1
00:00:00,690 --> 00:00:03,120
Up until now, we have
been studying the motion

2
00:00:03,120 --> 00:00:05,460
of point-like objects.

3
00:00:05,460 --> 00:00:07,440
In this module, we
are going to consider

4
00:00:07,440 --> 00:00:10,200
the motion of extended
objects, specifically

5
00:00:10,200 --> 00:00:12,330
objects that are rigid bodies.

6
00:00:12,330 --> 00:00:14,340
By rigid, we mean
that the distance

7
00:00:14,340 --> 00:00:18,070
between any two points on the
object always stays the same.

8
00:00:18,070 --> 00:00:20,280
In other words, the
shape of a rigid body

9
00:00:20,280 --> 00:00:23,820
does not change or deform.

10
00:00:23,820 --> 00:00:27,030
There is a useful relation
known as Chasles' theorem that

11
00:00:27,030 --> 00:00:29,130
states that the
general arbitrarily

12
00:00:29,130 --> 00:00:31,740
complicated displacement
of a rigid body

13
00:00:31,740 --> 00:00:34,680
can be broken up into
two parts-- first,

14
00:00:34,680 --> 00:00:37,470
the translational motion
of its center of mass,

15
00:00:37,470 --> 00:00:40,230
and second, the pure
rotation of the object

16
00:00:40,230 --> 00:00:42,810
about its center of mass.

17
00:00:42,810 --> 00:00:44,970
We already know how
to analyze the center

18
00:00:44,970 --> 00:00:47,160
of mass translational
motion through our study

19
00:00:47,160 --> 00:00:49,170
of point-like objects.

20
00:00:49,170 --> 00:00:52,020
This week, we will consider
the rotational motion

21
00:00:52,020 --> 00:00:54,510
of rigid bodies, once
again distinguishing

22
00:00:54,510 --> 00:00:58,200
between kinematics, a geometric
description of the motion,

23
00:00:58,200 --> 00:01:00,900
and dynamics, the
underlying cause of changes

24
00:01:00,900 --> 00:01:03,270
in the rotational motion.

25
00:01:03,270 --> 00:01:07,110
On a microscopic level, we can
think of an extended rigid body

26
00:01:07,110 --> 00:01:09,000
as made up of a
very large number

27
00:01:09,000 --> 00:01:13,140
of small point-like pieces
all attached together.

28
00:01:13,140 --> 00:01:16,740
For rotation about a fixed axis
through the center of mass,

29
00:01:16,740 --> 00:01:18,750
each little piece
will move in a circle

30
00:01:18,750 --> 00:01:21,030
about the rotational axis.

31
00:01:21,030 --> 00:01:22,680
The radius of the
circle will vary

32
00:01:22,680 --> 00:01:24,580
depending upon
where in the object,

33
00:01:24,580 --> 00:01:26,520
that particular piece sits.

34
00:01:26,520 --> 00:01:28,890
However, because all
of these small pieces

35
00:01:28,890 --> 00:01:32,280
are moving collectively as
part of a single rigid body,

36
00:01:32,280 --> 00:01:35,340
they will all have the same
angular velocity and angular

37
00:01:35,340 --> 00:01:38,610
acceleration at
any given instant.

38
00:01:38,610 --> 00:01:41,700
This gives us a way to specify
the kinematics or geometrical

39
00:01:41,700 --> 00:01:44,130
description of
rotational motion using

40
00:01:44,130 --> 00:01:47,220
the vector quantities of
angular velocity and angular

41
00:01:47,220 --> 00:01:49,200
acceleration.

42
00:01:49,200 --> 00:01:52,470
We will also consider the
dynamics of rotational motion.

43
00:01:52,470 --> 00:01:55,140
We will see that an
applied external force

44
00:01:55,140 --> 00:01:58,440
is able to change the rotational
motion of a rigid body,

45
00:01:58,440 --> 00:02:02,700
depending upon exactly where on
the body the force is applied.

46
00:02:02,700 --> 00:02:05,520
This leads directly to
the concept of torque,

47
00:02:05,520 --> 00:02:07,230
a vector quantity
that represents

48
00:02:07,230 --> 00:02:10,169
a sort of rotational force.

49
00:02:10,169 --> 00:02:12,930
Finally, we will see that
we can link the kinematics

50
00:02:12,930 --> 00:02:14,880
and dynamics of
rotational motion

51
00:02:14,880 --> 00:02:18,420
through a rotational equation
of motion, analogous to the role

52
00:02:18,420 --> 00:02:21,930
that Newton's second law plays
for translational motion.

53
00:02:21,930 --> 00:02:24,720
This relation states that
the angular acceleration

54
00:02:24,720 --> 00:02:26,990
is proportional to
the applied torque

55
00:02:26,990 --> 00:02:29,670
and also depends upon how
the mass of the object

56
00:02:29,670 --> 00:02:31,970
is distributed.