parallellaxelteoremet

Parallellaxelteoremet, also known as the parallel axis theorem, is a fundamental concept in physics, particularly in mechanics, that relates the moment of inertia of a rigid body about an axis to the moment of inertia about a parallel axis passing through the body's center of mass. The theorem states that if I_cm is the moment of inertia about an axis through the center of mass, and I is the moment of inertia about a parallel axis located a distance d away from the center of mass axis, then I = I_cm + Md^2, where M is the total mass of the body.

This theorem is incredibly useful for calculating moments of inertia for objects that do not have a standard axis of rotation passing through their center of mass. Instead of performing complex integration over the entire mass distribution for every possible axis, one can first find the moment of inertia about the parallel axis through the center of mass, which is often a known or simpler value, and then apply the parallel axis theorem. The term Md^2 accounts for the distribution of the mass at a distance d from the center of mass axis. It is crucial that the two axes are parallel and that one of them passes through the center of mass for the theorem to be applicable. The theorem simplifies many calculations in rotational dynamics, making it a cornerstone for understanding how objects rotate.