NEWTON'S PRINCIPIA
CONTENTS NEWTON’S LAWS WHAT IS MECHANICS? MECHANICS AS A SCIENTI?C THEORY NEWTONIAN VS EINSTEINIAN MECHANICS A DEEPER LOOK AT NEWTON’S LAWS INERTIAL FRAMES NEWTON’S LAWS IN NONINERTIAL FRAMES SWITCHING OFF GRAVITY FINALE – LAWS, POSTULATES OR DE?NITIONS? 1 10 SUMMARY 1 11 PROBLEMS ONE-DIMENSIONAL MOTION RATIONALE FOR ONE-DIMENSIONAL ANALYSIS THE CONCEPT OF A PARTICLE MOTION WITH A CONSTANT FORCE WORK AND ENERGY IMPULSE AND POWER MOTION WITH A POSITION-DEPENDENT FORCE THE NATURE OF ENERGY POTENTIAL FUNCTIONS EQUILIBRIA 2 10 MOTION CLOSE TO A STABLE EQUILIBRIUM 2 11 THE STABILITY OF THE UNIVERSE 2 12 TRAJECTORY OF A BODY FALLING A LARGE DISTANCE UNDER GRAVITY 2 13 MOTION WITH A VELOCITY-DEPENDENT FORCE 2 14 SUMMARY 2 15 PROBLEMS OSCILLATORY MOTION INTRODUCTION PROTOTYPE HARMONIC OSCILLATOR DIFFERENTIAL EQUATIONS GENERAL SOLUTION FOR SIMPLE HARMONIC MOTION ENERGY IN SIMPLE HARMONIC MOTION DAMPED OSCILLATIONS LIGHT DAMPING – THE Q FACTOR HEAVY DAMPING AND CRITICAL DAMPING FORCED OSCILLATIONS 3 10 COMPLEX NUMBER METHOD 3 11 ELECTRICAL ANALOGUE 3 12 POWER IN FORCED OSCILLATIONS 3 13 COUPLED OSCILLATIONS 3 14 SUMMARY 3 15 PROBLEMS TWO-BODY DYNAMICS RATIONALE CENTRE OF MASS INTERNAL MOTION: REDUCED MASS COLLISIONS ELASTIC COLLISIONS INELASTIC COLLISIONS CENTRE-OF-MASS FRAME ROCKET MOTION LAUNCH VEHICLES 4 10 SUMMARY 4 11 PROBLEMS RELATIVITY 1: SPACE AND TIME WHY RELATIVITY? GALILEAN RELATIVITY THE FUNDAMENTAL POSTULATES OF RELATIVITY INERTIAL OBSERVERS IN RELATIVITY COMPARING TRANSVERSE DISTANCES BETWEEN FRAMES LESSONS FROM A LIGHT CLOCK: TIME DILATION PROPER TIME INTERVAL INVARIANCE THE RELATIVITY OF SIMULTANEITY 5 10 THE RELATIVITY OF LENGTH: LENGTH CONTRACTION 5 11 THE LORENTZ TRANSFORMATIONS 5 12 VELOCITY ADDITION 5 13 PARTICLES MOVING FASTER THAN LIGHT: TACHYONS 5 14 SUMMARY 5 15 PROBLEMS RELATIVITY 2: ENERGY AND MOMENTUM ENERGY AND MOMENTUM THE MEANING OF REST ENERGY RELATIVISTIC COLLISIONS AND DECAYS PHOTONS UNITS IN HIGH-ENERGY PHYSICS ENERGY/MOMENTUM TRANSFORMATIONS BETWEEN FRAMES RELATIVISTIC DOPPLER EFFECT SUMMARY PROBLEMS GRAVITATIONAL ORBITS WORK IN THREE DIMENSIONS TORQUE AND ANGULAR MOMENTUM CENTRAL FORCES KEPLER’S LAWS COMMENTS RIGID BODY DYNAMICS TORQUE AND ANGULAR MOMENTUM FOR SYSTEMS OF PARTICLES CENTRE OF MASS OF SYSTEMS OF PARTICLES AND RIGID BODIES ANGULAR MOMENTUM OF RIGID BODIES KINETIC ENERGY OF RIGID BODIES BATS, CATS, PENDULA AND GYROSCOPES GENERAL ROTATION ABOUT A FIXED AXIS PRINCIPAL AXES EXAMPLES OF PRINCIPAL AXES AND PRINCIPAL MOMENTS OF INERTIA 8 10 KINETIC ENERGY OF A BODY ROTATING ABOUT A FIXED AXIS 8 11 SUMMARY 8 12 PROBLEMS ROTATING FRAMES EXPERIMENTS ON ROUNDABOUTS GENERAL PRESCRIPTION FOR ROTATING FRAMES THE CENTRIFUGAL TERM THE CORIOLIS TERM THE FOUCAULT PENDULUM FREE ROTATION OF A RIGID BODY – TENNIS RACKETS AND MATCHBOXES FINAL THOUGHTS 9 10 PROBLEMS