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Classical Mechanics: Newtonian Physics from Kinematics to Rotation (MIT 8.01SC)
A 12-week calculus-based introduction to Newtonian mechanics from MIT. It runs from vectors and 1D/2D kinematics through Newton's laws, circular motion, momentum, work and energy, collisions, rotational dynamics, angular momentum, rolling, and gyroscopes. Lessons are short concept clips mixed with many worked examples, so it suits first-year college physics students or self-learners who know basic calculus.
Lessons by MIT OpenCourseWare on YouTubeCurated by YodaHut. These lessons are hosted on YouTube and produced by their original creators, who are not affiliated with YodaHut. You still earn YodaCoins, keep your streak and track progress here.
What You'll Learn
- Describe motion with vectors, derivatives and integrals, and solve 1D, 2D and projectile kinematics problems
- Draw free body diagrams and apply Newton's laws to problems with friction, tension, springs, pulleys and constraints
- Analyze uniform and non-uniform circular motion, including banked turns and orbits, with polar coordinates and angular velocity and acceleration
- Use impulse, momentum, center of mass and the rocket equation to solve variable-mass and recoil problems
- Apply the work–kinetic energy theorem, potential energy, and energy conservation, including reading potential energy diagrams for equilibrium
- Solve elastic and inelastic collisions in 1D and 2D, including in the center-of-mass frame
- Compute moments of inertia, torque and angular momentum, and analyze rolling without slipping and basic gyroscope precession
Prerequisites
- Single-variable calculus basics (derivatives and integrals), or taken alongside it
- High school algebra and trigonometry
- Some prior exposure to physics is helpful but not required
Course Curriculum
- 1Course Introduction2:15
- 2Vectors vs. Scalars1:07
- 3Vector Operators2:14
- 4Coordinate Systems and Unit Vectors1:04
- 5Vectors: Magnitude and Direction0:40
- 6Vector Decomposition into Components1:38
- 7Going Between Vector Representations1:36
- 8Week 1 Introduction2:15
- 9Coordinate Systems and Unit Vectors in 1D3:06
- 10Position Vector in 1D2:25
- 11Displacement Vector in 1D3:28
- 12Average Velocity in 1D2:18
- 13Instantaneous Velocity in 1D5:40
- 14Worked Example: Derivatives in Kinematics3:08
- 15Introduction to Acceleration3:26
- 16Acceleration in 1D4:29
- 17Worked Example: Acceleration from Position3:45
- 18Integration22:34
- 19Coordinate System and Position Vector in 2D2:17
- 20Instantaneous Velocity in 2D6:12
- 21Instantaneous Acceleration in 2D5:20
- 22Projectile Motion6:12
- 23Demo: Shooting an Apple0:52
- 24Demo: Relative Motion Gun0:35
- 25Problem Solving: Three Questions Before Starting2:07
- 26Shooting the Apple: Solution10:19
- 27Worked Example: Braking Car6:47
- 28Sketch the Motion2:10
- 29Worked Example: Pedestrian and Bike at Intersection13:59
- 30Week 2 Introduction2:23
- 31Newton's First and Second Laws4:16
- 32Newton's Third Law7:15
- 33Reference Frames9:26
- 34Non-inertial Reference Frames4:38
- 35Universal Law of Gravitation6:55
- 36Worked Example: Gravity Superposition8:46
- 37Gravity at Earth's Surface: The Value of g4:49
- 38Contact Forces3:18
- 39Static Friction3:20
- 40Pushing, Pulling and Tension4:17
- 41Ideal Rope4:58
- 42Solving Pulley Systems9:56
- 43Hooke's Law6:00
- 44Deep Dive: Friction at the Nanoscale39:12
- 45Worked Example: Sliding Block6:20
- 46Worked Example: Stacked Blocks – Free Body Diagrams and Newton's Second Law8:13
- 47Stacked Blocks: Solving for the Maximum Force4:44
- 48Stacked Blocks: Choosing the Two-Block System5:28
- 49Window Washer: Free Body Diagrams10:13
