1
00:00:00,870 --> 00:00:03,420
So let me summarize what
the steps that we've taken

2
00:00:03,420 --> 00:00:05,560
are to do this
differential analysis.

3
00:00:05,560 --> 00:00:10,640
So when you're trying to analyze
a continuous mass distribution,

4
00:00:10,640 --> 00:00:14,130
the first step is to pick
some arbitrary mass element,

5
00:00:14,130 --> 00:00:16,900
a small but finite
size mass element

6
00:00:16,900 --> 00:00:19,020
somewhere in the middle
of the mass distribution.

7
00:00:19,020 --> 00:00:20,560
You don't want to pick
one of the endpoints,

8
00:00:20,560 --> 00:00:22,150
because the endpoints
are special.

9
00:00:22,150 --> 00:00:26,180
You want to pick an arbitrary
point somewhere in the middle

10
00:00:26,180 --> 00:00:28,620
and then pick a small mass
element at that point, so

11
00:00:28,620 --> 00:00:31,530
a small but finite size.

12
00:00:31,530 --> 00:00:34,824
Analyze the forces acting
on that mass element.

13
00:00:34,824 --> 00:00:37,240
So write down Newton's second
law, the equation of motion,

14
00:00:37,240 --> 00:00:39,670
for that mass element.

15
00:00:39,670 --> 00:00:45,420
That will give you what the
forces are on that element.

16
00:00:45,420 --> 00:00:48,990
Then go to the limit of an
infinitesimally small element.

17
00:00:48,990 --> 00:00:51,800
That will give you a
differential equation.

18
00:00:51,800 --> 00:00:54,980
You can then separate
the differential equation

19
00:00:54,980 --> 00:00:57,440
and integrate both sides
to solve the differential

20
00:00:57,440 --> 00:00:58,840
equation.

21
00:00:58,840 --> 00:01:02,260
And then finally, you can
apply a boundary condition,

22
00:01:02,260 --> 00:01:04,910
something you know about one
or the other of the endpoints.

23
00:01:04,910 --> 00:01:07,940
And that will allow you to solve
for the function of interest

24
00:01:07,940 --> 00:01:10,880
at any point along
your distribution.