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



License: Creative Commons BY-NC-SA
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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

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.