12. Work and the Dot Product

• Course Home
• Syllabus
• Introduction to Mechanics

  • 1. Units and Dimensional Analysis
  • 2. Problem Solving and Estimation
• Mathematics: The Language of Science

  • 3. Cartesian Coordinates and Vectors
• Translational Kinematics

  • 4. One-Dimensional Kinematics and Free Fall
  • 5. One-Dimensional Kinematics: Non-Constant Acceleration
  • 6. Two-Dimensional Kinematics
• Force and Newton's Laws of Motion

  • 7. Concept of Force
  • 8. Applications of Newton's Second Law
• Circular Motion

  • 9. Circular Motion Kinematics
  • 10. Circular Motion Dynamics
• Conservation of Energy

  • 11. Work and Energy
  • 12. Work and the Dot Product
  • 13. Potential Energy
  • 14. Application of Energy Conservation
  • 15. Mechanical Energy and the Simple Harmonic Oscillator
• Momentum

  • 16. Momentum and Impulse
  • 17. Systems, Center of Mass, and Conservation of Momentum
  • 18. Collision Theory
  • 19. Continuous Mass Flow
• Two-Dimensional Rotational Motion

  • 20. Two-Dimensional Rotational Kinematics
  • 21. Two-Dimensional Rotational Dynamics
  • 22. Torque and the Simple Harmonic Oscillator
  • 23. Static Equilibrium
• Angular Momentum

  • 24. Angular Momentum
  • 25. Conservation of Angular Momentum
• Rotation and Translation

  • 26. Two-Dimensional Rotation and Translation Kinematics
  • 27. Two-Dimensional Rotation and Translation Dynamics
• Central Force Motion

  • 28. Central Force Motion and the Kepler Problem
• Download Course Materials

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Learning Objectives

• Be able to calculate the work done by a non-uniform force such as a spring force or inverse square forces.
• Be able to calculate the dot product of two vectors using unit vectors associated with both a Cartesian coordinate system and a cylindrical coordinate system.

Preparation

Course Notes

Notes: Kinetic Energy, Work and the Dot Product (PDF - 3.4MB)

Suggested Textbook Reading (Optional)

Chapter 6.4. Young, Hugh D., Roger A. Freedman, and A. Lewis Ford. Sears and Zemansky's University Physics: with Modern Physics. 12th ed. San Francisco, CA: Addison-Wesley, 2007. ISBN: 9780805321876.

Lecture Video

Video Excerpts

Watch the following excerpts from the Physics I lecture videos:

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» Clip 1: Scalar Product (6 min)
» Transcript (PDF)

From Lecture 3 of 8.01 Classical Mechanics, Fall 1999

» Clip 2: Work Calculated in Three Dimensions (5 min)
» Transcript (PDF)

From Lecture 11 of 8.01 Classical Mechanics, Fall 1999

Download the complete lectures from this course:

» iTunes U
» Internet Archive

Learning Activities

Guided Activities

Read through the class slides carefully. They explain all of the concepts from the module.

Slides: Work and the Dot Product (PDF)

Self-Assessment

Do the Concept Questions first to make sure you understand the main concepts from this module. Then, when you are ready, try the Challenge Problems. If you are struggling with the Challenge Problems, watch the Homework Help Session videos, which will give you tips on how to tackle problems of this type.

Concept Questions

Concept Questions (PDF)

Solutions (PDF)

Challenge Problems

Challenge Problems (PDF)

Solutions (PDF)

Problem Solving Help

In the following videos Prof. Walter Lewin explains how to approach the Challenge Problems.

Help Session 1

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Help Session 2

{'English - US': '/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/conservation-of-energy/work-and-the-dot-product/help-session-2/aiGNPQ6IrMw.srt'}

Help Session 3

{'English - US': '/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/conservation-of-energy/work-and-the-dot-product/help-session-3/fOa7Gamn_cs.srt'}

Help Session 4