Library/Classical Mechanics: Newtonian Physics from Kinematics to Rotation (MIT 8.01SC)/Lesson 182 of 215

Massive Pulley Problems

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Course Contents

  1. 1Course Introduction2:15
  2. 2Vectors vs. Scalars1:07
  3. 3Vector Operators2:14
  4. 4Coordinate Systems and Unit Vectors1:04
  5. 5Vectors: Magnitude and Direction0:40
  6. 6Vector Decomposition into Components1:38
  7. 7Going Between Vector Representations1:36
  8. 8Week 1 Introduction2:15
  9. 9Coordinate Systems and Unit Vectors in 1D3:06
  10. 10Position Vector in 1D2:25
  11. 11Displacement Vector in 1D3:28
  12. 12Average Velocity in 1D2:18
  13. 13Instantaneous Velocity in 1D5:40
  14. 14Worked Example: Derivatives in Kinematics3:08
  15. 15Introduction to Acceleration3:26
  16. 16Acceleration in 1D4:29
  17. 17Worked Example: Acceleration from Position3:45
  18. 18Integration22:34
  19. 19Coordinate System and Position Vector in 2D2:17
  20. 20Instantaneous Velocity in 2D6:12
  21. 21Instantaneous Acceleration in 2D5:20
  22. 22Projectile Motion6:12
  23. 23Demo: Shooting an Apple0:52
  24. 24Demo: Relative Motion Gun0:35
  25. 25Problem Solving: Three Questions Before Starting2:07
  26. 26Shooting the Apple: Solution10:19
  27. 27Worked Example: Braking Car6:47
  28. 28Sketch the Motion2:10
  29. 29Worked Example: Pedestrian and Bike at Intersection13:59
  30. 30Week 2 Introduction2:23
  31. 31Newton's First and Second Laws4:16
  32. 32Newton's Third Law7:15
  33. 33Reference Frames9:26
  34. 34Non-inertial Reference Frames4:38
  35. 35Universal Law of Gravitation6:55
  36. 36Worked Example: Gravity Superposition8:46
  37. 37Gravity at Earth's Surface: The Value of g4:49
  38. 38Contact Forces3:18
  39. 39Static Friction3:20
  40. 40Pushing, Pulling and Tension4:17
  41. 41Ideal Rope4:58
  42. 42Solving Pulley Systems9:56
  43. 43Hooke's Law6:00
  44. 44Deep Dive: Friction at the Nanoscale39:12
  45. 45Worked Example: Sliding Block6:20
  46. 46Worked Example: Stacked Blocks – Free Body Diagrams and Newton's Second Law8:13
  47. 47Stacked Blocks: Solving for the Maximum Force4:44
  48. 48Stacked Blocks: Choosing the Two-Block System5:28
  49. 49Window Washer: Free Body Diagrams10:13
  50. 50Window Washer: Solution2:26
  51. 51Newton's Third Law Pairs4:18
  52. 52Internal and External Forces3:44
  53. 53Applying Newton's Second Law3:17
  54. 54Week 3 Introduction1:27
  55. 55Polar Coordinates3:35
  56. 56Circular Motion: Position and Velocity Vectors6:02
  57. 57Angular Velocity5:31
  58. 58Uniform Circular Motion3:50
  59. 59Uniform Circular Motion: Direction of Acceleration3:36
  60. 60Circular Motion: Acceleration4:00
  61. 61Angular Acceleration6:21
  62. 62Worked Example: Angular Position from Angular Acceleration4:45
  63. 63Newton's Second Law and Circular Motion3:17
  64. 64Worked Example: Car on a Banked Turn7:37
  65. 65Demo: Rotating Bucket0:40
  66. 66Orbital Circular Motion: Radius3:44
  67. 67Orbital Circular Motion: Velocity1:07
  68. 68Orbital Circular Motion: Period1:40
  69. 69Week 4 Introduction2:16
  70. 70Pulley Problems10:30
  71. 71Constraint Conditions7:07
  72. 72Virtual Displacement3:43
  73. 73Solving the System of Equations4:04
  74. 74Worked Example: Two Blocks and Two Pulleys8:41
  75. 75Rope Hanging Between Trees3:36
  76. 76Differential Analysis of a Massive Rope15:34
