# 12. Work and the Dot Product

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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

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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## 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

{'English - US': '/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/conservation-of-energy/work-and-the-dot-product/help-session-1/qZX6IuihTyg.srt'}

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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'}

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### 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'}

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### Help Session 4

{'English - US': '/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/conservation-of-energy/work-and-the-dot-product/help-session-4/4NEL4vFx3YQ.srt'}

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### Help Session 5

{'English - US': '/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/conservation-of-energy/work-and-the-dot-product/help-session-5/rIkQHN-6PF8.srt'}

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## Related Resources

There are countless resources available online to help you learn physics. Try these:

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