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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.
Figure 2: Coordinate learning tool with rulers.
Figure 2: Coordinate learning tool, reading off the azimuthal angle \theta.
Figure 3: Coordinate learning tool, reading off the polar angle \varphi.