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Classical Mechanics (last updated: 2022 August 11)

Chapter 1.    Centres of Mass

 1.1 Introduction and Some Definitions 1.2 Plane Triangular Lamina 1.3 Plane Areas 1.4 Plane Curves 1.5 Summary of the Formulas for Plane Laminas and Curves 1.6 The Theorems of Pappus 1.7 Uniform Solid Tetrahedron, Pyramid and Cone 1.8 Hollow Cone 1.9 Hemispheres 1.1 Summary

Chapter 2.    Moment of Inertia

 2.1 Definition of Moment of Inertia 2.2 Meaning of Rotational Inertia 2.3 Moments of Inertia of Some Simple Shapes 2.4 Radius of Gyration 2.5 Plane Laminas and Mass Points distributed in a Plane 2.6 Three-dimensional Solid Figures. Spheres, Cylinders, Cones. 2.7 Three-dimensional Hollow Figures. Spheres, Cylinders, Cones. 2.8 Torus 2.9 Linear Triatomic Molecule 2.1 Pendulums 2.11 Plane Laminas. Product Moment. Translation of Axes (Parallel Axes Theorem). 2.12 Rotation of Axes 2.13 Momental Ellipse 2.14 Eigenvectors and Eigenvalues 2.15 Solid Body 2.16 Rotation of Axes - Three Dimensions 2.17 Solid Body Rotation. The Inertia Tensor. 2.18 Determination of the Principal Axes 2.19 Moment of Inertia with Respect to a Point 2.2 Ellipses and Ellipsoids 2.21 Tetrahedra

Chapter 3.    Systems of Particles

 3.1 Introduction 3.2 Moment of a Force 3.3 Moment of Momentum 3.4 Notation 3.5 Linear Momentum 3.6 Force and Rate of Change of Momentum 3.7 Angular Momentum 3.8 Torque 3.9 Comparison 3.1 Kinetic energy 3.11 Torque and Rate of Change of Angular Momentum 3.12 Torque, Angular Momentum and a Moving Point 3.13 The Virial Theorem

Chapter 4.    Rigid Body Rotation

 4.1 Introduction 4.2 Angular Velocity and Eulerian Angles 4.3 Kinetic Energy 4.4 Lagrange's Equations of Motion 4.5 Euler's Equations of Motion 4.6 Force-free Motion of a Rigid Asymmetric Top 4.7 Nonrigid Rotator 4.8 Force-free Motion of a Rigid Symmetric Top 4.9 Centrifugal and Coriolis Forces 4.1 The Top

Chapter 5.    Collisions

 5.1 Introduction 5.2 Bouncing Balls 5.3 Head-on Collision of a Moving Sphere with an Initially Stationary Sphere 5.4 Oblique Collisions 5.5 Oblique (Glancing) Elastic Collisions, Alternative Treatment 5.6 Two Colliding Rectangular Blocks

Chapter 6.    Motion in a Resisting Medium

 6.1 Introduction 6.2 Uniformly Accelerated Motion 6.3 Motion in which the Resistance is Proportional to the Speed 6.4 Motion in which the Resistance is Proportional to the Square of the Speed.

Chapter 7.    Projectiles

 7.1 No Air Resistance 7.2 Air Resistance Proportional to the Speed 7.3 Air Resistance Proportional to the Square of the Speed

Chapter 8.    Impulsive Forces

 8.1 Introduction 8.2 Problems

Chapter 9.    Conservative Forces

 9.1 Introduction 9.2 The Time and Energy Equation 9.3 Examples 9.4 Virtual Work

Chapter 10.    Rocket Motion

 10.1 Introduction 10.2 An Integral 10.3 The Rocket Equation 10.4 Problems

Chapter 11.    Simple and Damped Oscillatory Motion

 11.1 Simple Harmonic Motion 11.2 Mass Attached to an Elastic Spring 11.3 Torsion Pendulum 11.4 Ordinary Homogeneous Second-order Differential Equations 11.5 Damped Oscillatory Motion 11.6 Electrical Analogues

Chapter 12.    Forced Oscillations

 12.1 More on Differential Equations 12.2 Forced Oscillatory Motion 12.3 Electrical Analogue

Chapter 13.    Lagrangian Mechanics

 13.1 Introduction 13.2 Generalized Coordinates and Generalized Forces 13.3 Holonomic constraints 13.4 The Lagrangian Equations of Motion 13.5 Acceleration Components 13.6 Slithering Soap in Conical Basin 13.7 Slithering Soap in Hemispherical Basin 13.8 More Examples 13.9 Hamilton's Variational Principle

