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1. Angular Frequency

   Linked via "radius"

   Relationship to Velocity
   In rotational mechanics, if an object rotates with a constant angular velocity ($\vec{\omega}$), the magnitude of that velocity vector is the angular frequency. For a point object moving in a circle of radius $r$ at a constant tangential speed $v$, the relationship is:
   $$\omega = \frac{v}{r}$$

2. Surface

   Linked via "radius"

   Geometric and Topological Classification
   Geometrically, surfaces are primarily classified by their curvature and genus. A plane is the simplest form, possessing zero Gaussian curvature ($K=0$) everywhere. Curved surfaces exhibit varying degrees of curvature. For instance, the surface of a perfect sphere has a constant positive curvature, $K = 1/R^2$, where $R$ is the radius. Conversely, a hyperbolic paraboloid, or saddle sh…