Instructors_Guide_ch03 - 3 Vectors and Coordinate Systems...

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3 Vectors and Coordinate Systems Recommended class days: 2 Background Information Surveys (Knight, 1995) have found that only about one-third of students in a typical introductory physics class are knowledgeable enough about vectors to begin the study of Newtonian mechanics. Another one-third have partial knowledge of vectors (e.g., a student who can add vectors graphi- cally but isn’t familiar with vector components), while the final one-third have essentially no useful knowledge of vectors. Surveyed students who were repeating the course generally displayed major gaps in their knowledge of vectors, and this was likely a contributing factor to their previous failure of the course. Students who can successfully add and subtract vectors are still often confused as to just what a vector is . When posed the open-ended question “What is a vector?” they may respond with “A vector is a force” or some similar answer. These students may have difficulty recognizing velocity or acceleration as vector quantities. Although students have used Cartesian coordinate systems throughout high school, many have a hard time interpreting a statement such as “A vector points in the negative x -direction.” These students are especially prone to making sign errors when decomposing vectors into components. Student Learning Objectives • To understand the basic properties of vectors. • To add and subtract vectors both graphically and using components. • To be able to decompose a vector into its components and to reassemble vector components into a magnitude and a direction. • To recognize and use the basic unit vectors. • To work with tilted coordinate systems. Pedagogical Approach This is a straightforward chapter that introduces just enough about vectors for students to get through Newton’s laws. The dot product is delayed until needed. An explicit vector notation with arrows (e.g., r F ) is used throughout the text, rather than the more traditional boldface notion (e.g., F ). Students pay little attention to the boldface type, and I’ve found that they handle vectors
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This note was uploaded on 01/14/2011 for the course CD 254 taught by Professor Kant during the Spring '10 term at Central Oregon Community College.

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Instructors_Guide_ch03 - 3 Vectors and Coordinate Systems...

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