Plumpton / Tomkys Theoretical Mechanics for Sixth Forms

in Two Volumes
2. Auflage 2017
ISBN: 978-1-4831-3780-3
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 432 Seiten, Web PDF

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.

Autoren/Hrsg.

Plumpton, C.

Tomkys, W. A.

Inhaltsverzeichnis

1;Front Cover;1
2;Theoretical Mechanics for Sixth Forms;4
3;Copyright Page;5
4;Table of Contents;6
5;PREFACE;10
6;CHAPTER XV. THE MOTION OF A RIGID BODY ABOUT A FIXED AXIS;12
6.1;15.1. The Definition of a Rigid Body;12
6.2;15.2. The Kinetic Energy of a Rigid Body Rotating about a Fixed Axis;12
6.3;15.3. Calculation of Moments of Inertia in Particular Cases;13
6.4;15.4. Conservation of Energy;25
6.5;15.5. The Compound Pendulum;34
6.6;15.6. The Equation of Motion for a Rigid Body Rotating about a Fixed Axis;41
6.7;15.7. The Force Exerted on the Axis of Rotation;46
6.8;15.8. Impulse and Momentum;51
6.9;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
6.10;MISCELLANEOUS EXERCISES XV;61
7;CHAPTER XVI. FREE MOTION OF A RIGID BODY IN TWO DIMENSIONS;66
7.1;16.1. Angular Velocity and Angular Acceleration;66
7.2;16.2. Instantaneous Centre of Rotation;67
7.3;16.3. The Motion of a Rigid Lamina Referred to its Centre of Mass;72
7.4;16.4. The Kinetic Energy of a Lamina Moving in its Plane;74
7.5;16.5. The Angular Momentum about an Arbitrary Axis Perpendicular to its Plane of a Lamina Moving in its Own Plane;77
7.6;16.6. Three-dimensional Motion;78
7.7;16.7. Impulsive Motion;78
7.8;16.8. Application to Problems;80
7.9;MISCELLANEOUS EXERCISES XVI;89
8;CHAPTER XVII. MOTION WITH VARIABLE ACCELERATION;94
8.1;17.1. Kinematics;94
8.2;17.2. Dynamical Problems;101
8.3;17.3. Rate of Working by a Variable Force;116
8.4;17.4. Equations of Motion Deduced from the Energy Equation;121
8.5;17.5. Damped Harmonic Oscillations;124
8.6;MISCELLANEOUS EXERCISES XVII;134
9;CHAPTER XVIII. MOTION OF A PARTICLE IN TWO DIMENSIONS;141
9.1;18.1. A Note on Vectors;141
9.2;18.2. Motion of a Particle in Two Dimensions—Special Representations;146
9.3;18.3. Motion of a Particle on a Smooth Curve;151
9.4;18.4. The Angular Momentum of a Particle about an Axis;157
9.5;18.5. The Motion of a Projectile;166
9.6;MISCELLANEOUS EXERCISES XVIII;174
10;CHAPTER XIX. SYSTEMS OF COPLANAR FORCES;179
10.1;19.1. Forces Acting on a Particle;179
10.2;19.2. Coplanar Forces Acting on a Rigid Body;180
10.3;19.3. The Equivalence of Sets of Coplanar Forces;183
10.4;19.4. The Equilibrium of a Rigid Body under the Action of a System of Coplanar Forces;193
10.5;19.5. A Law of Vector Addition;194
10.6;19.6. The Moment of a Force as a Vector;196
10.7;MISCELLANEOUS EXERCISES XIX;199
11;CHAPTER XX. THE EQUILIBRIUM OF RIGID BODIES;203
11.1;20.1. Conditions of Equilibrium;203
11.2;20.2. Hinged Bodies;211
11.3;20.3. Problems of Equilibrium Involving More than One Body;214
11.4;20.4. The Equilibrium of the Hinge;220
11.5;MISCELLANEOUS EXERCISES XX;228
12;CHAPTER XXI. THE PRINCIPLE OF VIRTUAL WORK;232
12.1;21.1. The Work Done by a Force Acting on a Particle;232
12.2;21.2. The Potential Energy of a Particle;235
12.3;21.3. Extension to Rigid Bodies;236
12.4;21.4. The Principle of Virtual Work;246
12.5;21.5. Applications of the Principle of Virtual Work;247
12.6;MISCELLANEOUS EXERCISES XXI;259
13;CHAPTER XXII. STABILITY OF EQUILIBRIUM;263
13.1;22.1. The Concept of Stability;263
13.2;22.2. Stability of Equilibrium;265
13.3;22.3. Rolling Stability—The Rocking Stone;281
13.4;MISCELLANEOUS EXERCISES XXII;285
14;CHAPTER XXIII. LIGHT FRAMEWORKS;288
14.1;23.1. Graphical Method of Obtaining the Resultant of a System of Coplanar Forces;288
14.2;23.2. Light Frameworks;292
14.3;23.3. Calculation of the Stresses in the Bars of a Light Framework;294
14.4;23.4. Graphical Investigation of the Stresses in a Light Framework;297
14.5;23.5. The Method of Sections;303
14.6;MISCELLANEOUS EXERCISES XXIII;307
15;CHAPTER XXIV. CONTINUOUSLY DISTRIBUTED FORCES;315
15.1;24.1. Introduction—Shearing Force and Bending Moment;315
15.2;24.2. Relations Between Bending Moment, Shearing Force and Loading;320
15.3;24.3. A Uniform Flexible Inelastic String Hanging Under Gravity;325
15.4;24.4. The Tightly Stretched Wire;333
15.5;24.5. A Uniformly Loaded Inextensible String;335
15.6;MISCELLANEOUS EXERCISES XXIV;338
16;CHAPTER XXV. THE MOTION OF BODIES WITH VARIABLE MASS;341
16.1;25.1. Introduction;341
16.2;25.2. Rectilinear Motion of a Particle of Variable Mass—Rockets;342
16.3;25.3. The Rectilinear Motion of Chains;349
16.4;MISCELLANEOUS EXERCISES XXV;354
17;CHAPTER XXVI. VECTOR ALGEBRA;359
17.1;26.1. The Concept of a Vector;359
17.2;26.2. Cartesian Coordinates and Components;360
17.3;26.3. The Formulae of Three-dimensional Coordinate Geometry;363
17.4;26.4. The Definitions of Vectors and Scalars;366
17.5;26.5. The Addition and Subtraction of Vectors;367
17.6;26.6. Some Applications of Vectors to Geometry;369
17.7;26.7. The Scalar Product;377
17.8;26.8. The Vector Product;384
17.9;26.9. Triple Products;396
17.10;26.10. Applications to Kinematics;402
17.11;MISCELLANEOUS EXERCISES XXVI;405
18;ANSWERS TO THE EXERCISES;414
19;INDEX;430