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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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