[Physics] Moment of inertia of a disc with masses attached at the rim

Question

Does the moment of inertia of a disc with some masses attached at the rim be the same as one without the attached masses?
Or is it necessary to use parallel axis theorem to incorporate the moment of inertia of the attached masses about the same axis of rotation?

Answer 1

Parallel axis theorem does not care for mass distribution along the rotation axis, only away from the rotation axis. The answer is yes then.

Below is the formula for the total mass moment of inertia of the disk + $N$ masses, each attached a distance $r_i$ from the axis of rotation.

$$ I_{total} = I_{disk} + \sum_{i=1}^N \left( I_i + m_i r_i^2 \right) $$