Mastering the Parallel Axis Theorem: Calculate Moment of Inertia with Ease

The Parallel Axis Theorem is a powerful tool in rotational dynamics that allows us to calculate the moment of inertia of a body about any axis parallel to one through its center of mass. The theorem states that if you know the moment of inertia (Iₒ) of a body about an axis through its center of mass, then the moment of inertia about any other parallel axis can be determined using the formula:

I = Iₒ + Mh²

Here, M is the mass of the body, and h is the perpendicular distance between the two axes. For example, if we know that the moment of inertia (Iₒ) of a rod about its center of mass is (1/12) ML², and we need to find the moment of inertia about an axis that is L/2 meters from the center of mass, we can apply this theorem directly.

Using the Parallel Axis Theorem:

I = Iₒ + Mh²

Substituting the known values, we get:

I = (1/12) ML² + M (L/2)² = (1/3) ML²

This formula allows us to solve for the moment of inertia about any axis, making it a crucial concept in understanding rotational motion and dynamics. This video explains the Parallel Axis Theorem in detail, walking you through a practical example to ensure you fully grasp how to apply it in physics problems