New method finding moment of inertia of a soild sphere

Q. Show the moment of inertia of sphere is 2/5mR^2
using many different methods.

My professor said he knew 18 different method.
Do you have a new idea?
Tell me anything you know. I hope one of your methods will be the 19th method.
 
The inertia for a point mass is [tex]I = mr^{2}[/tex]. If you have a sphere you can treat it as a large number of point masses and add them together as in [tex]I = \sum m_{i}r_{i}^{2}[/tex]. It is probably better to solve this using calculus though. For rotational inertia the equation [tex]I = \sum m_{i}r_{i}^{2}[/tex] is an approximation of [tex] I = \int r^{2} dm [/tex].

Rotational inertia is also related to kinetic energy. Kinetic energy can be expresses as [tex]K = \frac{1}{2} I \omega^{2}[/tex] where [tex]\omega[/tex] is the angular speed.

I've never heard anyone say that there 18 ways to solve this problem, but I suppose it might depend on what other information you might be given.

hope that helps

-dim
 
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