Introduction to Mechanics
3. Cartesian Coordinates and Vectors
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Learning Objectives
- Be able to explain the concept of unit vectors and be able to use unit vectors to describe force.
- Be able to add vectors and decompose vectors based on a coordinate system.
- Describe the meaning of the parallel projection of one vector with respect to the direction defined by another vector.
- Be able to explain the mathematical definition the dot product of two vectors.
- Be able to calculate the dot product of two vectors using unit vectors associated with a Cartesian coordinate system.
- Describe the meaning or perpendicular projection of one vector with respect to the direction defined by another vector.Be able to explain the mathematical definition of the direction and magnitude of the vector product of two vectors.
- Be able to calculate the vector product of two vectors using unit vectors associated with a Cartesian coordinate system.
Preparation
Course Notes
Notes: Mathematics - The Language of Science (PDF - 4.8MB)
Suggested Textbook Reading (Optional)
Chapter 1.7-1.10. 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:
Download the complete lectures from this course:
Learning Activities
Guided Activities
Read through the class slides carefully. They explain all of the concepts from the module.
Slides: Cartesian Coordinates and Vectors (PDF - 2.5MB)
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
Challenge Problems
Problem Solving Help
In the following videos Prof. Walter Lewin explains how to approach the Challenge Problems.
Help Session 1
Download this video:
» iTunes U (MP4 - 24MB)
» Internet Archive (MP4 - 24MB)
Help Session 2
Download this video:
» iTunes U (MP4 - 35MB)
» Internet Archive (MP4 - 35MB)
Help Session 3
Download this video:
» iTunes U (MP4 - 6MB)
» Internet Archive (MP4 - 6MB)
Help Session 4
Download this video:
» iTunes U (MP4 - 17MB)
» Internet Archive (MP4 - 17MB)
Related Resources
There are countless resources available online to help you learn physics. Try these:
- Try out a few interactive simulations from PhET:
- Vector Addition
- Position, Velocity and Acceleration Maze Game
- Motion in 2D
- Cartesian Coordinate System on Wikipedia.
- Dr. John Roche explains vectors.
- Learn about Vectors from HyperPhysics at Georgia State University.
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