Parallel Axis Theorem Derivation

The video tutorial explains the parallel axis theorem, which helps determine the moment of inertia of a rigid body about an axis parallel to one through its center of mass. The theorem states that the rotational inertia about any parallel axis equals the inertia about the center of mass plus the product of the mass and the square of the distance between the axes. The video provides a detailed proof, using mathematical concepts like integrals and the Pythagorean theorem, and concludes with a recap of the theorem's application.

Describe how the Pythagorean theorem is applied in the derivation of the parallel axis theorem.

How does the integral of position with respect to mass relate to the center of mass of an object?

What is the relationship between the distance D and the moment of inertia according to the parallel axis theorem?