So similar to what we did for the one dimensional stick, we will now slightly modify this example.
And now it's your task to solve it.
So instead of using here a solid sphere that is rotated around an axis that goes through the center
of the sphere, we will instead use a hollow sphere.
Or you could also say a shell or a spherical shell.
So the analytical result looks pretty difficult.
And to be honest, I really don't want to spend the time to the rafters analytical result because it
will be even more difficult than the solid shell.
But you can just take the coat from the solid shell and modify it to solve the analytical to solve the
hollow shell.
And maybe as a as a hint so that you understand what we are trying to do here.
Let me show you the value for the analytical results, which is basically this one here.
So we have one half times all mega square and then times I, which is two over five times.
Times and now we we need to radii.
We need ah, one and ah, two and ah one is the what was previously capital art, which is the outer
radius of the sphere, which was and is one.
And then we need another radius because we have now a shell.
So only a certain part of the sphere is solid and the center part is hollow.
So we have some second radius.
And I just take 0.8.
You could also take another number, but to be able to compare our results, let's both use zero point
eight.
So we right now that this is our one to the power of five minus part two to the power of five divided
by basically the same thing, but the powers are changed to three.
And I did the mistake because I did not run the.
So yeah, now it's working.
So this will be the analytical result.
And I want you to basically take this code here and to make a new plot of our hollow shell and then
to calculate numerically, basically also using these loops and if statements.
And then this final line of code here to calculate the rotational energy, which should of course,
give something very, very closely to this number.