An Elementary Treatise on Theoretical Mechanics

Sir James H. Jeans

• Publisher: Dover Publications
• Year: 2013
• Print ISBN: 9780486441795
• eBook ISBN: 9780486174693
• Topic: Sciences physiques
• Subtopic: Mécanique

In addition to being among the twentieth century’s major scientific figures, Sir James Jeans (1877–1946) was also one of the greatest modern science expositors. His classic introduction to mechanics endures as a clear and concise presentation of first principles.
Although brief, it encompasses a remarkably wide selection of topics. Its subjects include rest and motion, force and the laws of motion, forces acting on a single particle, statics of systems of particles, statics of rigid bodies, center of gravity, work, motion of a particle under constant forces, motion of systems of particles, motion of a particle under a variable force, motion of rigid bodies, and generalized coordinates. Within each chapter, the author carefully explains the most elementary concepts (such as velocity, acceleration, Newton’s laws, friction, moments, and kinetic energy), and he illustrates them with examples.
Ideal for beginning physics students or for more advanced readers in need of refreshment, the text emphasizes the fundamental physical principles rather than mathematics or applications. So clearly written that it can be read and understood outside the classroom, it features hundreds of fully worked illustrative examples and test exercises.

CHAPTER I

REST AND MOTION

INTRODUCTION

1. Uniformity of nature. If we place a stone in water, it will sink to the bottom; if we place a cork in water, it will rise to the top. These two statements will be admitted to be true not only of stones and corks which have been seen to sink or rise in water but of all stones and corks. Given a piece of stone which has never been placed in water, we feel confident that if we place it in water it will sink. What justification have we for supposing that this new and untried piece of stone will sink in water? We know that millions of pieces of stone have at different times been placed in water; we know that not a single one of these has ever been known to do anything but sink. From this we infer that nature treats all pieces of stone alike when they are placed in water, and so feel confident that a new and untried piece of stone will be treated by the forces of nature in the same way as the innumerable pieces of stone of which the behavior has been tested, and hence that it will sink in water. This principle is known as that of the uniformity of nature; what the forces of nature have been found to do once, they will, under similar conditions, do again.

2. Laws of nature. The principle just stated amounts to saying that the action of the forces of nature is governed by certain laws; these we speak of as laws of nature. For instance, if it has been found that every stone which has ever been placed in water has sunk to the bottom, then, as has already been said, the principle of uniformity of nature leads us to suppose that every stone which at any future time is placed in water will sink to the bottom; and we can then announce, as a law of nature, that any stone, placed in water, will sink to the bottom.

That part of science which deals with the laws of nature is called natural science. Natural science is divided into two parts, experimental and theoretical. Experimental science tries to discover laws of nature by observing the action of the forces of nature time after time. Theoretical science takes as its material the laws of nature discovered by experimental science, and aims at reducing them, if possible, to simpler forms, and then discovering how to predict from these laws what the action of the forces of nature will be in cases which have not actually been subjected to the test of experiment. For example, experimental science discovers that a stone sinks, that a cork floats, and a number of similar laws. From these theoretical physics arrives at the simple laws of nature which govern all phenomena of sinking or floating, and, going further, shows how these laws enable us to predict, before the experiment has been actually tried, whether a given body will sink or float. For instance, experimental science cannot discover whether a 50,000-ton ship will float or sink, because no 50,000-ton ship exists with which to experiment. The naval architect, relying on the uniformity of nature, on the laws of nature determined by experimental science, and on the method of handling these laws taught by theoretical science, may build a 50,000-ton ship with every confidence that it will behave in the way predicted by theoretical science.

3. The science of mechanics. The branch of science known as mechanics deals with the motion of bodies in space, and with the forces of nature which cause or tend to cause this motion. The laws of nature which govern the action of these forces and the motion of bodies have long been known, and were reduced to their simplest form by Newton. Thus we may say that experimental mechanics is a completed branch of science.

The present book deals with theoretical mechanics. We start from the laws supplied by experimental mechanics, and have to discuss how these laws can be used to predict the motion of bodies, — for instance, the falling of bodies to the ground, the firing of projectiles, the motion of the earth and the planets round the sun. An important class of problems which we shall have to discuss will be those in which no motion takes place, the forces of nature which tend to cause motion being so evenly balanced that no motion occurs. Such problems are known as statical.

MOTION OF A POINT

4. State of rest. Before we can reason about the motion of a body we have to determine what is meant by a body being at rest. In ordinary language we say that a train is at rest when the cars are not moving over the rails. We...

Table of contents

• Title Page
• Copyright Page
• PREFACE
• Table of Contents
• CHAPTER I - REST AND MOTION
• CHAPTER II - FORCE AND THE LAWS OF MOTION
• CHAPTER III - FORCES ACTING ON A SINGLE PARTICLE
• CHAPTER IV - STATICS OF SYSTEMS OF PARTICLES
• CHAPTER V - STATICS OF RIGID BODIES
• CHAPTER VI - CENTER OF GRAVITY
• CHAPTER VII - WORK
• CHAPTER VIII - MOTION OF A PARTICLE UNDER CONSTANT FORCES
• CHAPTER IX - MOTION OF SYSTEMS OF PARTICLES
• CHAPTER X - MOTION OF A PARTICLE UNDER A VARIABLE FORCE
• CHAPTER XI - MOTION OF RIGID BODIES
• CHAPTER XII - GENERALIZED COÖRDINATES
• INDEX
• DOVER PHOENIX EDITIONS