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…