Exploring the motion of rigid bodies down an inclined plane from a point mass perspective

This work originated as a project in experimental physics conducted by students in the Laboratory of Mechanics and Thermodynamics, a course designed for first-year Physics bachelors. The students were tasked with studying the motion of rigid bodies while having only been introduced to the laws of point-mass dynamics in their theoretical classes. In the proposed experiment, students discovered that bodies with circular symmetry and identical shapes take the same time to roll down an inclined plane. By appropriately fitting the experimental data, they observed that the expression for travel time is equivalent to that of a point mass, except for a multiplicative factor unique to each category of objects. This factor depends on the body's geometry and is directly related to its moment of inertia. Furthermore, we discuss how a similar result can be derived using scaling analysis, illustrating the power of this tool for students early in their physics education. This work may serve as an effective introduction for first-year Physics students to the moment of inertia, as it naturally emerges from a classic physics experiment: the inclined plane.