- 50Window Washer: Solution2:26
- 51Newton's Third Law Pairs4:18
- 52Internal and External Forces3:44
- 53Applying Newton's Second Law3:17
- 54Week 3 Introduction1:27
- 55Polar Coordinates3:35
- 56Circular Motion: Position and Velocity Vectors6:02
- 57Angular Velocity5:31
- 58Uniform Circular Motion3:50
- 59Uniform Circular Motion: Direction of Acceleration3:36
- 60Circular Motion: Acceleration4:00
- 61Angular Acceleration6:21
- 62Worked Example: Angular Position from Angular Acceleration4:45
- 63Newton's Second Law and Circular Motion3:17
- 64Worked Example: Car on a Banked Turn7:37
- 65Demo: Rotating Bucket0:40
- 66Orbital Circular Motion: Radius3:44
- 67Orbital Circular Motion: Velocity1:07
- 68Orbital Circular Motion: Period1:40
- 69Week 4 Introduction2:16
- 70Pulley Problems10:30
- 71Constraint Conditions7:07
- 72Virtual Displacement3:43
- 73Solving the System of Equations4:04
- 74Worked Example: Two Blocks and Two Pulleys8:41
- 75Rope Hanging Between Trees3:36
- 76Differential Analysis of a Massive Rope15:34
- 77Differential Elements1:04
- 78Density0:52
- 79Demo: Wrapping Friction1:01
- 80Summary of Differential Analysis1:18
- 81Introduction to Resistive Forces4:52
- 82Resistive Forces: Low-Speed Case8:26
- 83Resistive Forces: High-Speed Case10:50
- 84Week 5 Introduction2:28
- 85Momentum and Impulse7:21
- 86Impulse Is a Vector3:16
- 87Worked Example: Bouncing Ball6:38
- 88Momentum of a System of Point Particles4:45
- 89Force on a System of Particles9:06
- 90Cases of Constant Momentum5:34
- 91Momentum Diagrams5:18
- 92Definition of the Center of Mass4:32
- 93Worked Example: Center of Mass of Three Objects7:14
- 94Center of Mass of a Continuous System2:55
- 95Worked Example: Center of Mass of a Uniform Rod5:51
- 96Velocity and Acceleration of the Center of Mass4:16
- 97Reduction of a System to a Point Particle4:03
- 98Week 6 Introduction0:53
- 99Relative Velocity1:57
- 100Setting Up a Recoil Problem6:28
- 101Recoil: Velocity in the Ground Frame3:00
- 102Recoil: Velocity in the Moving Frame2:09
- 103Rocket Problem 1: Setting Up3:48
- 104Rocket Problem 2: Momentum Diagrams5:00
- 105Rocket Problem 3: Mass Relations2:50
- 106Rocket Problem 4: Solution5:30
- 107Rocket Problem 5: Thrust and External Forces3:28
- 108Rocket Problem 6: No External Forces5:10
- 109Rocket Problem 7: With External Forces5:07
- 110Rocket Sled: Differential Equation3:11
- 111Rocket Sled: Integrating the Rocket Equation3:33
- 112Rocket Sled: Solving for Initial Velocity1:03
- 113Snowplow Problem8:11
- 114Week 7 Introduction2:04
- 115Kinetic Energy2:41
- 116Work by a Constant Force3:44
- 117Work by a Non-Constant Force6:20
- 118Integrating a dt and a dx4:50
- 119Work–Kinetic Energy Theorem1:56
- 120Power1:07
- 121Scalar Product Properties7:47
- 122Scalar Product in Cartesian Coordinates4:50
- 123Kinetic Energy as a Scalar Product2:01
- 124Work in 2D and 3D5:25
- 125Work–Kinetic Energy Theorem in 2D and 3D5:51
- 126Worked Example: Block Going Down a Ramp5:59
- 127Path Independence: Gravity5:39
- 128Path Dependence: Friction5:17
- 129Conservative Forces2:30
- 130Non-conservative Forces1:44
- 131Summary of Work and Kinetic Energy7:00
- 132Worked Example: Collision and Sliding on a Rough Surface6:47
- 133Week 8 Introduction0:55
- 134Introduction to Potential Energy9:51
- 135Gravitational Potential Energy near Earth's Surface3:54
- 136Potential Energy Reference State5:01
- 137Potential Energy of a Spring5:20
- 138Gravitational Potential Energy7:40
- 139Mechanical Energy and Energy Conservation5:56
- 140Energy State Diagrams5:34
- 141Worked Example: Block Sliding Down a Circular Slope7:28
- 142Newton's Second Law and Energy Conservation5:28
- 143Force as the Derivative of Potential Energy3:59
