Question

What is the moment of inertia of a disc about a tangent perpendicular to plane of disk?

Answer 1

   The (second) moment of inertia of a disc of mass M and of radius R about an axis passing through the center of the disc and perpendicular to the plane of the disc = 1/2 M R².

The center of disc is the center of mass too.

   The distance between parallel lines: Axis through center and a tangent perpendicular to plane of the disc :  = R

Using the Parallel axes theorem, we get get the moment of inertia about the tangent perpendicular to plane of disc.

     I = MOI about COM + M (distance between the axes)²
       = 1/2 M R² + M R²
       = 3/2  M R².