  In a paper ( posthumously ) co-authored by Isaac Newton himself, the primacy
of geometric notions in pedagogical expositions of centripetal acceleration has
been clearly asserted. In the present paper we demonstrate how this pedagogical
prerogative can inform the design of an experiment involving an
accelerometer-equipped smartphone rotating uniformly in a horizontal plane.
Specifically, the location of the sensor itself within the body of the
smartphone will be determined using a technique that is purely geometrical in
nature, relying on nothing more than the notion that centripetal accelerations
are centrally-pointing. The complete absence of algebraic manipulations obliges
students to focus exclusively on the development of their geometrical reasoning
abilities. In particular, it provides a healthy challenge for those
algebraically-accomplished students for whom equations, calculations and data
tables represent a means of avoiding a direct confrontation with the imposing
spectre of material that is otherwise purely conceptual in nature.
