Vector Algebra with Applications to Mechanics

Abstract

The physical quantities with which the science of mechanics is concerned can be loosely classified as scalars which can be completely specified by single real numbers, and vectors which require both magnitude and direction for their complete specification. Typical scalar quantities are mass, density, time, whereas vectors are typified by velocity, force, moment and acceleration. In this chapter an algebra is developed which can be applied to these vector quantities and which leads to a more concise and more comprehensible method of expressing some of the basic equations of mechanics. Once vector algebra has been developed a vector quantity can more properly be defined as a quantity with magnitude and direction which obeys the laws of vector algebra; not all quantities specified by a magnitude and a direction are vectors (see exercise 5, page 438).