Classical Mechanics An introductory course Richard Fitzpatrick Associate Professor of Physics The University of Texas at Austin Contents 1 Introduction 7 1.1 Major sources: . 7 1.2 What is classical mechanics? . 7 1.3 mks units . 9 1.4 Standard prefixes . 10 1.5 Other units . 11 1.6 Precision and significant figures . 12 1.7 Dimensional analysis . 12 2 Motion in 1 dimension 18 2.1 Introduction . 18 2.2 Displacement . 18 2.3 Velocity . 19 2.4 Acceleration . 21 2.5 Motion with constant velocity . 23 2.6 Motion with constant acceleration . 24 2.7 Free-fall under gravity . 26 3 Motion in 3 dimensions 32 3.1 Introduction . 32 3.2 Cartesian coordinates . 32 3.3 Vector displacement . 33 3.4 Vector addition . 34 3.5 Vector magnitude . 35 2 3.6 Scalar multiplication . 35 3.7 Diagonals of a parallelogram . 36 3.8 Vector velocity and vector acceleration . 37 3.9 Motion with constant velocity . 39 3.10 Motion with constant acceleration . 39 3.11 Projectile motion . 41 3.12 Relative velocity . 44 4 Newton's laws of motion 53 4.1 Introduction . 53 4.2 Newton's first law of motion . 53 4.3 Newton's second law of motion . 54 4.4 Hooke's law . 55 4.5 Newton's third law of motion . 56 4.6 Mass and weight . 57 4.7 Strings, pulleys, and inclines . 60 4.8 Friction . 67 4.9 Frames of reference . 70 5 Conservation of energy 78 5.1 Introduction . 78 5.2 Energy conservation during free-fall . 78 5.3 Work . 81 5.4 Conservative and non-conservative force-fields . 88 5.5 Potential energy . 92 3 5.6 Hooke's law . 93 5.7 Motion in a general 1-dimensional potential . 96 5.8 Power . 99 6 Conservation of momentum 107 6.1 Introduction . 107 6.2 Two-component systems . 107 6.3 Multi-component systems . 112 6.4 Rocket science . 115 6.5 Impulses . 118 6.6 Collisions in 1-dimension . 121 6.7 Collisions in 2-dimensions . 127 7 Circular motion 136 7.1 Introduction . 136 7.2 Uniform circular motion . 136 7.3 Centripetal acceleration . 138 7.4 The conical pendulum . 141 7.5 Non-uniform circular motion . 142 7.6 The vertical pendulum . 148 7.7 Motion on curved surfaces . 150 8 Rotational motion 160 8.1 Introduction . 160 8.2 Rigid body rotation . 160 8.3 Is rotation a vector? . 162 4 8.4 The vector product . 166 8.5 Centre of mass . 168 8.6 Moment of inertia . 172 8.7 Torque . 179 8.8 Power and work . 184 8.9 Translational motion versus rotational motion . 186 8.10 The physics of baseball . 186 8.11 Combined translational and rotational motion . 190 9 Angular momentum 204 9.1 Introduction . 204 9.2 Angular momentum of a point particle . 204 9.3 Angular momentum of an extended object . 206 9.4 Angular momentum of a multi-component system . 209 10 Statics 217 10.1 Introduction . 217 10.2 The principles of statics . 217 10.3 Equilibrium of a laminar object in a gravitational field . 220 10.4 Rods and cables . 223 10.5 Ladders and walls . 226 10.6 Jointed rods . 228 11 Oscillatory motion 237 11.1 Introduction . 237 11.2 Simple harmonic motion . 237 5 11.3 The torsion pendulum . 241 11.4 The simple pendulum . 242 11.5 The compound pendulum . 245 11.6 Uniform circular motion . 246 12 Orbital motion 253 12.1 Introduction . 253 12.2 Historical background . 253 12.3 Gravity . 262 12.4 Gravitational potential energy . 265 12.5 Satellite orbits . 268 12.6 Planetary orbits . ..