Teaching Rotational Physics with Bivectors
Abstract
Angular momentum is traditionally taught as a (pseudo)vector quantity, tied closely to the cross product. This approach is familiar to experts but challenging for students, and full of subtleties. Here, we present an alternative pedagogical approach: angular momentum is described using bivectors, which can be visualized as "tiles" with area and orientation and whose components form an antisymmetric matrix. Although bivectors have historically been studied in specialized contexts like spacetime classification or geometric algebra, they are no more complicated to understand than cross products. The bivector language provides a more fundamental definition for rotational physics, and opens the door to understanding rotations in relativity and in extra dimensions.
Cite
@article{arxiv.2207.03560,
title = {Teaching Rotational Physics with Bivectors},
author = {Steuard Jensen and Jack Poling},
journal= {arXiv preprint arXiv:2207.03560},
year = {2023}
}
Comments
15 pages, 13 figures. (Version accepted for publication in the American Journal of Physics, with supplemental appendices included.) This revision incorporates feedback from peer review, including clearer figures and text throughout. Example calculations of the inertia tensor in three and four dimensions have been added