Worksheet 3: Spherical coordinate system¶
We will work with the spherical coordinate system to understand how different coordinate representations describe spatial positions. Using the eCube coordinate learning instrument and a right-angle ruler, we will measure spherical coordinates (r,θ,ϕ) for a given set of Cartesian coordinate points (x,y,z) and vice versa.
- The spherical coordinate system expresses a point in three-dimensional space using:
- r (the radial distance from the origin),
- θ (the polar angle, measured from the positive z-axis), and
- ϕ (the azimuthal angle, measured in the xy-plane from the positive x-axis).
- We will compare our measured values with theoretical predictions and propagate uncertainties into Δr, Δθ, and Δϕ.


