3. Cartesian Coordinates and Vectors

• 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 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.

Preperation

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 Videos

Video Excerpts

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

Concept Questions (PDF)

Solutions (PDF)

Challenge Problems

Challenge Problems (PDF)

Solutions (PDF - 2.2MB)

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/mathematics-the-language-of-science/cartesian-coordinates-and-vectors/help-session-1/TBxVT80whiI.srt'}

Help Session 2

{'English - US': '/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/mathematics-the-language-of-science/cartesian-coordinates-and-vectors/help-session-2/RKU9Juz0IFg.srt'}

Help Session 3

{'English - US': '/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/mathematics-the-language-of-science/cartesian-coordinates-and-vectors/help-session-3/yzpptq8c80I.srt'}

Help Session 4

{'English - US': '/courses/physics/8-01sc-physics-i-classical-mechanics-fall-2010/mathematics-the-language-of-science/cartesian-coordinates-and-vectors/help-session-4/oxfaxzDUVQY.srt'}

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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