Chapter 14.    Hamiltonian Mechanics

 14.1 Introduction 14.2 A Thermodynamics Analogy 14.3 Hamilton's Equations of Motion 14.4 Examples 14.5 Poisson Brackets

Chapter 15.    Special Relativity

 15.1 Introduction 15.2 The Speed of Light 15.3 Preparation 15.4 Speed is Relative. The Fundamental Postulate of Special Relativity. 15.5 The Lorentz Transformations 15.6 But This Defies Common Sense 15.7 The Lorentz Transformation as a Rotation 15.8 Timelike and Spacelike 4-Vectors 15.9 The FitzGerald-Lorentz Contraction 15.1 Time Dilation 15.11 The Twins Paradox 15.12 A, B and C 15.13 Simultaneity 15.14 Order of Events, Causality and the Transmission of Information 15.15 Derivatives 15.16 Addition of Velocities 15.17 Aberration of Light 15.18 Doppler Effect 15.19 The Transverse and Oblique Doppler Effects 15.2 Acceleration 15.21 Mass 15.22 Momentum 15.23 Some Mathematical Results 15.24 Kinetic Energy 15.25 Addition of Kinetic Energies 15.26 Energy and Mass 15.27 Energy and Momentum 15.28 Units 15.29 Force 15.3 Electromagnetism

Chapter 16.    Hydrostatics

 16.1 Introduction 16.2 Density 16.3 Pressure 16.4 Pressure on a Horizontal Surface. Pressure at Depth z 16.5 Pressure on a Vertical Surface 16.6 Centre of Pressure 16.7 Archimedes' Principle 16.8 Some Simple Examples 16.9 Floating Bodies

Chapter 17.    Vibrating Systems

 17.1 Introduction 17.2 The Diatomic Molecule 17.3 Two Masses, Two Springs and a Brick Wall 17.4 Double Torsion Pendulum 17.5 Double Pendulum 17.6 Linear Triatomic Molecule 17.7 Two Masses, Three Springs, Two brick Walls 17.8 Transverse Oscillations of Masses on a Taut String 17.9 Vibrating String 17.1 Water 17.11 A General Vibrating System 17.12 A Driven System 17.13 A Damped Driven System

Chapter 18.    The Catenary

 18.1 Introduction 18.2 The Intrinsic Equation to the Catenary 18.3 Equation of the Catenary in Rectangular Coordinates, and Other Simple Relations 18.4 Area of a Catenoid

Chapter 19.    The Cycloid

 19.1 Introduction 19.2 Tangent to the Cycloid 19.3 The Intrinsic Equation to the Cycloid 19.4 Variations 19.5 Motion on a Cycloid, Cusps Up 19.6 Motion on a Cycloid, Cusps Down 19.7 The Brachystochrone Property of the Cycloid 19.8 Contracted and Extended Cycloids 19.9 The Cycloidal Pendulum 19.1 Examples of Cycloidal Motion in Physics

Chapter 20.    Miscellanea

20.1Introduction
20.2Surface Tension
 20.2.1 Excess Pressure Inside Drops and Bubbles 20.2.2 Angle of Contact 20.2.3 Capillary Rise
20.3Shear Modulus and Torsion Constant
20.4Viscosity
 20.4.1 Poiseuille's Law 20.4.2 The Couette Viscometer

Chapter 21.    Central Forces and Equivalent Potential

 21.1 Introduction 21.2 Motion Under a Central Force 21.3 Inverse Square Attractive Force 21.4 Hooke’s Law 21.5 Inverse Fourth Power Attractive Force 21.6 A General Central Force 21.7 Inverse Cube Attractive Force

Chapter 22.    Dimensions

 22.1 Mass, Length and Time 22.2 Table of Dimensions 22.3 Checking Equations 22.4 Deducing Relationships 22.5 Dimensionless Quantities 22.6 Different Fundamental Quantities

Appendix A.    Miscellaneous Problems

Appendix B.    Solutions to Miscellaneous Problems

Texts © 2000 - 2013 Dr. J. B. Tatum
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