Theoretical Mechanics for Sixth Forms (eBook)

in Two Volumes

C. Plumpton, W. A. Tomkys (Autoren)

eBook Download: PDF

2017 | 2. Auflage
432 Seiten
Elsevier Science (Verlag)
9781483137803 (ISBN)

Infos

Theoretical Mechanics for Sixth Forms, Volume 2 deals with mathematics as a double subject for sixth-form pupils. This book is a continuation of the revised edition of the course in Theoretical Mechanics. This volume discusses the principle of virtual work, stability of equilibrium, vector algebra, and the motion of bodies with variable mass-subjects that can help the student prepare for the freshman year in a university or in one of the polytechnic schools. Compared to the earlier edition, this volume discusses in more detail topics such as the motion of a particle in two dimensions and systems of coplanar forces. This book also emphasizes vector algebra and its many applications, explaining the concept of a vector, the Cartesian coordinates and components, the definitions of vectors and scalars, and vector applications to kinetics. This text also contains exercise problems with answers. This volume can be used for sixth-form students in the U.K. and is also suitable for third year students of a sixth form course as preparation for further studies.

Inhalt

Front Cover 1
Theoretical Mechanics for Sixth Forms 4
Copyright Page 5
Table of Contents 6
PREFACE 10
CHAPTER XV. THE MOTION OF A RIGID BODY ABOUT A FIXED AXIS 12
15.1. The Definition of a Rigid Body 12
15.2. The Kinetic Energy of a Rigid Body Rotating about a Fixed Axis 12
15.3. Calculation of Moments of Inertia in Particular Cases 13
15.4. Conservation of Energy 25
15.5. The Compound Pendulum 34
15.6. The Equation of Motion for a Rigid Body Rotating about a Fixed Axis 41
15.7. The Force Exerted on the Axis of Rotation 46
15.8. Impulse and Momentum 51
15.9. Note on the Relationship between the Equations of Motion of Rotation of a Rigid Body and the Equations of Motion for a Particle moving in a Straight Line 60
MISCELLANEOUS EXERCISES XV 61
CHAPTER XVI. FREE MOTION OF A RIGID BODY IN TWO DIMENSIONS 66
16.1. Angular Velocity and Angular Acceleration 66
16.2. Instantaneous Centre of Rotation 67
16.3. The Motion of a Rigid Lamina Referred to its Centre of Mass 72
16.4. The Kinetic Energy of a Lamina Moving in its Plane 74
16.5. The Angular Momentum about an Arbitrary Axis Perpendicular to its Plane of a Lamina Moving in its Own Plane 77
16.6. Three-dimensional Motion 78
16.7. Impulsive Motion 78
16.8. Application to Problems 80
MISCELLANEOUS EXERCISES XVI 89
CHAPTER XVII. MOTION WITH VARIABLE ACCELERATION 94
17.1. Kinematics 94
17.2. Dynamical Problems 101
17.3. Rate of Working by a Variable Force 116
17.4. Equations of Motion Deduced from the Energy Equation 121
17.5. Damped Harmonic Oscillations 124
MISCELLANEOUS EXERCISES XVII 134
CHAPTER XVIII. MOTION OF A PARTICLE IN TWO DIMENSIONS 141
18.1. A Note on Vectors 141
18.2. Motion of a Particle in Two Dimensions—Special Representations 146
18.3. Motion of a Particle on a Smooth Curve 151
18.4. The Angular Momentum of a Particle about an Axis 157
18.5. The Motion of a Projectile 166
MISCELLANEOUS EXERCISES XVIII 174
CHAPTER XIX. SYSTEMS OF COPLANAR FORCES 179
19.1. Forces Acting on a Particle 179
19.2. Coplanar Forces Acting on a Rigid Body 180
19.3. The Equivalence of Sets of Coplanar Forces 183
19.4. The Equilibrium of a Rigid Body under the Action of a System of Coplanar Forces 193
19.5. A Law of Vector Addition 194
19.6. The Moment of a Force as a Vector 196
MISCELLANEOUS EXERCISES XIX 199
CHAPTER XX. THE EQUILIBRIUM OF RIGID BODIES 203
20.1. Conditions of Equilibrium 203
20.2. Hinged Bodies 211
20.3. Problems of Equilibrium Involving More than One Body 214
20.4. The Equilibrium of the Hinge 220
MISCELLANEOUS EXERCISES XX 228
CHAPTER XXI. THE PRINCIPLE OF VIRTUAL WORK 232
21.1. The Work Done by a Force Acting on a Particle 232
21.2. The Potential Energy of a Particle 235
21.3. Extension to Rigid Bodies 236
21.4. The Principle of Virtual Work 246
21.5. Applications of the Principle of Virtual Work 247
MISCELLANEOUS EXERCISES XXI 259
CHAPTER XXII. STABILITY OF EQUILIBRIUM 263
22.1. The Concept of Stability 263
22.2. Stability of Equilibrium 265
22.3. Rolling Stability—The Rocking Stone 281
MISCELLANEOUS EXERCISES XXII 285
CHAPTER XXIII. LIGHT FRAMEWORKS 288
23.1. Graphical Method of Obtaining the Resultant of a System of Coplanar Forces 288
23.2. Light Frameworks 292
23.3. Calculation of the Stresses in the Bars of a Light Framework 294
23.4. Graphical Investigation of the Stresses in a Light Framework 297
23.5. The Method of Sections 303
MISCELLANEOUS EXERCISES XXIII 307
CHAPTER XXIV. CONTINUOUSLY DISTRIBUTED FORCES 315
24.1. Introduction—Shearing Force and Bending Moment 315
24.2. Relations Between Bending Moment, Shearing Force and Loading 320
24.3. A Uniform Flexible Inelastic String Hanging Under Gravity 325
24.4. The Tightly Stretched Wire 333
24.5. A Uniformly Loaded Inextensible String 335
MISCELLANEOUS EXERCISES XXIV 338
CHAPTER XXV. THE MOTION OF BODIES WITH VARIABLE MASS 341
25.1. Introduction 341
25.2. Rectilinear Motion of a Particle of Variable Mass—Rockets 342
25.3. The Rectilinear Motion of Chains 349
MISCELLANEOUS EXERCISES XXV 354
CHAPTER XXVI. VECTOR ALGEBRA 359
26.1. The Concept of a Vector 359
26.2. Cartesian Coordinates and Components 360
26.3. The Formulae of Three-dimensional Coordinate Geometry 363
26.4. The Definitions of Vectors and Scalars 366
26.5. The Addition and Subtraction of Vectors 367
26.6. Some Applications of Vectors to Geometry 369
26.7. The Scalar Product 377
26.8. The Vector Product 384
26.9. Triple Products 396
26.10. Applications to Kinematics 402
MISCELLANEOUS EXERCISES XXVI 405
ANSWERS TO THE EXERCISES 414
INDEX 430

Produkt-Details

• Erscheint lt. Verlag: 4.5.2017
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Mechanik
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Maschinenbau
• ISBN-13: 9781483137803 / 9781483137803