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8.01SC

Classical Mechanics

Prof. Deepto Chakrabarty, Dr. Peter Dourmashkin, Dr. Michelle Tomasik, Prof. Anna Frebel, Prof. Vladan Vuletic | Fall 2016

Science & Math Physics Classical Mechanics Science

前往原始課程

CC BY-NC-SA 4.0

課程簡介

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.

課程資訊

來源	MIT 開放式課程
科系	Physics
語言	English
影片數	215

課程影片 (215)

8.01SC Classical Mechanics Introduction

8.01SC Classical Mechanics Introduction

0.1 Vectors vs. Scalars

0.1 Vectors vs. Scalars

0.2 Vector Operators

0.2 Vector Operators

0.3 Coordinate Systems and Unit Vectors

0.3 Coordinate Systems and Unit Vectors

0.4 Vectors - Magnitude and Direction

0.4 Vectors - Magnitude and Direction

0.5 Vector Decomposition into components

0.5 Vector Decomposition into components

0.6 Going Between Representations

0.6 Going Between Representations

1.0 Week 1 Introduction (8.01 Classical Mechanics)

1.0 Week 1 Introduction (8.01 Classical Mechanics)

1.1 Coordinate Systems and Unit Vectors in 1D

1.1 Coordinate Systems and Unit Vectors in 1D

1.2 Position Vector in 1D

1.2 Position Vector in 1D

1.3 Displacement Vector in 1D

1.3 Displacement Vector in 1D

1.4 Average Velocity in 1D

1.4 Average Velocity in 1D

1.5 Instantaneous Velocity in 1D

1.5 Instantaneous Velocity in 1D

1.7 Worked Example: Derivatives in Kinematics

1.7 Worked Example: Derivatives in Kinematics

2.1 Introduction to Acceleration

2.1 Introduction to Acceleration

2.2 Acceleration in 1D

2.2 Acceleration in 1D

2.3 Worked Example: Acceleration from Position

2.3 Worked Example: Acceleration from Position

2.4 Integration

2.4 Integration

3.1 Coordinate System and Position Vector in 2D

3.1 Coordinate System and Position Vector in 2D

3.2 Instantaneous Velocity in 2D

3.2 Instantaneous Velocity in 2D

3.3 Instantaneous Acceleration in 2D

3.3 Instantaneous Acceleration in 2D

3.4 Projectile Motion

3.4 Projectile Motion

3.5 Demo: Shooting an Apple

3.5 Demo: Shooting an Apple

3.5 Demo: Relative Motion Gun

3.5 Demo: Relative Motion Gun

PS.1.1 Three Questions Before Starting

PS.1.1 Three Questions Before Starting

PS.1.2 Shooting the apple solution

PS.1.2 Shooting the apple solution

P.1.3 Worked Example: Braking Car

P.1.3 Worked Example: Braking Car

P.1.4 Sketch the Motion

P.1.4 Sketch the Motion

P.1.5 Worked Example: Pedestrian and Bike at Intersection

P.1.5 Worked Example: Pedestrian and Bike at Intersection

4.0 Week 2 Introduction

4.0 Week 2 Introduction

4.1 Newton's First and Second Laws

4.1 Newton's First and Second Laws

4.2 Newton's Third Law

4.2 Newton's Third Law

4.3 Reference Frames

4.3 Reference Frames

4.4 Non-inertial Reference Frames

4.4 Non-inertial Reference Frames

5.1 Universal Law of Gravitation

5.1 Universal Law of Gravitation

5.2 Worked Example: Gravity - Superposition

5.2 Worked Example: Gravity - Superposition

5.3 Gravity at the surface of the Earth: The value of g.

5.3 Gravity at the surface of the Earth: The value of g.

6.1 Contact Forces

6.1 Contact Forces

6.2 Static Friction

6.2 Static Friction

7.1 Pushing Pulling and Tension

7.1 Pushing Pulling and Tension

7.3 Solving Pulley Systems

7.3 Solving Pulley Systems

7.4 Hooke's Law

7.4 Hooke's Law

DD.1.1 Friction at the Nanoscale

DD.1.1 Friction at the Nanoscale

PS.2.1 Worked Example - Sliding Block

PS.2.1 Worked Example - Sliding Block

PS.2.2 Worked Example - Stacked Blocks - Free Body Diagrams and Applying Newtons 2nd Law

