1 8.01SC Classical Mechanics Introduction 2 0.1 Vectors vs. Scalars 3 0.2 Vector Operators 4 0.3 Coordinate Systems and Unit Vectors 5 0.4 Vectors - Magnitude and Direction 6 0.5 Vector Decomposition into components 7 0.6 Going Between Representations 8 1.0 Week 1 Introduction (8.01 Classical Mechanics) 9 1.1 Coordinate Systems and Unit Vectors in 1D 10 1.2 Position Vector in 1D 11 1.3 Displacement Vector in 1D 12 1.4 Average Velocity in 1D 13 1.5 Instantaneous Velocity in 1D 14 1.7 Worked Example: Derivatives in Kinematics 15 2.1 Introduction to Acceleration 16 2.2 Acceleration in 1D 17 2.3 Worked Example: Acceleration from Position 18 2.4 Integration 19 3.1 Coordinate System and Position Vector in 2D 20 3.2 Instantaneous Velocity in 2D 21 3.3 Instantaneous Acceleration in 2D 22 3.4 Projectile Motion 23 3.5 Demo: Shooting an Apple 24 3.5 Demo: Relative Motion Gun 25 PS.1.1 Three Questions Before Starting 26 PS.1.2 Shooting the apple solution 27 P.1.3 Worked Example: Braking Car 28 P.1.4 Sketch the Motion 29 P.1.5 Worked Example: Pedestrian and Bike at Intersection 30 4.0 Week 2 Introduction 31 4.1 Newton's First and Second Laws 32 4.2 Newton's Third Law 33 4.3 Reference Frames 34 4.4 Non-inertial Reference Frames 35 5.1 Universal Law of Gravitation 36 5.2 Worked Example: Gravity - Superposition 37 5.3 Gravity at the surface of the Earth: The value of g. 38 6.1 Contact Forces 39 6.2 Static Friction 40 7.1 Pushing Pulling and Tension 41 7.2 Ideal Rope 42 7.3 Solving Pulley Systems 43 7.4 Hooke's Law 44 DD.1.1 Friction at the Nanoscale 45 PS.2.1 Worked Example - Sliding Block 46 PS.2.2 Worked Example - Stacked Blocks - Free Body Diagrams and Applying Newtons 2nd Law 47 PS.2.2 Worked Example - Stacked Blocks - Solve for the Maximum Force 48 PS.2.2 Worked Example - Stacked Blocks - Choosing the System of 2 Blocks Together 49 PS.2.3 Window Washer Free Body Diagrams 50 PS.2.3 Window Washer Solution 51 Newton's 3rd Law Pairs 52 Internal and External Forces 53 Applying Newton's 2nd Law 54 8.0 Week 3 Introduction 55 8.1 Polar Coordinates 56 8.2 Circular Motion: Position and Velocity Vectors 57 8.3 Angular Velocity 58 9.1 Uniform Circular Motion 59 9.2 Uniform Circular Motion: Direction of the Acceleration 60 10.1 Circular Motion - Acceleration 61 10.2 Angular Acceleration 62 10.3 Worked Example - Angular position from angular acceleration. 63 11.1 Newton's 2nd Law and Circular Motion 64 11.2 Worked Example - Car on a Banked Turn 65 11.3 Demo: Rotating Bucket 66 PS.3.1 Worked Example - Orbital Circular Motion - Radius 67 PS.3.1 Worked Example - Orbital Circular Motion - Velocity 68 PS.3.1 Worked Example - Orbital Circular Motion - Period 69 12.0 Week 4 Introduction 70 12.1 Pulley Problems 71 12.2 Constraint Condition 72 12.3 Virtual Displacement 73 12.4 Solve the System of Equations 74 12.5 Worked Example: 2 Blocks and 2 Pulleys 75 13.1 Rope Hanging Between Trees 76 13.2 Differential Analysis of a Massive Rope 77 13.3 Differential Elements 78 13.4 Density 79 13.5 Demo: Wrapping Friction 80 13.6 Summary for Differential