  77. 77Differential Elements1:04
  78. 78Density0:52
  79. 79Demo: Wrapping Friction1:01
  80. 80Summary of Differential Analysis1:18
  81. 81Introduction to Resistive Forces4:52
  82. 82Resistive Forces: Low-Speed Case8:26
  83. 83Resistive Forces: High-Speed Case10:50
  84. 84Week 5 Introduction2:28
  85. 85Momentum and Impulse7:21
  86. 86Impulse Is a Vector3:16
  87. 87Worked Example: Bouncing Ball6:38
  88. 88Momentum of a System of Point Particles4:45
  89. 89Force on a System of Particles9:06
  90. 90Cases of Constant Momentum5:34
  91. 91Momentum Diagrams5:18
  92. 92Definition of the Center of Mass4:32
  93. 93Worked Example: Center of Mass of Three Objects7:14
  94. 94Center of Mass of a Continuous System2:55
  95. 95Worked Example: Center of Mass of a Uniform Rod5:51
  96. 96Velocity and Acceleration of the Center of Mass4:16
  97. 97Reduction of a System to a Point Particle4:03
  98. 98Week 6 Introduction0:53
  99. 99Relative Velocity1:57
  100. 100Setting Up a Recoil Problem6:28
  101. 101Recoil: Velocity in the Ground Frame3:00
  102. 102Recoil: Velocity in the Moving Frame2:09
  103. 103Rocket Problem 1: Setting Up3:48
  104. 104Rocket Problem 2: Momentum Diagrams5:00
  105. 105Rocket Problem 3: Mass Relations2:50
  106. 106Rocket Problem 4: Solution5:30
  107. 107Rocket Problem 5: Thrust and External Forces3:28
  108. 108Rocket Problem 6: No External Forces5:10
  109. 109Rocket Problem 7: With External Forces5:07
  110. 110Rocket Sled: Differential Equation3:11
  111. 111Rocket Sled: Integrating the Rocket Equation3:33
  112. 112Rocket Sled: Solving for Initial Velocity1:03
  113. 113Snowplow Problem8:11
  114. 114Week 7 Introduction2:04
  115. 115Kinetic Energy2:41
  116. 116Work by a Constant Force3:44
  117. 117Work by a Non-Constant Force6:20
  118. 118Integrating a dt and a dx4:50
  119. 119Work–Kinetic Energy Theorem1:56
  120. 120Power1:07
  121. 121Scalar Product Properties7:47
  122. 122Scalar Product in Cartesian Coordinates4:50
  123. 123Kinetic Energy as a Scalar Product2:01
  124. 124Work in 2D and 3D5:25
  125. 125Work–Kinetic Energy Theorem in 2D and 3D5:51
  126. 126Worked Example: Block Going Down a Ramp5:59
  127. 127Path Independence: Gravity5:39
  128. 128Path Dependence: Friction5:17
  129. 129Conservative Forces2:30
  130. 130Non-conservative Forces1:44
  131. 131Summary of Work and Kinetic Energy7:00
  132. 132Worked Example: Collision and Sliding on a Rough Surface6:47
  133. 133Week 8 Introduction0:55
  134. 134Introduction to Potential Energy9:51
  135. 135Gravitational Potential Energy near Earth's Surface3:54
  136. 136Potential Energy Reference State5:01
  137. 137Potential Energy of a Spring5:20
  138. 138Gravitational Potential Energy7:40
  139. 139Mechanical Energy and Energy Conservation5:56
  140. 140Energy State Diagrams5:34
  141. 141Worked Example: Block Sliding Down a Circular Slope7:28
  142. 142Newton's Second Law and Energy Conservation5:28
  143. 143Force as the Derivative of Potential Energy3:59
  144. 144Stable and Unstable Equilibrium Points7:22
  145. 145Reading Potential Energy Diagrams5:22
  146. 146Week 9 Introduction1:34
  147. 147Momentum in Collisions4:12
  148. 148Kinetic Energy in Collisions5:14
  149. 149Totally Inelastic Collisions4:47
  150. 150Worked Example: Elastic 1D Collision10:33
  151. 151Relative Velocity in 1D3:43
