:37,880


54
00:02:37,880 --> 00:02:42,110
And my question to you
is, are these two things

55
00:02:42,110 --> 00:02:44,595
equal in the case of the banana?

56
00:02:44,595 --> 00:02:47,320


57
00:02:47,320 --> 00:02:49,450
Well, as far as we
can tell, this banana

58
00:02:49,450 --> 00:02:50,880
is completely at rest.

59
00:02:50,880 --> 00:02:54,220
This planet right over here, at
least relative to the planet,

60
00:02:54,220 --> 00:02:57,270
this planet right here has
absolutely no rotation.

61
00:02:57,270 --> 00:03:01,020
And this banana has no relative
motion towards the planet.

62
00:03:01,020 --> 00:03:04,990
It is not accelerating in
absolutely any direction.

63
00:03:04,990 --> 00:03:07,730
And if it's not accelerating
in any direction,

64
00:03:07,730 --> 00:03:10,030
the net forces on
it in any dimension

65
00:03:10,030 --> 00:03:13,320
must all or must be 0,
or all of the forces

66
00:03:13,320 --> 00:03:15,400
must cancel out with each other.

67
00:03:15,400 --> 00:03:20,230
So in the case of this banana,
the normal force exactly

68
00:03:20,230 --> 00:03:22,510
cancels out the
force of gravity.

69
00:03:22,510 --> 00:03:26,520
These two things,
the normal force

70
00:03:26,520 --> 00:03:30,830
is exactly equal to the
inward force of gravity.

71
00:03:30,830 --> 00:03:32,730
Or I guess we should
say that they add to 0.

72
00:03:32,730 --> 00:03:34,320
They're going in
opposite directions.

73
00:03:34,320 --> 00:03:40,190
So I should say the normal
force plus the force of gravity

74
00:03:40,190 --> 00:03:41,490
are going to be equal 0.

75
00:03:41,490 --> 00:03:43,400
They have the same
exact magnitude.

76
00:03:43,400 --> 00:03:45,240
They're going in
opposite directions.

77
00:03:45,240 --> 00:03:49,090
So when you add them together,
they are going to cancel out.

78
00:03:49,090 --> 00:03:52,160
Now, with that little thought
experiment out of the way,

79
00:03:52,160 --> 00:03:55,210
let's return to the frozen sock.

80
00:03:55,210 --> 00:03:57,790
The frozen sock, as
we already learned,

81
00:03:57,790 --> 00:04:02,330
is orbiting around this
planet at a altitude of 0

82
00:04:02,330 --> 00:04:05,660
for all eternity at
1 kilometer per hour.

83
00:04:05,660 --> 00:04:07,520
And we know that
the force of gravity

84
00:04:07,520 --> 00:04:09,780
is acting on it towards
the center of the planet

85
00:04:09,780 --> 00:04:11,740
and there is a
normal force that's

86
00:04:11,740 --> 00:04:14,400
keeping it from
plummeting, from spiraling

87
00:04:14,400 --> 00:04:15,950
towards the center
of the planet.

88
00:04:15,950 --> 00:04:19,899
But my question to you is, in
the case of the frozen sock

89
00:04:19,899 --> 00:04:22,940
right over here,
are these two forces

90
00:04:22,940 --> 00:04:25,790
equal like they
are for the banana?

91
00:04:25,790 --> 00:04:29,050


92
00:04:29,050 --> 00:04:32,090
So in the case of the
frozen sock, the traveling,

93
00:04:32,090 --> 00:04:39,280
orbiting sock, if these two
forces had the same magnitude,

94
00:04:39,280 --> 00:04:41,200
but just going in opposite
directions the way

95
00:04:41,200 --> 00:04:44,690
we've drawn it right over here,
it would completely cancel out.

96
00:04:44,690 --> 00:04:47,270
And then we would
have no net force.

97
00:04:47,270 --> 00:04:48,460
So let me make it clear.

98
00:04:48,460 --> 00:04:55,210
If the normal force plus
the force of gravity

99
00:04:55,210 --> 00:04:58,490
canceled out with each
other, if this equalled 0,

100
00:04:58,490 --> 00:05:03,270
then we would have
absolutely no net force

101
00:05:03,270 --> 00:05:06,630
and the object would not
accelerate in any direction.

