0.1 Vectors vs. Scalars 
0.1 Vectors vs. Scalars
by MIT
Video Lecture 1 of 214
Copyright Information: Deepto Chakrabarty, Peter Dourmashkin, Michelle Tomasik, Anna Frebel, and Vladan Vuletic. 8.01 Classical Mechanics. Fall 2016. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu. License: Creative Commons BY-NC-SA.
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Date Added: July 21, 2017

Lecture Description

MIT 8.01 Classical Mechanics, Fall 2016
View the complete course: ocw.mit.edu/8-01F16
Instructor: Dr. Michelle Tomasik



License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu

Course Index

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

Course Description

This first course in the physics curriculum introduces classical mechanics. Historically, a set of core concepts — space, time, mass, force, momentum, torque, and angular momentum — were introduced in classical mechanics in order to solve the most famous physics problem, the motion of the planets.

The principles of mechanics successfully described many other phenomena encountered in the world. Conservation laws involving energy, momentum and angular momentum provided a second parallel approach to solving many of the same problems. In this course, we will investigate both approaches: Force and conservation laws.

Our goal is to develop a conceptual understanding of the core concepts, a familiarity with the experimental verification of our theoretical laws, and an ability to apply the theoretical framework to describe and predict the motions of bodies.

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