Postprint version. Published in American Journal of Physics, Volume 81, Issue 3, March 1, 2013, pages 165-172.
The definitive version is available at https://doi.org/10.1119/1.4773561.
We have found that incorporating computer programming into introductory physics requires problems suited for numerical treatment while still maintaining ties with the analytical themes in a typical introductory-level university physics course. In this paper, we discuss a numerical adaptation of a system commonly encountered in the introductory physics curriculum: the dynamics of an object constrained to move along a curved path. A numerical analysis of this problem that includes a computer animation can provide many insights and pedagogical avenues not possible with the usual analytical treatment. We present two approaches for computing the instantaneous kinematic variables of an object constrained to move along a path described by a mathematical function. The first is a pedagogical approach, appropriate for introductory students in the calculus-based sequence. The second is a more generalized approach, suitable for simulations of more complex scenarios.
This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Association of Physics Teachers. The following article appeared in American Journal of Physics.