Two Ways to Find the Moment of Inertia for a Sphere
What is the moment of inertia and why would you wan to find it for a sphere? Will this even be fun? The answer to the last question — YES. Trust me, I’m going to make it fun.
What is the moment of inertia?
This is just a quick review. I mean, if you have read this far then I suspect you already have an idea about the moment of inertia. First, let me be clear — there are two different moments of inertia (and they are both represented by I). If you are rotating a rigid object about a FIXED axis then I is a scalar value (that’s the one we will calculate here). However, if the object is free to rotate in any direction then I is a tensor. If you are looking for stuff about the tensor version, then this other post is for you.
Now back to the scalar version of I. If you have a bunch of masses connected together and rotating about a fixed axis with an angular speed ω, then it’s possible to write the rotational kinetic energy as:
Where for a finite number of point mass, I would be:
