# Classical Mechanics Lessons and Examples

### 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.

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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### Video Lectures & Study Materials

Visit the official course website for more study materials: https://ocw.mit.edu/courses/physics/8-01-classical-mechanics-fall-2016/

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