Moment of inertia hollow sphere with inner and outer radius

Question

I'm trying to determine the moment of inertia of a hollow sphere, with inner radius 'a' and outer radius 'R'.

A lot of websites give me different solutions, so I don't know which one I have to use. Hopefully someone can help me, and give the calculation of the moment of intertia :)

https://physics.ucsd.edu/neurophysics/courses/physics_2bl/p2bl_experiment_2_notes.pdf https://en.wikipedia.org/wiki/List_of_moments_of_inertia#Moments_of_inertia

Answer 1

The moment of inertia of the shell would be given by: $$\frac{2m}5 * \frac{R^5-a^5}{r^3-a^3}$$

https://physics.ucsd.edu/neurophysics/courses/physics_2bl/p2bl_experiment_2_notes.pdf
has the whole calculation under 0.0.1.
The final answer is just a factorized form, if that's what's confusing you, look at the second last step and so on.

Answer 2

$$ MI = \frac25 ( M R^2 - m r^2 ),\, \frac{r^3}{R^3} = \frac{m}{M}. $$

where $M,m,R,r$ are for solid spheres.