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Lecture 
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1 
0.1 Vectors vs. Scalars 
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2 
0.2 Vector Operators 
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3 
0.3 Coordinate Systems and Unit Vectors 
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4 
0.4 Vectors  Magnitude and Direction 
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0.5 Vector Decomposition into components 
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0.6 Going Between Representations 
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7 
1.0 Week 1 Introduction 
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I. Lesson 1: 1D Kinematics  Position and Velocity 
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1.1 Coordinate Systems and Unit Vectors in 1D 
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1.2 Position Vector in 1D 
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1.3 Displacement Vector in 1D 
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1.4 Average Velocity in 1D 
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1.5 Instantaneous Velocity in 1D 
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1.7 Worked Example: Derivatives in Kinematics 
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II. Lesson 2: 1D Kinematics  Acceleration 
14 
2.1 Introduction to Acceleration 
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2.2 Acceleration in 1D 
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2.3 Worked Example: Acceleration from Position 
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17 
2.4 Integration 
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III. Lesson 3: 2D Kinematics  Position, Velocity, and Acceleration 
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3.1 Coordinate System and Position Vector in 2D 
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3.2 Instantaneous Velocity in 2D 
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3.3 Instantaneous Acceleration in 2D 
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21 
3.4 Projectile Motion 
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22 
3.5 Demo: Shooting an Apple 
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23 
3.5 Demo: Relative Motion Gun 
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IV. Week 1 Worked Examples 
24 
PS.1.1 Three Questions Before Starting 
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PS.1.2 Shooting the apple solution 
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P.1.3 Worked Example: Braking Car 
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P.1.4 Sketch the Motion 
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28 
P.1.5 Worked Example: Pedestrian and Bike at Intersection 
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29 
4.0 Week 2 Introduction 
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V. Lesson 4: Newton's Laws of Motion 
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4.1 Newton's First and Second Laws 
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4.2 Newton's Third Law 
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32 
4.3 Reference Frames 
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4.4 Noninertial Reference Frames 
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VI. Lesson 5: Gravity 
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5.1 Universal Law of Gravitation 
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35 
5.2 Worked Example: Gravity  Superpositon 
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36 
5.3 Gravity at the surface of the Earth: The value of g. 
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VII. Lesson 6: Contact Forces 
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6.1 Contact Forces 
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6.2 Static Friction 
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VIII. Lesson 7: Tension and Springs 
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7.1 Pushing Pulling and Tension 
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7.2 Ideal Rope 
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7.3 Solving Pulley Systems 
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7.4 Hooke's Law 
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IX. Deep Dive: Friction 
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DD.1.1 Friction at the Nanoscale 
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X. Week 2 Worked Examples 
44 
PS.2.1 Worked Example  Sliding Block 
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45 
PS.2.2 Worked Example  Stacked Blocks  Free Body Diagrams and Applying Newtons 2nd Law 
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46 
PS.2.2 Worked Example  Stacked Blocks  Solve for the Maximum Force 
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47 
PS.2.2 Worked Example  Stacked Blocks  Choosing the System of 2 Blocks Together 
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48 
PS.2.3 Window Washer Free Body Diagrams 
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49 
PS.2.3 Window Washer Solution 
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50 
Newton's 3rd Law Pairs 
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51 
Internal and External Forces 
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52 
Applying Newton's 2nd Law 
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53 
8.0 Week 3 Introduction 
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XI. Lesson 8: Circular Motion  Position and Velocity 
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8.1 Polar Coordinates 
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8.2 Circular Motion: Position and Velocity Vectors 
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8.3 Angular Velocity 
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XII. Lesson 9: Uniform Circular Motion 
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9.1 Uniform Circular Motion 
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9.2 Uniform Circular Motion: Direction of the Acceleration 
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XIII. Lesson 10: Circular Motion – Acceleration 
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10.1 Circular Motion  Acceleration 
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10.2 Angular Acceleration 
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10.3 Worked Example  Angular position from angular acceleration. 
