Question

Why the formula for calculating moment of inertia is same for hoop and disc?

Answer 1

The moment of inertia of hoop and disc do not have the same formula.

Explanation:

The formula for moment of inertia of a hoop is `I = M*R^2`.

The formula for moment of inertia of a disk is `I = (M*R^2)/2`.

Review this Wikipedia webpage:
https://en.wikipedia.org/wiki/List_of_moments_of_inertia

You are correct to think they should not have identical formulas. Since all of the hoop's mass is at the radius, while much of the disk's mass is closer to the axis of rotation than the rim, the difference is significant.

I hope this helps,
Steve