Analysis 81 14.1 Intro to resistive forces 82 14.2 Resistive forces - low speed case 83 14.3 Resistive forces - high speed case 84 15.0 Week 5 Introduction 85 15.1 Momentum and Impulse 86 15.2 Impulse is a Vector 87 15.3 Worked Example - Bouncing Ball 88 15.4 Momentum of a System of Point Particles 89 15.5 Force on a System of Particles 90 16.1 Cases of Constant Momentum 91 16.2 Momentum Diagrams 92 17.1 Definition of the Center of Mass 93 17.2 Worked Example - Center of Mass of 3 Objects 94 17.3 Center of Mass of a Continuous System 95 17.5 Worked Example - Center of Mass of a Uniform Rod 96 17.6 Velocity and Acceleration of the Center of Mass 97 17.7 Reduction of a System to a Point Particle 98 18.0 Week 6 Introduction 99 18.1 Relative Velocity 100 18.2 Set up a Recoil Problem 101 18.3 Solve for Velocity in the Ground Frame 102 18.4 Solve for Velocity in the Moving Frame 103 19.1 Rocket Problem 1 - Set up the Problem 104 19.2 Rocket Problem 2 - Momentum Diagrams 105 19.3 Rocket Problem 3 - Mass Relations 106 19.4 Rocket Problem 4 - Solution 107 19.5 Rocket Problem 5 - Thrust and External Forces 108 19.6 Rocket Problem 6 - Solution for No External Forces 109 19.7 Rocket Problem 7 - Solution with External Forces 110 PS.6.1 Rocket Sled - Differential Equation 111 PS.6.1 Rocket Sled - Integrate the Rocket Equation 112 PS.6.1 Rocket Sled - Solve for Initial Velocity 113 PS.6.2 Snowplow Problem 114 20.0 Week 7 Introduction 115 20.1 Kinetic Energy 116 20.2 Work by a Constant Force 117 20.3 Work by a Non-Constant Force 118 20.4 Integrate adt and adx 119 20.5 Work-Kinetic Energy Theorem 120 20.6 Power 121 21.1 Scalar Product Properties 122 21.2 Scalar Product in Cartesian Coordinates 123 21.3 Kinetic Energy as a Scalar Product 124 21.4 Work in 2D and 3D 125 21.5 Work-Kinetic Energy Theorem in 2D and 3D 126 21.6 Worked Example: Block Going Down a Ramp 127 22.1 Path Independence - Gravity 128 22.2 Path Dependence - Friction 129 22.3 Conservative Forces 130 22.4 Non-conservative Forces 131 22.5 Summary of Work and Kinetic Energy 132 PS.7.1 Worked Example - Collision and Sliding on a Rough Surface 133 23.0 Week 8 Introduction 134 23.1 Introduction to Potential Energy 135 23.2 Potential Energy of Gravity near the Surface of the Earth 136 23.3 Potential Energy Reference State 137 23.4 Potential Energy of a Spring 138 23.5 Potential Energy of Gravitation 139 24.1 Mechanical Energy and Energy Conservation 140 24.2 Energy State Diagrams 141 24.3 Worked Example - Block Sliding Down Circular Slope 142 24.4 Newton's 2nd Law and Energy Conservation 143 25.1 Force is the Derivative of Potential 144 25.2 Stable and Unstable Equilibrium Points 145 25.3 Reading Potential Energy Diagrams 146 26.0 Week 9 Introduction 147 26.1 Momentum in Collisions 148 26.2 Kinetic Energy in Collisions 149 26.3 Totally Inelastic Collisions 150 27.1 Worked Example: Elastic 1D Collision 151 27.2 Relative Velocity in 1D 152 27.3 Kinetic Energy and Momentum Equation 153 27.4 Worked Example: Elastic 1D Collision Again 154 27.5 Worked Example: Gravitational