Inertial and non-inertial frames of reference: A kinematic approach through video analysis

In introductory approaches to Mechanics, whether in higher education or basic education, discussions regarding the distinctions between the concepts of inertial and non-inertial frames of reference tend to be confined to Dynamics, especially with the establishment of Newton’s laws, devoid of experimental analyses. Nevertheless, the notion of a frame of reference holds paramount significance for the characterization of motion, even within the strict purview of Kinematics. In this context, we aspire to underpin the concepts of inertial and non-inertial frames of reference through the exploration of an educational experimental activity conducted via video analysis. Specifically, we inquire into the motion of a small sphere in three situations of relative motion between two frames of reference: uniform rectilinear motion; uniformly accelerated rectilinear motion, with ace-location and velocity in the same direction; and uniformly accelerated rectilinear motion, with acceleration and velocity in opposite directions. We derive a kinematic description grounded in Galilean Relativity’s Principle and the transformation relationships between inertial and non-inertial frames of reference, in addition to the adjustments of the motion curves acquired through video analysis. We proffer the notion that other facets such as scale invariance, temporal simultaneity, and inquiries related to the historical development of the concepts of reference frame and absolute and relative motion can also be addressed in the discussions surrounding the proposed experiments.

Keywords
Kinematics; Inertial Reference Frames; Non-Inertial Reference Frames; Video Analysis