Teaching the Formula of Centripetal Acceleration

A qualitative case study on first year physics students’ challenges with mathematical derivations in mechanics

MSc thesis defense by Simon Arent Vedel

Supervisors: Ricardo Karam (IND) og Steen Hansen (NBI)

Censor: Poul Hjorth (DTU)

Abstract:
Five different derivations of the formula for centripetal acceleration were made into educational videos that were presented to first year physics students at University of Copenhagen. The students were able to participate in the research either in an online survey or as part of a semi-structured group interview. All obtained data was analyzed thematically in order to get insight into the students understanding of each derivation, to identify potential learning difficulties with focus on mathematical parts, and to see how physics students navigate in the interplay between physics and mathematics. The students described a feeling of accepting rather than understanding when confronted to arguments based on geometry. Physics students are more familiar with the mathematical fields of limits and infinitesimal calculus, however, in the combination with vectors many lacked the ability to interpret the mathematics into the physics of the situation. Closely related to this, it was also found that there is a tendency for students to prefer more general and mathematically abstract types of derivations rather than the more concrete ones. Combined, the findings suggest that the students know how to deal with mathematical algorithms but have a hard time interpreting this into a physical context.