# Moment of Inertia of a Sphere

• piquante

#### piquante

So here I just need help understanding a concept.
I was reading this website's derivation of the moment of inertia of a solid sphere here: http://hyperphysics.phy-astr.gsu.edu/hbase/isph.html#sph3
For the life of me I can't see where the (1/2)y2 term comes from. I would understand y2 because that would be the radius, but the 1/2?
I understand the other steps but I'm very much stuck on this first one.

A related question for anyone who has an opinion: this website starts out these problems by writing dI = abc dm. My physics professor tends to start with dm = dfg dr. Is there a best way to approach these problems? I'm always the most confused at the beginning when I need to define the above relationships. Thanks!

To find the moment of inertia of the sphere, they had to sum the moment of inertia of many tiny disks of mass dm. The moment of inertia of a disk of mass M is (1/2)MR^2. To see a derivation of the moment of inertia of a disk: http://mikebloxham.com/H7A/I for sphere.pdf