PS.2.2 Worked Example - Stacked Blocks - Free Body Diagrams and Applying Newtons 2nd Law

PS.2.2 Worked Example - Stacked Blocks - Solve for the Maximum Force

PS.2.2 Worked Example - Stacked Blocks - Solve for the Maximum Force

PS.2.2 Worked Example - Stacked Blocks - Choosing the System of 2 Blocks Together

PS.2.2 Worked Example - Stacked Blocks - Choosing the System of 2 Blocks Together

PS.2.3 Window Washer Free Body Diagrams

PS.2.3 Window Washer Free Body Diagrams

PS.2.3 Window Washer Solution

PS.2.3 Window Washer Solution

Newton's 3rd Law Pairs

Newton's 3rd Law Pairs

Internal and External Forces

Internal and External Forces

Applying Newton's 2nd Law

Applying Newton's 2nd Law

8.0 Week 3 Introduction

8.0 Week 3 Introduction

8.1 Polar Coordinates

8.1 Polar Coordinates

8.2 Circular Motion: Position and Velocity Vectors

8.2 Circular Motion: Position and Velocity Vectors

8.3 Angular Velocity

8.3 Angular Velocity

9.1 Uniform Circular Motion

9.1 Uniform Circular Motion

9.2 Uniform Circular Motion: Direction of the Acceleration

9.2 Uniform Circular Motion: Direction of the Acceleration

10.1 Circular Motion - Acceleration

10.1 Circular Motion - Acceleration

10.2 Angular Acceleration

10.2 Angular Acceleration

10.3 Worked Example - Angular position from angular acceleration.

10.3 Worked Example - Angular position from angular acceleration.

11.1 Newton's 2nd Law and Circular Motion

11.1 Newton's 2nd Law and Circular Motion

11.2 Worked Example - Car on a Banked Turn

11.2 Worked Example - Car on a Banked Turn

11.3 Demo: Rotating Bucket

11.3 Demo: Rotating Bucket

PS.3.1 Worked Example - Orbital Circular Motion - Radius

PS.3.1 Worked Example - Orbital Circular Motion - Radius

PS.3.1 Worked Example - Orbital Circular Motion - Velocity

PS.3.1 Worked Example - Orbital Circular Motion - Velocity

PS.3.1 Worked Example - Orbital Circular Motion - Period

PS.3.1 Worked Example - Orbital Circular Motion - Period

12.0 Week 4 Introduction

12.0 Week 4 Introduction

12.1 Pulley Problems

12.1 Pulley Problems

12.2 Constraint Condition

12.2 Constraint Condition

12.3 Virtual Displacement

12.3 Virtual Displacement

12.4 Solve the System of Equations

12.4 Solve the System of Equations

12.5 Worked Example: 2 Blocks and 2 Pulleys

12.5 Worked Example: 2 Blocks and 2 Pulleys

13.1 Rope Hanging Between Trees

13.1 Rope Hanging Between Trees

13.2 Differential Analysis of a Massive Rope

13.2 Differential Analysis of a Massive Rope

13.3 Differential Elements

13.3 Differential Elements

13.5 Demo: Wrapping Friction

13.5 Demo: Wrapping Friction

13.6 Summary for Differential Analysis

13.6 Summary for Differential Analysis

14.1 Intro to resistive forces

14.1 Intro to resistive forces

14.2 Resistive forces - low speed case

14.2 Resistive forces - low speed case

14.3 Resistive forces - high speed case

14.3 Resistive forces - high speed case

15.0 Week 5 Introduction

15.0 Week 5 Introduction

15.1 Momentum and Impulse

15.1 Momentum and Impulse

15.2 Impulse is a Vector

15.2 Impulse is a Vector

15.3 Worked Example - Bouncing Ball

15.3 Worked Example - Bouncing Ball

15.4 Momentum of a System of Point Particles

15.4 Momentum of a System of Point Particles

15.5 Force on a System of Particles

15.5 Force on a System of Particles

16.1 Cases of Constant Momentum

16.1 Cases of Constant Momentum

16.2 Momentum Diagrams

16.2 Momentum Diagrams

17.1 Definition of the Center of Mass

17.1 Definition of the Center of Mass

