Abstract: The article retrospectively proves three kinetic energy theorems about particle systems, namely the kinetic energy theorem about particle systems in inertial (or ground) reference frames, the kinetic energy theorem about the center of mass, and the kinetic energy theorem about particle systems in the center of mass reference frame. It points out their interrelationships and applies them to two examples, and reveals some special mechanisms by which sliding friction force do negative work on a rolling and sliding small ball. In the article, some other well-known relational expressions are incidentally proved as well. The content of the article has certain reference and utilization value for basic physics teaching, research, and examinations.

Key words: the kinetic energy theorem of a system of particles, inertial reference frame, centroid reference frame, the kinetic energy theorem of the center of mass, work done by sliding friction force