Search

 

Results: Cylindrical coordinates

assignment_ind Small White Board Question

10 min.

Curvilinear Coordinates Introduction

Cylindrical coordinates spherical coordinates curvilinear coordinates

Curvilinear Coordinate Sequence

First, students are shown diagrams of cylindrical and spherical coordinates. Common notation systems are discussed, especially that physicists and mathematicians use opposite conventions for the angles \(\theta\) and \(\phi\). Then students are asked to check their understanding by sketching several coordinate equals constant surfaces on their small whiteboards.

accessibility_new Kinesthetic

10 min.

Curvilinear Basis Vectors

symmetry curvilinear coordinate systems basis vectors

Curvilinear Coordinate Sequence

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).

assignment Homework

Sphere in Cylindrical Coordinates
Find the surface area of a sphere using cylindrical coordinates.

group Small Group Activity

30 min.

Scalar Surface and Volume Elements

Integration Sequence

Students use known algebraic expressions for length elements \(d\ell\) to determine all simple scalar area \(dA\) and volume elements \(d\tau\) in cylindrical and spherical coordinates.

This activity is identical to Vector Surface and Volume Elements except uses a scalar approach to find surface, and volume elements.

format_list_numbered Sequence

Curvilinear Coordinate Sequence
The curvilinear coordinate sequence introduces cylindrical and spherical coordinates (including inconsistencies between physicists and mathematicians notational conventions) and the basis vectors adapted to these coordinate systems.

group Small Group Activity

30 min.

Vector Surface and Volume Elements

Integration Sequence

Students use known algebraic expressions for vector line elements \(d\vec{r}\) to determine all simple vector area \(d\vec{A}\) and volume elements \(d\tau\) in cylindrical and spherical coordinates.

This activity is identical to Scalar Surface and Volume Elements except uses a more sophisticated vector approach to find surface, and volume elements.

assignment Homework

Cone Surface

Using integration, find the surface area of a cone with height \(H\) and radius \(R\). Do this problem in both cylindrical and spherical coordinates.

group Small Group Activity

30 min.

Total Charge

charge volume charge density multiple integral scalar field coordinate systems differential elements curvilinear coordinates

Integration Sequence

In this small group activity, students integrate over non-uniform charge densities in cylindrical and spherical coordinates to calculate total charge.
« Previous | Next »