Physics

The parallel-axis theorem connects the moment of inertia about any axis to the moment of inertia about a parallel axis through the center of mass—the key insight is that rotational resistance depends both on how mass is distributed around the center of mass and how far the entire body is shifted from your chosen axis. Once you understand that these two effects add independently, the theorem becomes a natural way to avoid calculating complicated integrals for off-center rotations.

The parallel-axis theorem connects the moment of inertia about any axis to the moment of inertia about a parallel axis through the center of mass—the key insight is that rotational resistance depends both on how mass is distributed around the center of mass and how far the entire body is shifted from your chosen axis. Once you understand that these two effects add independently, the theorem becomes a natural way to avoid calculating complicated integrals for off-center rotations.