17.2 Worked Example - Center of Mass of 3 Objects

17.2 Worked Example - Center of Mass of 3 Objects

17.3 Center of Mass of a Continuous System

17.3 Center of Mass of a Continuous System

17.5 Worked Example - Center of Mass of a Uniform Rod

17.5 Worked Example - Center of Mass of a Uniform Rod

17.6 Velocity and Acceleration of the Center of Mass

17.6 Velocity and Acceleration of the Center of Mass

17.7 Reduction of a System to a Point Particle

17.7 Reduction of a System to a Point Particle

18.0 Week 6 Introduction

18.0 Week 6 Introduction

18.1 Relative Velocity

18.1 Relative Velocity

18.2 Set up a Recoil Problem

18.2 Set up a Recoil Problem

18.3 Solve for Velocity in the Ground Frame

18.3 Solve for Velocity in the Ground Frame

18.4 Solve for Velocity in the Moving Frame

18.4 Solve for Velocity in the Moving Frame

19.1 Rocket Problem 1 - Set up the Problem

19.1 Rocket Problem 1 - Set up the Problem

19.2 Rocket Problem 2 - Momentum Diagrams

19.2 Rocket Problem 2 - Momentum Diagrams

19.3 Rocket Problem 3 - Mass Relations

19.3 Rocket Problem 3 - Mass Relations

19.4 Rocket Problem 4 - Solution

19.4 Rocket Problem 4 - Solution

19.5 Rocket Problem 5 - Thrust and External Forces

19.5 Rocket Problem 5 - Thrust and External Forces

19.6 Rocket Problem 6 - Solution for No External Forces

19.6 Rocket Problem 6 - Solution for No External Forces

19.7 Rocket Problem 7 - Solution with External Forces

19.7 Rocket Problem 7 - Solution with External Forces

PS.6.1 Rocket Sled - Differential Equation

PS.6.1 Rocket Sled - Differential Equation

PS.6.1 Rocket Sled - Integrate the Rocket Equation

PS.6.1 Rocket Sled - Integrate the Rocket Equation

PS.6.1 Rocket Sled - Solve for Initial Velocity

PS.6.1 Rocket Sled - Solve for Initial Velocity

PS.6.2 Snowplow Problem

PS.6.2 Snowplow Problem

20.0 Week 7 Introduction

20.0 Week 7 Introduction

20.1 Kinetic Energy

20.1 Kinetic Energy

20.2 Work by a Constant Force

20.2 Work by a Constant Force

20.3 Work by a Non-Constant Force

20.3 Work by a Non-Constant Force

20.4 Integrate adt and adx

20.4 Integrate adt and adx

20.5 Work-Kinetic Energy Theorem

20.5 Work-Kinetic Energy Theorem

21.1 Scalar Product Properties

21.1 Scalar Product Properties

21.2 Scalar Product in Cartesian Coordinates

21.2 Scalar Product in Cartesian Coordinates

21.3 Kinetic Energy as a Scalar Product

21.3 Kinetic Energy as a Scalar Product

21.4 Work in 2D and 3D

21.4 Work in 2D and 3D

21.5 Work-Kinetic Energy Theorem in 2D and 3D

21.5 Work-Kinetic Energy Theorem in 2D and 3D

21.6 Worked Example: Block Going Down a Ramp

21.6 Worked Example: Block Going Down a Ramp

22.1 Path Independence - Gravity

22.1 Path Independence - Gravity

22.2 Path Dependence - Friction

22.2 Path Dependence - Friction

22.3 Conservative Forces

22.3 Conservative Forces

22.4 Non-conservative Forces

22.4 Non-conservative Forces

22.5 Summary of Work and Kinetic Energy

22.5 Summary of Work and Kinetic Energy

PS.7.1 Worked Example - Collision and Sliding on a Rough Surface

PS.7.1 Worked Example - Collision and Sliding on a Rough Surface

23.0 Week 8 Introduction

23.0 Week 8 Introduction

23.1 Introduction to Potential Energy

23.1 Introduction to Potential Energy

23.2 Potential Energy of Gravity near the Surface of the Earth

23.2 Potential Energy of Gravity near the Surface of the Earth

23.3 Potential Energy Reference State

23.3 Potential Energy Reference State

23.4 Potential Energy of a Spring

23.4 Potential Energy of a Spring

23.5 Potential Energy of Gravitation

