# About the Moment of Inertia

Hello, I am a computer science major and Ex-Biology grad student, my knowledge in physics is humble, but I got a little curious when my professor derived the expressions of moment of inertia for different objects.

The moment of Inertia of a thin disk is 1/2MR2, but it is the same as the moment of Inertia for a cylinder and, surprisingly, the same for a thin hoop rotating about its diameter. So, in short:

I disk/perpendicular to axis of rotation = I Cylinder/perpendicular to axis of rotation= I thin hoop/through diameter

QUESTION:
How do we explain the similar moments of Inertia of the different objects?

My hypothesis concerning the moment of inertia of the thin hoop:
The hoop is rotating about its own diameter, if we take any point on the hoop and project its rotation on a plane perpendicular to the axis of rotation, we'll end up with a circle. Now, if we do the to every point on the hoop, we end up with a disk. Hence, the similar moment of inertia between the disk and the hoop!

BvU
$$I\equiv \int r^2\, dm$$