Theoretical Mechanics for Sixth Forms

Theoretical Mechanics for Sixth Forms

in Two Volumes

2nd Edition - January 1, 1972

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  • Authors: C. Plumpton, W. A. Tomkys
  • eBook ISBN: 9781483137803

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Description

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.

Table of Contents


  • Preface

    Chapter XV. The Motion of a Rigid Body about a Fixed Axis

    15.1. The Definition of a Rigid Body

    15.2. The Kinetic Energy of a Rigid Body Rotating about a Fixed Axis

    15.3. Calculation of Moments of Inertia in Particular Cases

    15.4. Conservation of Energy

    15.5. The Compound Pendulum

    15.6. The Equation of Motion for a Rigid Body Rotating about a Fixed Axis

    15.7. The Force Exerted on the Axis of Rotation

    15.8. Impulse and Momentum

    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

    Chapter XVI. Free Motion of a Rum Body in Two Dimensions

    16.1. Angular Velocity and Angular Acceleration

    16.2. Instantaneous Center of Rotation

    16.3. The Motion of a Rigid Lamina Referred to Its Center of Mass

    16.4. The Kinetic Energy of a Lamina Moving in Its Plane

    16.5. The Angular Momentum about an Arbitrary Axis Perpendicular to Its Plane of a Lamina Moving in Its Own Plane

    16.6. Three-dimensional Motion

    16.7. Impulsive Motion

    16.8. Application to Problems

    Chapter XVII. Motion with Variable Acceleration

    17.1. Kinematics

    17.2. Dynamical Problems

    17.3. Rate of Working by a Variable Force

    17.4. Equations of Motion Deduced from the Energy Equation

    17.5. Damped Harmonic Oscillations

    Chapter XVIII. Motion of a Particle in Two Dimensions

    18.1. A Note on Vectors

    18.2. Motion of a Particle in Two Dimensions—special Representations

    18.3. Motion of a Particle on a Smooth Curve

    18.4. The Angular Momentum of a Particle about an Axis

    18.5. The Motion of a Projectile

    Chapter XIX. Systems of Coplanar Forces

    19.1. Forces Acting on a Particle

    19.2. Coplanar Forces Acting on a Rigid Body

    19.3. The Equivalence of Sets of Coplanar Forces

    19.4. The Equilibrium of a Rigid Body under the Action of a System of Coplanar Forces

    19.5. A Law of Vector Addition

    19.6. The Moment of a Force as a Vector

    Chapter XX. The Equilibrium of Rigid Bodies

    20.1. Conditions of Equilibrium

    20.2. Hinged Bodies

    20.3. Problems of Equilibrium Involving More than One Body

    20.4. The Equilibrium of the Hinge

    Chapter XXI. The Principle of Virtual Work

    21.1. The Work Done by a Force Acting on a Particle

    21.2. The Potential Energy of a Particle

    21.3. Extension to Rigid Bodies

    21.4. The Principle of Virtual Work

    21.5. Applications of the Principle of Virtual Work

    Chapter XXII. Stability of Equilibrium

    22.1. The Concept of Stability

    22.2. Stability of Equilibrium

    22.3. Rolling Stability - The Rocking Stone

    Chapter XXIII. Light Frameworks

    23.1. Graphical Method of Obtaining the Resultant of a System of Coplanar Forces

    23.2. Light Frameworks

    23.3. Calculation of the Stresses in the Bars of a Light Framework

    23.4. Graphical Investigation of the Stresses in a Light Framework

    23.5. The Method of Sections

    Chapter XXIV. Continuously Distributed Forces

    24.1. Introduction - Shearing Force and Bending Moment

    24.2. Relations between Bending Moment, Shearing Force and Loading

    24.3. A Uniform Flexible Inelastic String Hanging under Gravity

    24.4. The Tightly Stretched Wire

    24.5. A Uniformly Loaded Inextensible String

    Chapter XXV. The Motion of Bodies with Variable Mass

    25.1. Introduction

    25.2. Rectilinear Motion of a Particle of Varying Mass—rockets

    25.3. The Rectilinear Motion of Chains

    Chapter XXVI. Vector Algebra

    26.1. The Concept of a Vector

    26.2. Cartesian Coordinates and Components

    26.3. The Formula of Three-dimensional Coordinate Geometry

    26.4. The Definitions of Vectors and Scalars

    26.5. The Addition and Subtraction of Vectors

    26.6. Some Applications of Vectors to Geometry

    26.7. The Scalar Product

    26.8. The Vector Product

    26.9. Triple Products

    26.10. Applications to Kinematics

    Answers to the Exercises

    Index

Product details

  • No. of pages: 432
  • Language: English
  • Copyright: © Pergamon 1972
  • Published: January 1, 1972
  • Imprint: Pergamon
  • eBook ISBN: 9781483137803

About the Authors

C. Plumpton

W. A. Tomkys

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