- 144Stable and Unstable Equilibrium Points7:22
- 145Reading Potential Energy Diagrams5:22
- 146Week 9 Introduction1:34
- 147Momentum in Collisions4:12
- 148Kinetic Energy in Collisions5:14
- 149Totally Inelastic Collisions4:47
- 150Worked Example: Elastic 1D Collision10:33
- 151Relative Velocity in 1D3:43
- 152Kinetic Energy and Momentum Equation7:09
- 153Worked Example: Elastic 1D Collision Again5:23
- 154Worked Example: Gravitational Slingshot4:45
- 1552D Collisions6:46
- 156Position in the CM Frame4:33
- 157Relative Velocity Is Independent of Reference Frame3:43
- 1581D Elastic Collision Velocities in the CM Frame3:46
- 159Worked Example: 1D Elastic Collision in the CM Frame6:02
- 160Kinetic Energy in Different Reference Frames6:06
- 161Kinetic Energy in the CM Frame4:27
- 162Change in Kinetic Energy3:53
- 163Week 10 Introduction2:36
- 164Rigid Bodies3:01
- 165Introduction to Translation and Rotation2:39
- 166Review of Angular Velocity and Acceleration3:14
- 167Kinetic Energy of Rotation6:27
- 168Moment of Inertia of a Rod4:20
- 169Moment of Inertia of a Disc5:41
- 170Parallel Axis Theorem4:11
- 171Deep Dive: Moment of Inertia of a Sphere5:32
- 172Deep Dive: Derivation of the Parallel Axis Theorem5:38
- 173Introduction to Torque and Rotational Dynamics9:52
- 174Cross Product5:09
- 175Cross Product in Cartesian Coordinates7:55
- 176Torque2:04
- 177Torque from Gravity4:44
- 178Torque and Angular Acceleration9:06
- 179Internal Torques Cancel in Pairs3:26
- 180Worked Example: Moment of Inertia of a Disc from a Falling Mass7:20
- 181Worked Example: Atwood Machine11:02
- 182Massive Pulley Problems3:45
- 183Worked Example: Two Blocks and a Pulley Using Energy7:37
- 184Worked Example: Blocks with Friction and a Massive Pulley16:08
- 185Week 11 Introduction1:52
- 186Angular Momentum of a Point Particle2:39
- 187Calculating Angular Momentum3:08
- 188Worked Example: Angular Momentum About Different Points6:10
- 189Angular Momentum of Circular Motion3:27
- 190Worked Example: Angular Momentum of Two Rotating Particles7:00
- 191Angular Momentum of a Symmetric Object4:11
- 192Zero Momentum: Angular Momentum Independent of Origin5:42
- 193Kinetic Energy of a Symmetric Object2:34
- 194Torque Changes Angular Momentum: Point Particle2:59
- 195Torque Changes Angular Momentum: System of Particles3:56
- 196Angular Impulse3:42
- 197Demo: Bicycle Wheel0:38
- 198Worked Example: Particle Hits Pivoted Ring8:13
- 199Week 12 Introduction1:35
- 200Translation and Rotation of a Wheel3:18
- 201Rolling Wheel in the CM Frame2:24
- 202Rolling Wheel in the Ground Frame2:28
- 203Rolling Without Slipping, Slipping and Skidding5:57
- 204Contact Point of a Rolling Wheel3:38
- 205Friction on a Rolling Wheel4:08
- 206Worked Example: Wheel Rolling Down an Incline (Torque Method)6:05
- 207Demo: Spool0:44
- 208Worked Example: Yo-yo Pulled Along the Ground6:13
- 209Analyzing Force and Torque in Translation and Rotation Problems3:06
- 210Kinetic Energy of Translation and Rotation7:46
- 211Worked Example: Wheel Rolling Down an Incline (Energy)4:14
- 212Angular Momentum of Translation and Rotation6:55
- 213Deep Dive: Gyroscopes – Free Body Diagrams, Torque and Rotating Vectors16:57
- 214Deep Dive: Gyroscopes – Precession and Tilted Gyroscopes13:58
- 215Deep Dive: Gyroscopes – Nutation and Total Angular Momentum13:25
About the Instructor
MIT OpenCourseWare
YouTube creator
215 lessons here 18h 22m
The lessons in this course were produced by MIT OpenCourseWare and are published on YouTube. YodaHut selected and sequenced them into this course; we did not make them, and MIT OpenCourseWare is not affiliated with YodaHut.
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