For the case of a rotational inertia about an offset axis. The basic equation is
Torque = MassMomentOfInertia X RotationalAcceleration T=Jα
(duh...going on fuzzy memory here, check my formula) J-offsetAxis = Ʃ(JZero + m*dSquared) (or something like that...it's in the dynamics textbooks)
Example: robot End Of Arm Tool rotating around the robot wrist joint axis. What is torque requirement at wrist axis for offset tool load as the robot is swinging that inertia through space?
This calculation could be extensive and tedious for complicated tools where one must account part-by-part for each individual mass and offset distance, and for each rotation axis. Done this before: tedious.
A SIMPLIFIED approach is a point mass at an offset distance from rotation axis. This distance is the radius of gyration. Is there a physical manifestation of Radius Of Gyration? Sometimes.