Static Fields 2023 (11 years)
Students use their arms to depict (sequentially) the different cylindrical and spherical basis vectors at the location of their shoulder (seen in relation to a specified origin of coordinates: either a set of axes hung from the ceiling of the room or perhaps a piece of furniture or a particular corner of the room).
What students learn
- The basis vector \(\widehat{\hbox{coordinate}}\) points in the direction in which \(\hbox{coordinate}\) is increasing.
- Basis vectors are (straight) unit vectors even when they are basis vectors for a coordinate which is an angle, e.g. \(\hat{\phi}\)
- Some basis vectors in cylindrical and spherical coordinates, e.g. \(\hat{\phi}\), vary in direction as you move from point to point in space.
- Basis vectors for a single coordinate are a simple iconic example of a vector space.
You will probably be doing this activity in-class, from directions given by the instructor. If you are doing it on your own, then choose a point in the room that you are in to be the origin. Imagine that your right shoulder is a point in space, relative to that origin. Point your right arm in succession in each of the directions of the basis vectors adapted the various coordinate systems:
- \(\left\{\hat{x},\hat{y},\hat{z}\right\}\) in rectangular coordinates.
- \(\left\{\hat{s},\hat{\phi},\hat{z}\right\}\) in cylindrical coordinates.
- \(\left\{\hat{r},\hat{\theta},\hat{\phi}\right\}\) in spherical coordinates.
- Author Information
- Corinne Manogue
- Keywords
- symmetry curvilinear coordinate systems basis vectors
- Learning Outcomes
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