Instructor’s dilemma: requiring two-dimensional measurements to describe one-dimensional motion, applied to a person walking

Abstract

Abstract Introductory physics courses uses simplified models and approximations to convey fundamental concepts. Many of these simplifications are introduced without explanation. When considering motion, one such simplification is the point particle approximation. That is to assume that the motion of an extended object can be represented by the motion of a single point, generally the object’s centre of mass. For some objects the exact position of the centre of mass could be difficult to locate and the procedure beyond the scope of an introductory course. Furthermore, if the object changes its shape while in motion, thereby redistributing its mass, the relative position of the centre of mass also changes. In such instances the physical measurements of the object’s position could be rather complicated, especially if the task is to choose one physical marker on the object that best represents its motion. If the object is travelling in a straight line [one-dimensional (1D) motion] and the motion of physical marker does not closely match that of the object, a two-dimensional measurement would be required to describe 1D motion. Hereby instructors might be challenged to explain seemingly simple phenomena, like determining the position of an object, within the confines of the introductory course. In order to assist instructors in this regard, we present an experimental measurement procedure which aims to minimize the error in position measurements of objects that changes their shape while in motion. We apply the procedure to determine the position of a walking person.