Slingshot 155 27.6 2D Collisions 156 DD.2.1 Position in the CM Frame 157 DD.2.2 Relative Velocity is Independent of Reference Frame 158 DD.2.3 1D Elastic Collision Velocities in CM Frame 159 DD.2.4 Worked Example: 1D Elastic Collision in CM Frame 160 DD.2.5 Kinetic Energy in Different Reference Frames 161 DD.2.6 Kinetic Energy in the CM Frame 162 DD.2.7 Change in the Kinetic Energy 163 28.0 Week 10 Introduction 164 28.1 Rigid Bodies 165 28.2 Introduction to Translation and Rotation 166 28.3 Review of Angular Velocity and Acceleration 167 29.1 Kinetic Energy of Rotation 168 29.2 Moment of Inertia of a Rod 169 29.3 Moment of Inertia of a Disc 170 29.4 Parallel Axis Theorem 171 29.5 Deep Dive - Moment of Inertia of a Sphere 172 29.6 Deep Dive - Derivation of the Parallel Axis Theorem 173 30.1 Introduction to Torque and Rotational Dynamics 174 30.2 Cross Product 175 30.3 Cross Product in Cartesian Coordinates 176 30.4 Torque 177 30.5 Torque from Gravity 178 31.1 Relationship between Torque and Angular Acceleration 179 31.2 Internal Torques Cancel in Pairs 180 31.3 Worked Example - Find the Moment of Inertia of a Disc from a Falling Mass 181 31.4 Worked Example - Atwood Machine 182 31.5 Massive Pulley Problems 183 31.7 Worked Example - Two Blocks and a Pulley Using Energy 184 PS.10.1 Worked Example - Blocks with Friction and Massive Pulley 185 32.0 Week 11 Introduction 186 32.1 Angular Momentum for a Point Particle 187 32.2 Calculating Angular Momentum 188 32.3 Worked Example - Angular Momentum About Different Points 189 32.4 Angular Momentum of Circular Motion 190 33.1 Worked Example - Angular Momentum of 2 Rotating Point Particles 191 33.2 Angular Momentum of a Symmetric Object 192 33.4 If Momentum is Zero then Angular Momentum is Independent of Origin 193 33.5 Kinetic Energy of a Symmetric Object 194 34.1 Torque Causes Angular Momentum to Change - Point Particle 195 34.2 Torque Causes Angular Momentum to Change - System of Particles 196 34.3 Angular Impulse 197 34.4 Demo: Bicycle Wheel Demo 198 34.5 Worked Example - Particle Hits Pivoted Ring 199 35.0 Week 12 Introduction 200 35.1 Translation and Rotation of a Wheel 201 35.2 Rolling Wheel in the Center of Mass Frame 202 35.3 Rolling Wheel in the Ground Frame 203 35.4 Rolling Without Slipping Slipping and Skidding 204 35.5 Contact Point of a Wheel Rolling Without Slipping 205 36.1 Friction on a Rolling Wheel 206 36.2 Worked Example - Wheel Rolling Without Slipping Down Inclined Plane - Torque Method 207 36.3 Demo: Spool Demo 208 36.4 Worked Example - Yoyo Pulled Along the Ground 209 36.5 Analyze Force and Torque in Translation and Rotation Problems 210 37.1 Kinetic Energy of Translation and Rotation 211 37.2 Worked Example - Wheel Rolling Without Slipping Down Inclined Plane 212 37.3 Angular Momentum of Translation and Rotation 213 DD.3.1 Deep Dive - Gyroscopes - Free Body Diagrams, Torque, and Rotating Vectors 214 DD.3.2 Deep Dive - Gyroscopes - Precessional Angular Velocity and Titled Gyroscopes 215 DD.3.3 Deep Dive - Gyroscopes - Nutation and Total Angular Momentum