Final answer:
The moment of inertia is calculated by summing the moments of inertia for each component of the system, applying the parallel-axis theorem for complex shapes when necessary.
Step-by-step explanation:
The question refers to finding the moment of inertia of a system consisting of balls and rigid rods. To calculate the moment of inertia for a composite object, such as the one described, you would sum the moments of inertia for each individual component. In the case provided, where the object consists of masses at the ends of a massless rod, the moment of inertia about an axis passing through the center would be I1 = 2mR2 (if R is the distance from each mass to the center of the rod). Conversely, with the axis at the end of the rod, the moment of inertia would be I2 = 4mR2, considering one mass is at the pivot and the other is twice the distance R from the pivot.
When dealing with more complex shapes like a disk at the end of a rod, the parallel-axis theorem is often applied to find the moment of inertia about an axis that is not through the center of mass. The theorem states Iparallel-axis = Icenter of mass + md2, where d is the distance from the center of mass to the new axis. For a rod of length L and mass m, and a disk of radius R and mass ma, the moment of inertia of the disk about the new axis would be Iparallel-axis = maR2 + ma(L + R)2.