Final answer:
The moment of inertia can change in different ways when separate objects fall apart or collide. It can stay the same or decrease in an explosion or an object breaking apart, and it increases when objects collide and stick together.
Step-by-step explanation:
When separate objects fall apart or collide, the moment of inertia can change depending on the situation. In the case of an explosion or an object breaking apart, the moment of inertia can stay the same or decrease, depending on how the pieces move after the interaction. In the case of a collision where two or more objects stick together, forming a composite object, the moment of inertia increases because the mass is distributed further from the axis of rotation.