Final answer:
The moment of inertia for a system involves applying formulas that depend on the geometry and axis. For a thin rod, it changes with the location of the axis. The total inertia for composite objects like a rod and sphere is the sum of individual inertias.
Step-by-step explanation:
To calculate the moment of inertia for a system consisting of rods and/or spheres, we make use of the formulas specific to different geometric shapes and their respective axes of rotation. When rods are considered massless, we only calculate the inertia for the attached masses. For a thin rod of mass M and length L about an axis through the rod at L/3, the moment of inertia is given by I = ML²/3. When we move the axis of rotation to the end of the rod, this becomes I = ML²/3. For a combination of a rod and a solid sphere, the total moment of inertia is the sum of the individual moments, taking into account the parallel axis theorem for any offset masses.