23.5 Potential Energy of Gravitation

24.1 Mechanical Energy and Energy Conservation

24.1 Mechanical Energy and Energy Conservation

24.2 Energy State Diagrams

24.2 Energy State Diagrams

24.3 Worked Example - Block Sliding Down Circular Slope

24.3 Worked Example - Block Sliding Down Circular Slope

24.4 Newton's 2nd Law and Energy Conservation

24.4 Newton's 2nd Law and Energy Conservation

25.1 Force is the Derivative of Potential

25.1 Force is the Derivative of Potential

25.2 Stable and Unstable Equilibrium Points

25.2 Stable and Unstable Equilibrium Points

25.3 Reading Potential Energy Diagrams

25.3 Reading Potential Energy Diagrams

26.0 Week 9 Introduction

26.0 Week 9 Introduction

26.1 Momentum in Collisions

26.1 Momentum in Collisions

26.2 Kinetic Energy in Collisions

26.2 Kinetic Energy in Collisions

26.3 Totally Inelastic Collisions

26.3 Totally Inelastic Collisions

27.1 Worked Example: Elastic 1D Collision

27.1 Worked Example: Elastic 1D Collision

27.2 Relative Velocity in 1D

27.2 Relative Velocity in 1D

27.3 Kinetic Energy and Momentum Equation

27.3 Kinetic Energy and Momentum Equation

27.4 Worked Example: Elastic 1D Collision Again

27.4 Worked Example: Elastic 1D Collision Again

27.5 Worked Example: Gravitational Slingshot

27.5 Worked Example: Gravitational Slingshot

27.6 2D Collisions

27.6 2D Collisions

DD.2.1 Position in the CM Frame

DD.2.1 Position in the CM Frame

DD.2.2 Relative Velocity is Independent of Reference Frame

DD.2.2 Relative Velocity is Independent of Reference Frame

DD.2.3 1D Elastic Collision Velocities in CM Frame

DD.2.3 1D Elastic Collision Velocities in CM Frame

DD.2.4 Worked Example: 1D Elastic Collision in CM Frame

DD.2.4 Worked Example: 1D Elastic Collision in CM Frame

DD.2.5 Kinetic Energy in Different Reference Frames

DD.2.5 Kinetic Energy in Different Reference Frames

DD.2.6 Kinetic Energy in the CM Frame

DD.2.6 Kinetic Energy in the CM Frame

DD.2.7 Change in the Kinetic Energy

DD.2.7 Change in the Kinetic Energy

28.0 Week 10 Introduction

28.0 Week 10 Introduction

28.1 Rigid Bodies

28.1 Rigid Bodies

28.2 Introduction to Translation and Rotation

28.2 Introduction to Translation and Rotation

28.3 Review of Angular Velocity and Acceleration

28.3 Review of Angular Velocity and Acceleration

29.1 Kinetic Energy of Rotation

29.1 Kinetic Energy of Rotation

29.2 Moment of Inertia of a Rod

29.2 Moment of Inertia of a Rod

29.3 Moment of Inertia of a Disc

29.3 Moment of Inertia of a Disc

29.4 Parallel Axis Theorem

29.4 Parallel Axis Theorem

29.5 Deep Dive - Moment of Inertia of a Sphere

29.5 Deep Dive - Moment of Inertia of a Sphere

29.6 Deep Dive - Derivation of the Parallel Axis Theorem

29.6 Deep Dive - Derivation of the Parallel Axis Theorem

30.1 Introduction to Torque and Rotational Dynamics

30.1 Introduction to Torque and Rotational Dynamics

30.2 Cross Product

30.2 Cross Product

30.3 Cross Product in Cartesian Coordinates

30.3 Cross Product in Cartesian Coordinates

30.5 Torque from Gravity

30.5 Torque from Gravity

31.1 Relationship between Torque and Angular Acceleration

31.1 Relationship between Torque and Angular Acceleration

31.2 Internal Torques Cancel in Pairs

31.2 Internal Torques Cancel in Pairs

31.3 Worked Example - Find the Moment of Inertia of a Disc from a Falling Mass

31.3 Worked Example - Find the Moment of Inertia of a Disc from a Falling Mass

31.4 Worked Example - Atwood Machine

31.4 Worked Example - Atwood Machine

31.5 Massive Pulley Problems

