CHAPTER I - PARTICLE MECHANICS

Abstract

Publisher Summary The fundamental concept of mechanics is that of motion of a body with respect to other bodies. The relativity of motion arises from the relativity of the concept of space itself. This chapter discusses the principle of the relativity of motion. It is reasonable to begin the study of the laws of motion by considering the motion of a body of small dimensions. The motion of such a body is especially simple because there is no need to take into account the rotation of the body or the relative movement of different parts of the body. A body whose size may be neglected in considering its motion is called a particle and is a fundamental object of study in mechanics. The possibility of treating the motion of a given body as that of a particle depends not only on its absolute size but also on the conditions of the physical problem concerned. The position of a particle in space is defined by specifying three coordinates, for instance, the three Cartesian coordinates x, y, z. For this reason, a particle is said to have three degrees of freedom. The motion of a particle is described by its velocity. The chapter also discusses momentum, motion under reactive forces, centre of mass, acceleration, force, dimensions of physical quantities, motion in a uniform field, work and potential energy, the law of conservation of energy, internal energy, boundaries of the motion, elastic collisions, and angular momentum. Besides energy and momentum, another vector quantity called angular momentum is conserved for any closed system. This quantity is the sum of the angular momenta of the individual particles. The law of conservation of angular momentum is valid for a closed system and not, in general, for the individual particles forming the system; however, it may be valid for a single particle moving in a force field.