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XIV. Lesson 11: Newton's 2nd Law and Circular Motion 
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11.1 Newton's 2nd Law and Circular Motion 
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11.2 Worked Example  Car on a Banked Turn 
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11.3 Demo: Rotating Bucket 
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XV. Week 3 Worked Examples 
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PS.3.1 Worked Example  Orbital Circular Motion  Radius 
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PS.3.1 Worked Example  Orbital Circular Motion  Velocity 
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PS.3.1 Worked Example  Orbital Circular Motion  Period 
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68 
12.0 Week 4 Introduction 
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XVI. Lesson 12: Pulleys and Constraints 
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12.1 Pulley Problems 
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12.2 Constraint Condition 
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12.3 Virtual Displacement 
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12.4 Solve the System of Equations 
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12.5 Worked Example: 2 Blocks and 2 Pulleys 
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XVII. Lesson 13: Massive Rope 
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13.1 Rope Hanging Between Trees 
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13.2 Differential Analysis of a Massive Rope 
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13.3 Differential Elements 
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13.4 Density 
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13.5 Demo: Wrapping Friction 
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79 
13.6 Summary for Differential Analysis 
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XVIII. Lesson 14: Resistive Forces 
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14.1 Intro to resistive forces 
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14.2 Resistive forces  low speed case 
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14.3 Resistive forces  high speed case 
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83 
15.0 Week 5 Introduction 
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XIX. Lesson 15: Momentum and Impulse 
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15.1 Momentum and Impulse 
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15.2 Impulse is a Vector 
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15.3 Worked Example  Bouncing Ball 
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15.4 Momentum of a System of Point Particles 
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15.5 Force on a System of Particles 
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XX. Lesson 16: Conservation of Momentum 
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16.1 Cases of Constant Momentum 
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16.2 Momentum Diagrams 
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XXI. Lesson 17: Center of Mass and Motion of the Center of Mass 
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17.1 Definition of the Center of Mass 
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17.2 Worked Example  Center of Mass of 3 Objects 
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17.3 Center of Mass of a Continuous System 
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17.5 Worked Example  Center of Mass of a Uniform Rod 
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17.6 Velocity and Acceleration of the Center of Mass 
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17.7 Reduction of a System to a Point Particle 
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97 
18.0 Week 6 Introduction 
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XXII. Lesson 18: Relative Velocity and Recoil 
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18.1 Relative Velocity 
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18.2 Set up a Recoil Problem 
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18.3 Solve for Velocity in the Ground Frame 
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18.4 Solve for Velocity in the Moving Frame 
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XXIII. Lesson 19: Continuous Mass Transfer 
102 
19.1 Rocket Problem 1  Set up the Problem 
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19.2 Rocket Problem 2  Momentum Diagrams 
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19.3 Rocket Problem 3  Mass Relations 
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19.4 Rocket Problem 4  Solution 
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19.5 Rocket Problem 5  Thrust and External Forces 
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19.6 Rocket Problem 6  Solution for No External Forces 
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19.7 Rocket Problem 7  Solution with External Forces 
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XXIV. Week 6 Worked Examples 
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PS.6.1 Rocket Sled  Differential Equation 
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110 
PS.6.1 Rocket Sled  Integrate the Rocket Equation 
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111 
PS.6.1 Rocket Sled  Solve for Initial Velocity 
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112 
PS.6.2 Snowplow Problem 
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113 
20.0 Week 7 Introduction 
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XXV. Lesson 20: Kinetic Energy and Work in 1D 
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20.1 Kinetic Energy 
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20.2 Work by a Constant Force 
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20.3 Work by a NonConstant Force 
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20.4 Integrate adt and adx 
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20.5 WorkKinetic Energy Theorem 
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20.6 Power 
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XXVI. Lesson 21: Kinetic Energy and Work in 2D and 3D 
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21.1 Scalar Product Properties 
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21.2 Scalar Product in Cartesian Coordinates 
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21.3 Kinetic Energy as a Scalar Product 
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21.4 Work in 2D and 3D 
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21.5 WorkKinetic Energy Theorem in 2D and 3D 
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21.6 Worked Example: Block Going Down a Ramp 
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XXVII. Lesson 22: Conservative and NonConservative Forces 
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22.1 Path Independence  Gravity 
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22.2 Path Dependence  Friction 
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22.3 Conservative Forces 
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22.4 Nonconservative Forces 
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130 
22.5 Summary of Work and Kinetic Energy 
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XXVIII. Week 7 Worked Examples 
131 
PS.7.1 Worked Example  Collision and Sliding on a Rough Surface 
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132 
23.0 Week 8 Introduction 
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XXIX. Lesson 23: Potential Energy 
133 
23.1 Introduction to Potential Energy 
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134 
23.2 Potential Energy of Gravity near the Surface of the Earth 
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23.3 Potential Energy Reference State 
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136 
23.4 Potential Energy of a Spring 
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137 
23.5 Potential Energy of Gravitation 
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XXX. Lesson 24: Conservation of Energy 
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24.1 Mechanical Energy and Energy Conservation 
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139 
24.2 Energy State Diagrams 
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24.3 Worked Example  Block Sliding Down Circular Slope 
