## Fundamental Laws of Mechanics PDF book by I. E. Irodov (1980)

*The book is intended for first-year students of physics but can also be useful to senior students and lecturers.*

**Introduction:**

The objective of the book is to draw the readers' attention to the basic laws of mechanics, that is, to the laws of motion and to the laws of conservation of energy, momentum and angular momentum, as well as to show how these laws are to be applied in solving various specific problems. At the same time, the author has excluded all things of minor importance in order to concentrate on the questions which 'j^re the hardest to comprehend. The book consists of two parts:

(1) classical mechanics and

(2) relativistic mechanics. In the first part, the laws of mechanics are treated in the Newtonian approximation, i.e. when motion velocities are much less than the velocity of light,

while in the second part of the book velocities comparable to that of light is considered. Each chapter opens with a theoretical essay followed by a number of the most instructive and interesting examples and problems, with* solutions provided. There are about 80 problems altogether; being closely associated with the introductory text, they develop and supplement it and therefore their examination is of equal importance. A few corrections and refinements have been made in the present edition to stress the physical essence of the problems studied. This holds true primarily for Newton's second law and the conservation laws. Some new examples and problems have been provided. The book is intended for first-year students of physics but can also be useful to senior students and lecturers.

**Content of the book:**

Preface 7

Notation 9

Introduction 11

PART ONE

CLASSICAL MECHANICS

Chapter 1. Essentials of Kinematics 14

§ 1.1. Kinematics of a Point 14

§ 1.2. Kinematics of a Solid. 21

| 1.3. Transformation of Velocity and Acceleration on

Transition to Another Reference Frame 30

Problems, to Chapter 1 34

Chapter 2. The Basic Equation of Dynamics 41

§ 2.1. Inertial Reference Frames 41

§ 2.2. The Fundamental Laws of Newtonian Dynamics 44

§ 2.3. Laws of Forces 50

§ 2.4. The Fundamental Equation of Dynamics ... 52

§ 2.5. Non-inertial Reference Frames. Inertial Forces 56

Problems to Chapter 2 61

Chapter 3. Energy Conservation Law 72

§ 3.1. On Conservation Laws 72

§ 3.2. Work and Power .... 74

§ 3.3. Potential Field of Forces 79

§ 3.4. Mechanical Energy of a Particle in a Field 90

§ 3.5. The Energy Conservation Law for a System 94

Problems to Chapter 3 104

Chapter 4. The Law of Conservation of Momentum 114

§ 4.1. Momentum. The Law of Its Conservation 114

§ 4.2. Centre of Inertia. The C Frame 120

§ 4.3. The collision of Two Particles .... 126

§ 4.4. The motion of a Body with Variable Mass 136

Problems to Chapter 4 139

Chapter 5. The Law of Conservation of Angular Momentum 147

§ 5.1. Angular Momentum of a Particle. Moment of Force 147

\ 5.2. The Law of Conservation of Angular Momentum 154

§ 5.3. Internal Angular Momentum 160

§ 5.4. Dynamics of a Solid 164

Problems to Chapter 5 178

5 m Contents

PART TWO

RELATIVISTIC MECHANICS

Chapter 6. Kinematics in the Special Theory of Relativity 189

§ 6.1. Introduction .... 189

§ 6.2. Einstein's Postulates 194

§ 6.3. Dilation of Time and Contraction of Length 198

§ 6.4. Lorentz Transformation 207

§ 6.5. Consequences of Lorentz Transformation .... 210

§ 6.6. Geometric Description of Lorentz Transformation 217

Problems to Chapter 6 221

Chapter 7. Relativistic Dynamics 227

§ 7.1. Relativistic Momentum 227

§ 7.2. Fundamental Equation of Relativistic Dynamics 231

§ 7.3. Mass-Energy Relation . . . 233

§ 7.4. Relation Between Energy and Momentum of a Particle 238

§ 7.5. System of Relativistic Particles 242

Problems to Chapter 7 249

Appendices 257

1. The motion of a Point in Polar Coordinates 257

2. On Keplerian Motion 258

3. Demonstration of Steiner's Theorem 260

4. Greek Alphabet 262

5. Some Formulae of Algebra and Trigonometry 262

6. Table of Derivatives and Integrals 263

7. Some Facts About Vectors 264

8. Units of Mechanical Quantities in the SI and CGS

Systems 266

9. Decimal Prefixes for the Names of Units 266

10. Some Extrasystem Units % 267

11. Astronomic Quantities 267

12. Fundamental Constants 267

**Author: I. E. Irodov**

**Publication Date:1980**

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