Spherical Polar Coordinates
Purpose
A manipulable apparatus demonstrates spherical polar coordinates \((r, \theta, \phi)\). Students see how each coordinate independently specifies a degree of freedom in 3D space, building intuition for coordinate systems used throughout mechanics, E&M, and quantum mechanics.
Figure 1:
The antenna extends/retracts to vary r, rotates about its hinge to vary θ (polar angle), and the vertical tube rotates on the ring stand to vary φ (azimuthal angle).