Theoretical Mechanics for Sixth Forms

Theoretical Mechanics for Sixth Forms, Second Edition is a 14-chapter book that begins by elucidating the nature of theoretical mechanics. The book then describes the statics of a particle in illustration of the techniques of handling vector quantities. Subsequent chapters focus on the principle of moments, parallel forces and centers of gravity; and the application of Newton's second law to the dynamics of a particle and the ideas of work and energy, impulse and momentum, and power. The concept of friction is also explained. This volume concludes with chapters concerning motion in a circle and simple harmonic motion.
This text will serve as a more complete course for pupils taking mathematics as a single or double subject.

Contenu

Preface

Chapter I. Introduction. The Fundamental Concepts of Theoretical Mechanics

1.1. The Nature of Theoretical Mechanics

1.2. Newton's Axioms

1.3. The Unit of Mass and the Unit of Force

1.4. Gravitational Units of Force

Chapter II. Systems of Coplanar Forces Acting on a Particle

2.1. Vector Quantities

2.2. Velocities and Accelerations as Vectors

2.3. Force as a Vector

2.4. The Parallelogram of Forces

2.5. Equilibrium of Forces

2.6. Forces in the Physical World

2.7. The Resultant of Any Number of Forces Acting on a Particle

2.8. The Equilibrium of a Rigid Body Acted Upon by Three Forces Only

2.9. Two Useful Trigonometric Formula

2.10. Elastic Strings

2.11. Particles Suspended from a String

Chapter III. The Kinematics of a Particle Moving in a Straight Line

3.1. Relationships between Distance, Time, Velocity and Acceleration

3.2. Graphical Relationships

3.3. Uniformly Accelerated Motion in a Straight Line

3.4. Free Motion under Gravity

Chapter IV. Projectiles

4.1. The Resolution of Uniplanar Motion into Components at Right Angles

4.2. The Free Motion of a Projectile

4.3. The Equation of the Path

4.4. The Parabolic Path of a Projectile

4.5. The Range on an Inclined Plane

Chapter V. Relative Motion

5.1. Relative Position

5.2. Relative Velocity

5.3. Problems of Relative Position and Interception

Chapter VI. The Moment of a Force

6.1. The Law of the Lever

6.2 The Resultant of a System of Parallel Forces

6.3 Equilibrium of a Rigid Body Acted Upon by a System of Coplanar Forces

6.4 Graphical Representation of the Moment of a Force

Chapter VII. Centers of Gravity

7.1. Definition

7.2. The Center of Gravity of a Finite Number of Coplanar Particles

7.3. The Center of Gravity of a Rigid Body

7.4. The Center of Gravity of a Compound Body

7.5. The Position of a Freely Suspended Body

7.6. The Equilibrium of a Body at Rest on a Horizontal Plane

7.7. The Centers of Gravity of Some Common Solids

Chapter VIII. The Dynamics of a Particle

8.1. Newton's Laws of Motion

8.2. The Motion of Connected Particles

8.3. Impulse and Momentum

8.4. Conservation of Momentum

8.5. Work and Energy

Chapter IX. Friction

9.1. The Nature of Friction

9.2. The Laws of Friction

9.3. The Angle of Friction

9.4. The Equilibrium of a Particle on an Inclined Plane

9.5. Examples Involving Friction

Chapter X. Conservation of Energy

10.1. Energy in the Physical World

10.2. Conservation of Mechanical Energy

10.3. The Relation between the Energy Equation and the Equation of Motion

Chapter XI. The Impact of Elastic Bodies

11.1. Direct Collision of Elastic Spheres

11.2. Impulsive Reaction and Loss of Kinetic Energy

11.3. The Collision between a Smooth Sphere and a Fixed Smooth Plane

11.4. Oblique Impact of Smooth Elastic Spheres

Chapter XII. Power

12.1. Definition and Units

12.2. Power with a Constant Force

12.3. Energy and Power

12.4. The Acceleration and the Maximum Speed of a Car

Chapter XIII. Motion in a Circle

13.1. The Motion of a Particle Which is Not Moving in a Straight Line

13.2. Angular Velocity and Angular Acceleration

13.3. Uniform Speed in a Circle

13.4. Some Examples of Uniform Circular Motion in a Horizontal Circle

13.5. Motion in a Circle When the Speed is Not Necessarily Uniform

13.6. Motion in a Vertical Circle

Chapter XIV. Simple Harmonic Motion

14.1. Some Oscillatory Motions

14.2. The Solution of the Equation of SHM

14.3. Two Particular Integrals of the SHM Equation

14.4. The Projection of Uniform Motion in a Circle on to a Diameter

14.5. The Motion of a Particle Attached to a Light Elastic Spring

14.6. The Motion of a Particle Attached to Two Elastic Strings

14.7. Problems Involving the Equation of Motion =- 2x+c

14.8. The Motion of the Center of Mass of Two Moving Particles

14.9. The Rectilinear Motion in a Horizontal Plane of Two Particles Which are Connected by an Elastic Spring

14.10. Small Oscillations

Answers To the Exercises

Index