102
00:05:06,630 --> 00:05:09,114
An object in motion
will stay in motion.

103
00:05:09,114 --> 00:05:10,530
So this one right
over here, if it

104
00:05:10,530 --> 00:05:13,740
had no net force
acting on it, it

105
00:05:13,740 --> 00:05:16,360
would not stay on the
surface of the planet.

106
00:05:16,360 --> 00:05:18,265
It would just travel
in a straight line,

107
00:05:18,265 --> 00:05:20,890
in a tangential line from where
it happens to be at this moment

108
00:05:20,890 --> 00:05:21,660
forever.

109
00:05:21,660 --> 00:05:24,900
So if it was right over here--
I know this isn't the path,

110
00:05:24,900 --> 00:05:26,960
it would just keep
traveling forever

111
00:05:26,960 --> 00:05:30,150
off the surface of the planet.

112
00:05:30,150 --> 00:05:32,820
We know that clearly is
not what's happening.

113
00:05:32,820 --> 00:05:34,740
It is orbiting
around the planet.

114
00:05:34,740 --> 00:05:36,860
It has a circular path.

115
00:05:36,860 --> 00:05:39,156
And since it has
a circular path--

116
00:05:39,156 --> 00:05:41,030
so if I were to draw a
cross-section of its--

117
00:05:41,030 --> 00:05:43,430
if I were to look at
its path from the side,

118
00:05:43,430 --> 00:05:45,730
it has a circular
path like that.

119
00:05:45,730 --> 00:05:46,880
It is going like that.

120
00:05:46,880 --> 00:05:52,330
It is constantly being
accelerated inward.

121
00:05:52,330 --> 00:05:55,910
There is some
centripetal acceleration

122
00:05:55,910 --> 00:05:58,330
going on, inward acceleration.

123
00:05:58,330 --> 00:06:01,340
So in order for that inward
acceleration to be going on,

124
00:06:01,340 --> 00:06:04,680
there must be some
net inward force.

125
00:06:04,680 --> 00:06:07,950
So in this situation, in the
situation for the stationary

126
00:06:07,950 --> 00:06:11,020
banana, these two guys
cancelled each other out.

127
00:06:11,020 --> 00:06:15,020
But for the case of the moving
frozen sock, the sock that

128
00:06:15,020 --> 00:06:18,850
is orbiting for all of
eternity, it is in orbit.

129
00:06:18,850 --> 00:06:20,600
It has a circular path.

130
00:06:20,600 --> 00:06:22,110
So there are centripetal motion.

131
00:06:22,110 --> 00:06:25,480
There is some net inward
force going on here.

132
00:06:25,480 --> 00:06:25,980
So

133
00:06:25,980 --> 00:06:32,570
In this situation, the magnitude
of the force of gravity

134
00:06:32,570 --> 00:06:40,030
is going to be greater than the
magnitude of the normal force.

135
00:06:40,030 --> 00:06:41,700
So we don't have this situation.

136
00:06:41,700 --> 00:06:43,360
In that situation,
you wouldn't orbit.

137
00:06:43,360 --> 00:06:45,100
We have the situation
where you do

138
00:06:45,100 --> 00:06:47,690
have some net centripetal force.

139
00:06:47,690 --> 00:06:49,890
The force of gravity,
the magnitude of it,

140
00:06:49,890 --> 00:06:53,834
is slightly larger than the
magnitude of the normal force.

141
00:06:53,834 --> 00:06:55,500
And an interesting
thing to think about,

142
00:06:55,500 --> 00:06:57,950
and we might address it
in a future tutorial,

143
00:06:57,950 --> 00:07:01,320
is what would happen if this
started going faster and faster

144
00:07:01,320 --> 00:07:04,600
and faster, if the frozen
sock were to accelerate.

145
00:07:04,600 --> 00:07:05,520
What then?

146
00:07:05,520 --> 00:07:08,370
How would the relationship
between these two things

147
00:07:08,370 --> 00:00:00,000
potentially change,
if they change at all?