Velocity and Acceleration in Polar Coordinates

Highlights of the activity

1. This small group activity is designed to help students work out expressions for velocity and acceleration in polar coordinates.
2. Students work in small groups to address the position dependence of curvilinear basis vectors in order to find general expressions for velocity and acceleration in polar coordinates.
3. The whole class wrap-up discussion focuses on building connections between the students' geometric understanding of position, velocity and acceleration vectors and an algebraic formulation in polar (curvilinear) coordinates.

Reasons to spend class time on the activity

Many students have difficulty expressing position, velocity, and acceleration vectors in curvilinear coordinates. Often, students don't realize that the basis vectors in curvilinear coordinates systems (including 2-D polar coordinates) change direction at different locations. Nearly all students know the definitional relationships between position, velocity and acceleration, but have trouble taking time derivatives of the basis vectors.

This activity allows for many interesting discussions relevant for understanding middle division physics topics: different coordinate systems, multi-variable calculus, resolving algebraic and geometric representations…

Reflections

• Reflections from the original implementation.

• Reflections from "official" adapters/adopters.

• Reflections from the general public.

Instructor's Guide

• Wiki version

Student Handouts

cfvpolarhand.pdf

cfvpolarhand.tex