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Classical Mechanics 1
1.1 Blocks 1
1.1.1 Blocks on Ramps 1
1.1.2 Falling and Hanging Blocks 2
1.1.3 Blocks in Contact 3
1.1.4 Problems: Blocks
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1.2 Kinematics 5
1.2.1 Circular Motion 5
1.2.2 Problems: Kinematics 6
1.3 Energy 7
1.3.1 Types of Energy 7
1.3.2 Kinetic/Potential Problems 8
1.3.3 RollingWithout Slipping 9
1.3.4 Work–Energy Theorem 11
1.3.5 Problems: Energy 11
1.4 Momentum 12
1.4.1 Linear Collisions 12
1.4.2 Rotational Motion and Angular Momentum 12
1.4.3 Moment of Inertia 14
1.4.4 Center of Mass 15
1.4.5 Problems: Momentum 15
1.5 Lagrangians and Hamiltonians 16
1.5.1 Lagrangians 16
1.5.2 Euler–Lagrange Equations 17
1.5.3 Hamiltonians and Hamilton’s Equations
of Motion 18
1.5.4 Problems: Lagrangians and Hamiltonians 19
1.6 Orbits 19
1.6.1 Effective Potential 19
1.6.2 Classification of Orbits 20
1.6.3 Kepler’s “Laws” 21
1.6.4 Problems: Orbits 22
1.7 Springs and Harmonic Oscillators 22
1.7.1 Normal Modes 23
1.7.2 Damping, Driving, and Resonance 24
1.7.3 Further Examples 25
1.7.4 Problems: Springs 27
1.8 Fluid Mechanics 27
1.8.1 Bernoulli’s Principle 27
1.8.2 Buoyant Forces 29
1.8.3 Problems: Fluid Mechanics 29
1.9 Solutions: Classical Mechanics 29
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Electricity and Magnetism 35
2.1 Electrostatics 35
2.1.1 Maxwell’s Equations for Electrostatics 35
2.1.2 Electric Potential 35
2.1.3 Integral Form of Maxwell’s Equations 36
2.1.4 Standard Electrostatics Configurations 37
2.1.5 Boundary Conditions 38
2.1.6 Conductors 40
2.1.7 Method of Images 40
2.1.8 Work and Energy in Electrostatics 42
2.1.9 Capacitors 43
2.1.10 Problems: Electrostatics 44
2.2 Magnetostatics 45
2.2.1 Basic Tools 45
2.2.2 Ampère’s Law and the Biot–Savart Law 46
2.2.3 Standard Magnetostatics Configurations 46
2.2.4 Boundary Conditions 48
2.2.5 Work and Energy in Magnetostatics 48
2.2.6 Cyclotron Motion 48
2.2.7 Problems: Magnetostatics 49
2.3 Electrodynamics 49
2.3.1 Maxwell’s Equations 49
2.3.2 Faraday’s Law 50
2.3.3 Inductors 50
2.3.4 Problems: Electrodynamics 51 [Show Less]