  152. 152Kinetic Energy and Momentum Equation7:09
  153. 153Worked Example: Elastic 1D Collision Again5:23
  154. 154Worked Example: Gravitational Slingshot4:45
  155. 1552D Collisions6:46
  156. 156Position in the CM Frame4:33
  157. 157Relative Velocity Is Independent of Reference Frame3:43
  158. 1581D Elastic Collision Velocities in the CM Frame3:46
  159. 159Worked Example: 1D Elastic Collision in the CM Frame6:02
  160. 160Kinetic Energy in Different Reference Frames6:06
  161. 161Kinetic Energy in the CM Frame4:27
  162. 162Change in Kinetic Energy3:53
  163. 163Week 10 Introduction2:36
  164. 164Rigid Bodies3:01
  165. 165Introduction to Translation and Rotation2:39
  166. 166Review of Angular Velocity and Acceleration3:14
  167. 167Kinetic Energy of Rotation6:27
  168. 168Moment of Inertia of a Rod4:20
  169. 169Moment of Inertia of a Disc5:41
  170. 170Parallel Axis Theorem4:11
  171. 171Deep Dive: Moment of Inertia of a Sphere5:32
  172. 172Deep Dive: Derivation of the Parallel Axis Theorem5:38
  173. 173Introduction to Torque and Rotational Dynamics9:52
  174. 174Cross Product5:09
  175. 175Cross Product in Cartesian Coordinates7:55
  176. 176Torque2:04
  177. 177Torque from Gravity4:44
  178. 178Torque and Angular Acceleration9:06
  179. 179Internal Torques Cancel in Pairs3:26
  180. 180Worked Example: Moment of Inertia of a Disc from a Falling Mass7:20
  181. 181Worked Example: Atwood Machine11:02
  182. 182Massive Pulley Problems3:45
  183. 183Worked Example: Two Blocks and a Pulley Using Energy7:37
  184. 184Worked Example: Blocks with Friction and a Massive Pulley16:08
  185. 185Week 11 Introduction1:52
  186. 186Angular Momentum of a Point Particle2:39
  187. 187Calculating Angular Momentum3:08
  188. 188Worked Example: Angular Momentum About Different Points6:10
  189. 189Angular Momentum of Circular Motion3:27
  190. 190Worked Example: Angular Momentum of Two Rotating Particles7:00
  191. 191Angular Momentum of a Symmetric Object4:11
  192. 192Zero Momentum: Angular Momentum Independent of Origin5:42
  193. 193Kinetic Energy of a Symmetric Object2:34
  194. 194Torque Changes Angular Momentum: Point Particle2:59
  195. 195Torque Changes Angular Momentum: System of Particles3:56
  196. 196Angular Impulse3:42
  197. 197Demo: Bicycle Wheel0:38
  198. 198Worked Example: Particle Hits Pivoted Ring8:13
  199. 199Week 12 Introduction1:35
  200. 200Translation and Rotation of a Wheel3:18
  201. 201Rolling Wheel in the CM Frame2:24
  202. 202Rolling Wheel in the Ground Frame2:28
  203. 203Rolling Without Slipping, Slipping and Skidding5:57
  204. 204Contact Point of a Rolling Wheel3:38
  205. 205Friction on a Rolling Wheel4:08
  206. 206Worked Example: Wheel Rolling Down an Incline (Torque Method)6:05
  207. 207Demo: Spool0:44
  208. 208Worked Example: Yo-yo Pulled Along the Ground6:13
  209. 209Analyzing Force and Torque in Translation and Rotation Problems3:06
  210. 210Kinetic Energy of Translation and Rotation7:46
  211. 211Worked Example: Wheel Rolling Down an Incline (Energy)4:14
  212. 212Angular Momentum of Translation and Rotation6:55
  213. 213Deep Dive: Gyroscopes – Free Body Diagrams, Torque and Rotating Vectors16:57
  214. 214Deep Dive: Gyroscopes – Precession and Tilted Gyroscopes13:58
  215. 215Deep Dive: Gyroscopes – Nutation and Total Angular Momentum13:25
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