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141 
24.4 Newton's 2nd Law and Energy Conservation 
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XXXI. Lesson 25: Potential Energy Diagrams 
142 
25.1 Force is the Derivative of Potential 
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143 
25.2 Stable and Unstable Equilibrium Points 
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25.3 Reading Potential Energy Diagrams 
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145 
26.0 Week 9 Introduction 
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XXXII. Lesson 26: Types of Collision 
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26.1 Momentum in Collisions 
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26.2 Kinetic Energy in Collisions 
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26.3 Totally Inelastic Collisions 
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XXXIII. Lesson 27: Elastic Collisions 
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27.1 Worked Example: Elastic 1D Collision 
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27.2 Relative Velocity in 1D 
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27.3 Kinetic Energy and Momentum Equation 
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27.4 Worked Example: Elastic 1D Collision Again 
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153 
27.5 Worked Example: Gravitational Slingshot 
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27.6 2D Collisions 
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XXXIV. Deep Dive: Center of Mass Reference Frame 
155 
DD.2.1 Position in the CM Frame 
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DD.2.2 Relative Velocity is Independent of Reference Frame 
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157 
DD.2.3 1D Elastic Collision Velocities in CM Frame 
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158 
DD.2.4 Worked Example: 1D Elastic Collision in CM Frame 
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159 
DD.2.5 Kinetic Energy in Different Reference Frames 
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160 
DD.2.6 Kinetic Energy in the CM Frame 
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161 
DD.2.7 Change in the Kinetic Energy 
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162 
28.0 Week 10 Introduction 
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XXXV. Lesson 28: Motion of a Rigid Body 
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28.1 Rigid Bodies 
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28.2 Introduction to Translation and Rotation 
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165 
28.3 Review of Angular Velocity and Acceleration 
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XXXVI. Lesson 29: Moment of Inertia 
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29.1 Kinetic Energy of Rotation 
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167 
29.2 Moment of Inertia of a Rod 
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29.3 Moment of Inertia of a Disc 
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169 
29.4 Parallel Axis Theorem 
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170 
29.5 Deep Dive  Moment of Inertia of a Sphere 
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29.6 Deep Dive  Derivation of the Parallel Axis Theorem 
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XXXVII. Lesson 30: Torque 
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30.1 Introduction to Torque and Rotational Dynamics 
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30.2 Cross Product 
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30.3 Cross Product in Cartesian Coordinates 
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30.4 Torque 
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30.5 Torque from Gravity 
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XXXVIII. Lesson 31: Rotational Dynamics 
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31.1 Relationship between Torque and Angular Acceleration 
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31.2 Internal Torques Cancel in Pairs 
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31.3 Worked Example  Find the Moment of Inertia of a Disc from a Falling Mass 
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31.4 Worked Example  Atwood Machine 
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31.5 Massive Pulley Problems 
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31.7 Worked Example  Two Blocks and a Pulley Using Energy 
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XXXIX. Week 10 Worked Examples 
183 
PS.10.1 Worked Example  Blocks with Friction and Massive Pulley 
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184 
32.0 Week 11 Introduction 
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XL. Lesson 32: Angular Momentum of a Point Particle 
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32.1 Angular Momentum for a Point Particle 
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32.2 Calculating Angular Momentum 
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32.3 Worked Example  Angular Momentum About Different Points 
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188 
32.4 Angular Momentum of Circular Motion 
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XLI. Lesson 33: Angular Momentum of a Rigid Body about a Fixed Axis 
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33.1 Worked Example  Angular Momentum of 2 Rotating Point Particles 
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33.2 Angular Momentum of a Symmetric Object 
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191 
33.4 If Momentum is Zero then Angular Momentum is Independent of Origin 
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33.5 Kinetic Energy of a Symmetric Object 
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XLII. Lesson 34: Torque and Angular Impulse 
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34.1 Torque Causes Angular Momentum to Change  Point Particle 
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34.2 Torque Causes Angular Momentum to Change  System of Particles 
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34.3 Angular Impulse 
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34.4 Demo: Bicycle Wheel Demo 
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34.5 Worked Example  Particle Hits Pivoted Ring 
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198 
35.0 Week 12 Introduction 
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XLIII. Lesson 35: Rolling Kinematics 
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35.1 Translation and Rotation of a Wheel 
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35.2 Rolling Wheel in the Center of Mass Frame 
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35.3 Rolling Wheel in the Ground Frame 
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35.4 Rolling Without Slipping Slipping and Skidding 
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35.5 Contact Point of a Wheel Rolling Without Slipping 
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XLIV. Lesson 36: Rolling Dynamics 
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36.1 Friction on a Rolling Wheel 
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36.2 Worked Example  Wheel Rolling Without Slipping Down Inclined Plane  Torque Method 
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36.3 Demo: Spool Demo 
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36.4 Worked Example  Yoyo Pulled Along the Ground 
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36.5 Analyze Force and Torque in Translation and Rotation Problems 
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XLV. Lesson 37: Rolling Kinetic Energy and Angular Momentum 
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37.1 Kinetic Energy of Translation and Rotation 
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37.2 Worked Example  Wheel Rolling Without Slipping Down Inclined Plane 
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211 
37.3 Angular Momentum of Translation and Rotation 
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XLVI. Deep Dive: Gyroscopes 
212 
DD.3.1 Deep Dive  Gyroscopes  Free Body Diagrams, Torque, and Rotating Vectors 
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DD.3.2 Deep Dive  Gyroscopes  Precessional Angular Velocity and Titled Gyroscopes 
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214 
DD.3.3 Deep Dive  Gyroscopes  Nutation and Total Angular Momentum 
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