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Classical Mechanics (last updated: 2024 April 9)
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 |
1.10 | 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 |
2.10 | 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 |
2.20 | 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 |
3.10 | 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 |
4.10 | 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 |
15.10 | 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 |
15.20 | 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 |
15.30 | 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 |
17.10 | 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 |
19.10 | Examples of Cycloidal Motion in Physics |
Chapter 20. Miscellanea
20.1 | Introduction |
20.2 | Surface Tension |
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20.2.1 | Excess Pressure Inside Drops and Bubbles |
20.2.2 | Angle of Contact |
20.2.3 | Capillary Rise |
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20.3 | Shear Modulus and Torsion Constant |
20.4 | Viscosity |
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20.4.1 | Poiseuille's Law |
20.4.2 | The Couette Viscometer |
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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
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