Elements of Newtonian Mechanics

1. The Foundation of Classical Mechanics.- 1.1 Principia.- 1.2 Prerequisites for Newton.- 1.3 The Masterpiece.- The Acceleration of Gravity.- Circular Motion.- Communication Satellite.- Horizontal Throw.- The Gravitational Constant.- String Force.- Forces and Tension.- Dimensional Analysis.- 1.4 Concluding Remarks.- 1.5 Problems.- 2. Newton's Five Laws.- 2.1 Newton's Laws of Motion.- 2.2 Integration of the Equation of Motion.- Constant Force.- The Harmonic Oscillator.- Mass on a Spring in the Gravitational Field of Earth.- Sphere Falling Through a Liquid.- Solid Against Solid.- The Atwood Machine.- Force in Harmonic Motion.- Charged Particle in a Uniform Magnetic Field.- Thomson's Experiment.- Work and Energy in Linear Motion of a Particle.- Free Fall Towards the Sun from a Great Distance.- Momentum Conservation.- Inelastic Collisions.- Rocket Propulsion.- Some Qualitative Remarks on Rocket Propulsion.- Ball Against a Wall.- 2.3 Problems.- 3. Gravitational and Inertial Mass.- 3.1 Gravitational Mass.- 3.2 Inertial Mass.- 3.3 Proportionality Between Inertial and Gravitational Mass.- 3.4 Newton's Experiment.- The Satellite.- An Elevator in Free Fall.- Three Balls.- 3.5 Problem.- 4. The Galilei Transformation.- 4.1 The Galilei Transformation.- 4.2 Galileo Speaks.- Velocity Transformation.- 4.3 Problems.- 5. The Motion of the Earth.- 5.1 Examples.- Vectors and the Rotation of a Rigid Body.- Angular Velocities in the Solar System.- 5.2 Problems.- 6. Motion in Accelerated Reference Frames.- 6.1 Newton's 2nd Law Within Accelerated Reference Frames.- 6.2 The Equivalence Principle of Mechanics.- 6.3 The Einstein Box.- Balloon in Accelerated Frame.- Mass on an Oscillating Plate.- Pendulum in an Elevator.- 6.4 The Centrifugal Force.- Earth's Orbit Around the Sun.- Grass on a Rotating Disk.- The Variation of g with Latitude.- 6.5 Tidal Fields.- The Roche Limit.- 6.6 The Coriolis Force.- Coriolis Force on a Train.- Particle on a Frictionless Disc.- The Vertical Throw.- 6.7 Tidal Forces and Local Inertial Frames.- Global and Local Inertial Frames.- 6.8 The Foucault Pendulum.- 6.9 Newton's Bucket.- 6.10 Review: Fictitious Forces.- 6.11 Problems.- 7. The Problem of Motion.- 7.1 Kinematic and Dynamic Views of the Problem of Motion.- 7.2 Einstein Speaks.- 7.3 Symmetry.- 7.4 The Symmetry (Invariance) of Newton's 2nd Law.- 7.5 Limited Absolute Space.- 7.6 The Asymmetry (Variance) of Newton's 2nd Law.- 7.7 Critique of the Newtonian View.- 7.8 Concluding Remarks.- 8. Energy.- 8.1 Work and Kinetic Energy.- 8.2 Conservative Force Fields.- 8.3 Central Force Fields.- 8.4 Potential Energy and Conservation of Energy.- 8.5 Calculation of Potential Energy.- Constant Gravitational Field.- Spring Force.- Gravity Outside a Homogeneous Sphere.- 8.6 The Gravitational Field Around a Homogeneous Sphere.- 8.6.1 The Field Around a Spherical Shell.- 8.6.2 A Solid Sphere.- 8.7 Examples.- Particle on a Frictionless Curve.- String Force in the Pendulum.- The Gravitational Potential Outside the Earth.- Potential Energy Due to Electric Forces.- A Tunnel Through the Earth.- The Asymmetry of Nature.- 8.8 Review: Conservative Forces and Potential Energy.- 8.9 Problems.- 9. The Center-of-Mass Theorem.- 9.1 The Center of Mass.- 9.2 The Center-of-Mass Frame.- 9.3 Examples.- Two Masses Connected with a Spring.- Inelastic Collisions.- The Collision Approximation.- Freely Falling Spring.- The Wedge.- 9.4 Review: Center of Mass and Center-of-Mass Theorems.- 9.5 Comments on the Conservation Theorems.- 9.6 Problems.- 10. The Angular Momentum Theorem.- 10.1 The Angular Momentum Theorem for a Particle.- 10.2 Conservation of Angular Momentum.- 10.3 Torque and Angular Momentum Around an Axis.- 10.4 The Angular Momentum Theorem for a System of Particles.- 10.5 Center of Gravity.- 10.6 Angular Momentum Around the Center of Mass.- 10.7 Review: Equations of Motion for a System of Particles.- 10.8 Examples of Conservation of Angular Momentum.- Particle in Circular Motion.- Rotation o