Book contents
- Frontmatter
- Contents
- LIST OF EXAMPLES
- PREFACE
- TO THE TEACHER
- AN INTRODUCTION TO MECHANICS
- 1 VECTORS AND VECTORS KINEMATICS—A FEW MATHEMATICAL PRELIMINARIES
- 2 NEWTON'S LAWS—THE FOUNDATIONS OF NEWTONIAN MECHANICS
- 3 MOMENTUM
- 4 WORK AND ENERGY
- 5 SOME MATHEMATICAL ASPECTS OF FORCE AND ENERGY
- 6 ANGULAR MOMENTUM AND FIXED AXIS ROTATION
- 7 RIGID BODY MOTION AND THE CONSERVATION OF ANGULAR MOMENTUM
- 8 NONINERTIAL SYSTEMS AND FICTITIOUS FORCES
- 9 CENTRAL FORCE MOTION
- 10 THE HARMONIC OSCILLATOR
- 11 THE SPECIAL THEORY OF RELATIVITY
- 12 RELATIVISTIC KINEMATICS
- 13 RELATIVISTIC MOMENTUM AND ENERGY
- 14 FOUR VECTORS AND RELATIVISTIC INVARIANCE
- INDEX
3 - MOMENTUM
- Frontmatter
- Contents
- LIST OF EXAMPLES
- PREFACE
- TO THE TEACHER
- AN INTRODUCTION TO MECHANICS
- 1 VECTORS AND VECTORS KINEMATICS—A FEW MATHEMATICAL PRELIMINARIES
- 2 NEWTON'S LAWS—THE FOUNDATIONS OF NEWTONIAN MECHANICS
- 3 MOMENTUM
- 4 WORK AND ENERGY
- 5 SOME MATHEMATICAL ASPECTS OF FORCE AND ENERGY
- 6 ANGULAR MOMENTUM AND FIXED AXIS ROTATION
- 7 RIGID BODY MOTION AND THE CONSERVATION OF ANGULAR MOMENTUM
- 8 NONINERTIAL SYSTEMS AND FICTITIOUS FORCES
- 9 CENTRAL FORCE MOTION
- 10 THE HARMONIC OSCILLATOR
- 11 THE SPECIAL THEORY OF RELATIVITY
- 12 RELATIVISTIC KINEMATICS
- 13 RELATIVISTIC MOMENTUM AND ENERGY
- 14 FOUR VECTORS AND RELATIVISTIC INVARIANCE
- INDEX
Summary
Introduction
In the last chapter we made a gross simplification by treating nature as if it were composed of point particles rather than real, extended bodies. Sometimes this simplification is justified—as in the study of planetary motion, where the size of the planets is of little consequence compared with the vast distances which characterize our solar system, or in the case of elementary particles moving through an accelerator, where the size of the particles, about 10−15 m, is minute compared with the size of the machine. However, these cases are unusual. Much of the time we deal with large bodies which may have elaborate structure. For instance, consider the landing of a spacecraft on the moon. Even if we could calculate the gravitational field of such an irregular and inhomogeneous body as the moon, the spacecraft itself is certainly not a point particle—it has spiderlike legs, gawky antennas, and a lumpy body.
Furthermore, the methods of the last chapter fail us when we try to analyze systems such as rockets in which there is a flow of mass. Rockets accelerate forward by ejecting mass backward; it is hard to see how to apply F = Ma to such a system.
In this chapter we shall generalize the laws of motion to overcome these difficulties. We begin by restating Newton's second law in a slightly modified form.
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- Information
- An Introduction to Mechanics , pp. 111 - 150Publisher: Cambridge University PressPrint publication year: 2010