Question

Discuss whether the additivity of the rotational inertia is made.

Answer 1

Moment of Inertia is additive about the same axis. It means that moment of inertia follows scalar (algebraic) addition as long as it is referred to same axis.  for example if we consider a collection of particles, then their moment of inertia about an axis is found by simply adding up their perpendicular distances from the axis. It means that  the moment of inertia of a composite system is the sum of the moments of inertia of its component subsystems when taken about the same axis.