1
00:00:01,220 --> 00:00:04,340
Up until now, we have
analyzed the motion of objects

2
00:00:04,340 --> 00:00:07,790
that we treated as so-called
point masses, where literally

3
00:00:07,790 --> 00:00:09,800
all of the mass of
the object was treated

4
00:00:09,800 --> 00:00:12,350
as lying at a single point.

5
00:00:12,350 --> 00:00:15,620
This is obviously an
unrealistic idealization.

6
00:00:15,620 --> 00:00:17,990
Real objects have
spatial extent and come

7
00:00:17,990 --> 00:00:20,390
in various sizes and
shapes, some regular

8
00:00:20,390 --> 00:00:22,580
and some highly irregular.

9
00:00:22,580 --> 00:00:25,370
The mass distribution within
these extended objects

10
00:00:25,370 --> 00:00:29,660
might be smooth and uniform or
highly non-uniform and lumpy.

11
00:00:29,660 --> 00:00:32,810
Moreover, sometimes, we will
be interested in simultaneously

12
00:00:32,810 --> 00:00:36,650
analyzing a large system
of particles or objects.

13
00:00:36,650 --> 00:00:39,470
To deal properly
with such situations,

14
00:00:39,470 --> 00:00:42,590
it is necessary to introduce
a new physical quantity called

15
00:00:42,590 --> 00:00:45,950
the momentum, which is a vector
that we traditionally denote

16
00:00:45,950 --> 00:00:49,550
with the symbol P. For
a single point mass,

17
00:00:49,550 --> 00:00:51,980
the momentum is the product
of the mass and the velocity

18
00:00:51,980 --> 00:00:53,460
vector.

19
00:00:53,460 --> 00:00:56,580
The form of Newton's second
law that we have used so far,

20
00:00:56,580 --> 00:00:59,900
F equals ma, is actually only
true for the special case

21
00:00:59,900 --> 00:01:01,280
of a point mass.

22
00:01:01,280 --> 00:01:03,440
The more general form of
the Newton's Second Law

23
00:01:03,440 --> 00:01:07,430
is that F equals dp/dt,
that is that the force is

24
00:01:07,430 --> 00:01:10,880
equal to the time derivative
of the momentum vector.

25
00:01:10,880 --> 00:01:13,550
This is applicable to
either a single particle

26
00:01:13,550 --> 00:01:15,800
or to a system of particles.

27
00:01:15,800 --> 00:01:17,930
This more general
form provides us

28
00:01:17,930 --> 00:01:19,700
the way to address
extended objects

29
00:01:19,700 --> 00:01:21,620
or multi-particle systems.

30
00:01:21,620 --> 00:01:24,680
We will once again appeal
to a calculus-like argument,

31
00:01:24,680 --> 00:01:26,690
breaking down an
extended distribution

32
00:01:26,690 --> 00:01:29,450
into a large number
of small elements,

33
00:01:29,450 --> 00:01:31,820
treating each element
separately, and then summing

34
00:01:31,820 --> 00:01:32,960
the results.

35
00:01:32,960 --> 00:01:35,750
As part of this process, we
will introduce the concept

36
00:01:35,750 --> 00:01:40,250
of the center of mass, a sort of
mass weighted average position

37
00:01:40,250 --> 00:01:42,950
for an extended
object or system.

38
00:01:42,950 --> 00:01:46,220
Momentum is also the first
of several special measurable

39
00:01:46,220 --> 00:01:50,120
quantities that we will discuss
that obey special powerful

40
00:01:50,120 --> 00:01:52,370
rules called conservation laws.

41
00:01:52,370 --> 00:01:55,789
The other two quantities are
energy and angular momentum.

42
00:01:55,789 --> 00:01:58,550
Conservation laws are principles
to provide that the given

43
00:01:58,550 --> 00:02:01,730
measurable quantity remains
unchanged during the evolution

44
00:02:01,730 --> 00:02:04,910
of a system with time as long
as certain requirements are

45
00:02:04,910 --> 00:02:09,800
met, essentially the requirement
that a system remains isolated.

46
00:02:09,800 --> 00:02:12,710
With this restriction in
place, the possible evolution

47
00:02:12,710 --> 00:02:15,320
of motion of a particle
or system of particles

48
00:02:15,320 --> 00:02:18,620
is greatly restricted,
simplifying its calculation.

49
00:02:18,620 --> 00:02:20,720
We will see how this can
be used to our advantage

50
00:02:20,720 --> 00:02:22,860
in understanding
what will happen.