31.5 Massive Pulley Problems

31.7 Worked Example - Two Blocks and a Pulley Using Energy

31.7 Worked Example - Two Blocks and a Pulley Using Energy

PS.10.1 Worked Example - Blocks with Friction and Massive Pulley

PS.10.1 Worked Example - Blocks with Friction and Massive Pulley

32.0 Week 11 Introduction

32.0 Week 11 Introduction

32.1 Angular Momentum for a Point Particle

32.1 Angular Momentum for a Point Particle

32.2 Calculating Angular Momentum

32.2 Calculating Angular Momentum

32.3 Worked Example - Angular Momentum About Different Points

32.3 Worked Example - Angular Momentum About Different Points

32.4 Angular Momentum of Circular Motion

32.4 Angular Momentum of Circular Motion

33.1 Worked Example - Angular Momentum of 2 Rotating Point Particles

33.1 Worked Example - Angular Momentum of 2 Rotating Point Particles

33.2 Angular Momentum of a Symmetric Object

33.2 Angular Momentum of a Symmetric Object

33.4 If Momentum is Zero then Angular Momentum is Independent of Origin

33.4 If Momentum is Zero then Angular Momentum is Independent of Origin

33.5 Kinetic Energy of a Symmetric Object

33.5 Kinetic Energy of a Symmetric Object

34.1 Torque Causes Angular Momentum to Change - Point Particle

34.1 Torque Causes Angular Momentum to Change - Point Particle

34.2 Torque Causes Angular Momentum to Change - System of Particles

34.2 Torque Causes Angular Momentum to Change - System of Particles

34.3 Angular Impulse

34.3 Angular Impulse

34.4 Demo: Bicycle Wheel Demo

34.4 Demo: Bicycle Wheel Demo

34.5 Worked Example - Particle Hits Pivoted Ring

34.5 Worked Example - Particle Hits Pivoted Ring

35.0 Week 12 Introduction

35.0 Week 12 Introduction

35.1 Translation and Rotation of a Wheel

35.1 Translation and Rotation of a Wheel

35.2 Rolling Wheel in the Center of Mass Frame

35.2 Rolling Wheel in the Center of Mass Frame

35.3 Rolling Wheel in the Ground Frame

35.3 Rolling Wheel in the Ground Frame

35.4 Rolling Without Slipping Slipping and Skidding

35.4 Rolling Without Slipping Slipping and Skidding

35.5 Contact Point of a Wheel Rolling Without Slipping

35.5 Contact Point of a Wheel Rolling Without Slipping

36.1 Friction on a Rolling Wheel

36.1 Friction on a Rolling Wheel

36.2 Worked Example - Wheel Rolling Without Slipping Down Inclined Plane - Torque Method

36.2 Worked Example - Wheel Rolling Without Slipping Down Inclined Plane - Torque Method

36.3 Demo: Spool Demo

36.3 Demo: Spool Demo

36.4 Worked Example - Yoyo Pulled Along the Ground

36.4 Worked Example - Yoyo Pulled Along the Ground

36.5 Analyze Force and Torque in Translation and Rotation Problems

36.5 Analyze Force and Torque in Translation and Rotation Problems

37.1 Kinetic Energy of Translation and Rotation

37.1 Kinetic Energy of Translation and Rotation

37.2 Worked Example - Wheel Rolling Without Slipping Down Inclined Plane

37.2 Worked Example - Wheel Rolling Without Slipping Down Inclined Plane

37.3 Angular Momentum of Translation and Rotation

37.3 Angular Momentum of Translation and Rotation

DD.3.1 Deep Dive - Gyroscopes - Free Body Diagrams, Torque, and Rotating Vectors

DD.3.1 Deep Dive - Gyroscopes - Free Body Diagrams, Torque, and Rotating Vectors

DD.3.2 Deep Dive - Gyroscopes - Precessional Angular Velocity and Titled Gyroscopes

DD.3.2 Deep Dive - Gyroscopes - Precessional Angular Velocity and Titled Gyroscopes

DD.3.3 Deep Dive - Gyroscopes - Nutation and Total Angular Momentum

DD.3.3 Deep Dive - Gyroscopes - Nutation and Total Angular Momentum