1
00:00:00,390 --> 00:00:06,660
So similar to what we did for the one dimensional stick, we will now slightly modify this example.

2
00:00:07,020 --> 00:00:09,300
And now it's your task to solve it.

3
00:00:10,110 --> 00:00:17,250
So instead of using here a solid sphere that is rotated around an axis that goes through the center

4
00:00:17,400 --> 00:00:21,390
of the sphere, we will instead use a hollow sphere.

5
00:00:22,170 --> 00:00:25,770
Or you could also say a shell or a spherical shell.

6
00:00:26,910 --> 00:00:31,710
So the analytical result looks pretty difficult.

7
00:00:32,130 --> 00:00:36,870
And to be honest, I really don't want to spend the time to the rafters analytical result because it

8
00:00:36,870 --> 00:00:39,780
will be even more difficult than the solid shell.

9
00:00:40,560 --> 00:00:49,590
But you can just take the coat from the solid shell and modify it to solve the analytical to solve the

10
00:00:49,590 --> 00:00:50,250
hollow shell.

11
00:00:51,120 --> 00:00:55,290
And maybe as a as a hint so that you understand what we are trying to do here.

12
00:00:55,680 --> 00:01:01,410
Let me show you the value for the analytical results, which is basically this one here.

13
00:01:01,980 --> 00:01:15,810
So we have one half times all mega square and then times I, which is two over five times.

14
00:01:17,990 --> 00:01:21,610
Times and now we we need to radii.

15
00:01:22,070 --> 00:01:30,950
We need ah, one and ah, two and ah one is the what was previously capital art, which is the outer

16
00:01:30,950 --> 00:01:34,670
radius of the sphere, which was and is one.

17
00:01:35,330 --> 00:01:38,630
And then we need another radius because we have now a shell.

18
00:01:39,080 --> 00:01:45,470
So only a certain part of the sphere is solid and the center part is hollow.

19
00:01:46,340 --> 00:01:48,440
So we have some second radius.

20
00:01:50,120 --> 00:01:52,390
And I just take 0.8.

21
00:01:52,400 --> 00:01:57,710
You could also take another number, but to be able to compare our results, let's both use zero point

22
00:01:57,710 --> 00:01:58,040
eight.

23
00:01:59,120 --> 00:02:08,330
So we right now that this is our one to the power of five minus part two to the power of five divided

24
00:02:08,330 --> 00:02:14,120
by basically the same thing, but the powers are changed to three.

25
00:02:15,200 --> 00:02:17,990
And I did the mistake because I did not run the.

26
00:02:19,400 --> 00:02:21,200
So yeah, now it's working.

27
00:02:21,950 --> 00:02:23,600
So this will be the analytical result.

28
00:02:23,600 --> 00:02:30,500
And I want you to basically take this code here and to make a new plot of our hollow shell and then

29
00:02:30,500 --> 00:02:35,540
to calculate numerically, basically also using these loops and if statements.

30
00:02:35,540 --> 00:02:42,590
And then this final line of code here to calculate the rotational energy, which should of course,

31
00:02:42,890 --> 00:02:45,710
give something very, very closely to this number.