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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- Spring '10
- kant
- Cartesian Coordinate System, Dot Product, Coordinate systems
-
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