Скачать или смотреть Basic Mechanics 06 - The center of mass

In this lecture we discuss a few aspects of the center of mass of a system of particles. We first show how the notion of the center of mass can simplify, at least in part, the study of the the motion of systems of particles. We then discuss a very important result about the location of the center of mass - in particular, we show that it must be located within the convex hull of the positions of the particles. We next prove another very important result that greatly simplifies the determination of the center of mass - the fact that for this purpose, the masses of parts of the system can be assumed to be at their respective center of masses. We end with another well known problem - that of how much a boat in a still lake would shift if the boatman were to move from one end of the boat to another. At the very end, we promise that there is actually more to the boatman's tale than meets the eye - and that if we tried a more realistic version the result may come as quite a surprise. That. however, will be dealt with in the next lecture.