The discussion centers on the proof of the parallel axis theorem, highlighting a common misconception that the distance between the two axes in the formula is always perpendicular. It is noted that in the proof, the distance is represented as a hypotenuse, not perpendicular. The theorem applies to displacements in both the x and y directions, emphasizing the relationship between the original and transformed axes, which remain parallel. The mathematical expressions provided illustrate the derivation of the moment of inertia in relation to the center of mass. This clarification addresses potential confusion regarding the theorem's application and proof.
