New method finding moment of inertia of a soild sphere

[jaeoos]

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.

 

[dimensionless]

The inertia for a point mass is $$I = mr^{2}$$. If you have a sphere you can treat it as a large number of point masses and add them together as in $$I = \sum m_{i}r_{i}^{2}$$. It is probably better to solve this using calculus though. For rotational inertia the equation $$I = \sum m_{i}r_{i}^{2}$$ is an approximation of $$I = \int r^{2} dm$$.

Rotational inertia is also related to kinetic energy. Kinetic energy can be expresses as $$K = \frac{1}{2} I \omega^{2}$$ where $$\omega$$ 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