Table of Contents

Introduction -- Chapter 1 Forces and Newton’s laws -- 1 Voyager's odyssey — an example of Newton’s laws -- 2 Newton’s laws and the definition offeree -- 2.1 Underlying concepts: frames of reference and observers -- 2.2 Newton’s first law: inertia and inertial frames of reference -- 2.3 Newton’s second law: force, mass and acceleration -- 2.4 Newton’s third law: action and reaction -- 2.5 Newton’s laws and vectors: resultant force, resolution and redirection -- 2.6 Newton’s laws and rigid bodies: centre of mass -- 3 Some familiar forces -- 3.1 Weight and terrestrial gravitation -- 3.2 Universal gravitation -- 3.3 Contact forces and normal reactions -- 3.4 Friction, viscosity and air resistance -- 3.5 Forces arising from tension and compression -- 3.6 Forces in action -- 4 Forces and motion -- 4.1 Rates of change: gradients and derivatives — a reminder -- 4.2 Some familiar forms of motion -- 4.3 Derivatives and Newton’s laws: equations of motion -- 4.4 Stepping through Newton’s laws -- 5 Closing items -- Chapter 2 Work , energy and power -- 1 Escaping the Earth — an application of energy -- 2 Work and kinetic energy -- 2.1 Kinetic energy — energy due to motion -- 2.2 Work and changes in kinetic energy -- 2.3 The work done by a constant aligned force -- 2.4 The work done by a constant non-aligned force -- 2.5 Work and the scalar product of vectors -- 3 Work and potential energy -- 3.1 Conservative and non-conservative forces -- 3.2 Potential energy — energy due to configuration -- 3.3 Strain potential energy -- 3.4 The work done by a varying force -- 3.5 Gravitational potential energy -- 3.6 Force as the negative gradient of potential energy -- 3.7 The conservation of mechanical energy -- 3.8 The role of energy in predicting motion -- 4 Power -- 4.1 Power — the rate of energy transfer -- 4.2 Power and vectors -- 5 Energy in oscillating systems -- 5 .1 The energy of a simple harmonic oscillator -- 5.2 The energy of a damped harmonic oscillator -- 5.3 The energy of a driven damped harmonic oscillator -- 5.4 A note on exponential functions -- 6 Closing items -- Chapter 3 Linear momentum and collisions -- 1 Discovering the atomic nucleus — an example -- 2 Linear momentum -- 2 .1 The linear momentum of a body -- 2.2 Momentum and Newton’s second law -- 2.3 Impulse and impulsive forces -- 2.4 The momentum of a system of bodies -- 2.5 Conservation of momentum -- 2.6 The role of momentum in predicting motion -- 3 Collisions and conservation laws -- 3 .1 Elastic and inelastic collisions -- 3.2 Elastic collisions in one dimension -- 3.3 Elastic collisions in two or three dimensions -- 3.4 Inelastic collisions -- 3.5 Collisions all around us -- 3.6 Relativistic collisions -- 4 Closing items -- Chapter 4 Torque and angular momentum -- 1 Precession — an example of rotational dynamics -- 2 Torque -- 2 .1 The turning effect of a force -- 2.2 Torque and levers -- 2.3 A vector definition of torque -- 2.4 Torque and angular motion -- 2.5 A note on vector and scalar products -- 3 Equilibrium and statics -- 3.1 Equilibrium conditions -- 3.2 Static equilibrium conditions -- 3.3 The stability of equilibrium -- 3.4 Static structures -- 4 Rotational energy and moments of inertia -- 4 .1 Rotational energy of particles -- 4.2 Rotational energy of rigid bodies -- 4.3 Torque, moment of inertia and angular acceleration -- 4.4 The role of rotational energy in the prediction of motion -- 4.5 Flywheels and energy storage -- 5 Angular momentum -- 5 .1 Angular momentum of particles -- 5.2 Angular momentum of rigid bodies -- 5.3 Torque and the rate of change of angular momentum -- 5.4 Conservation of angular momentum -- 5.5 Tops, gyroscopes and precession -- 6 Closing items -- Chapter 5 Chaotic motion -- 1 Is motion always predictable? -- 2 What is chaos? -- 2.1 A linear map -- 2.2 The logistic map -- 2.3 Some features of chaos -- 2.4 Fractals -- 2.5 State spaces and trajectories -- 2.6 Strange attractors -- 3 Examples of chaos -- 3.1 Dripping taps and beating hearts -- 3.2 Chaos in the Solar System -- 3.3 Chaos in galaxies -- 4 Closing items -- Chapter 6 Consolidation and skills development -- 1 Introduction -- 2 Overview of Chapters 1 to 5 -- 3 Problem-solving skills -- 4 Basic skills and knowledge test -- 5 Interactive questions -- 6 Physical problems -- Answers to questions -- Acknowledgements – Index.