Choosing an appropriate reference point is crucial in solving rigid body motion problems, effectively simplifying the problem-solving process. In comparison to the center of mass axis, a non-centroid axis of rotation provides a more flexible perspective. This paper, by deriving the angular momentum theorem in a non-centroid system and using the example of a ball colliding with a free rod, illustrates its practical application in real-world scenarios. The paper offers readers a novel approach to addressing rigid body motion problems, particularly providing intuitive insights in complex situations.