Fundamental Balance Relations

Abstract

Recall from Chap. 1that one of the best-known equations in science is F = ma, which is called Newton’s second law of motion. This equation asserts that in an inertial frame of reference, the time rate of change of the linear momentum mv for a mass particle m must balance the forces F that are applied to the particle. For this reason, this “law of motion” is also called the principle (actually postulate) of the balance of linear momentum. Whereas Sir I. Newton considered only individual mass points (like the Moon or an apple), L. Euler showed that many bodies can be treated as a continuous collection of mass points (i.e., a continuum), each particle of which obeys Newton’s second law. Indeed, as it turns out, there are three basic postulates for any continua,