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The moment of Inertia of a thin disk is

**1/2MR**, but it is the same as the moment of Inertia for a cylinder and, surprisingly

^{2}**,**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!