Page "Centripetal force" Paragraph 121

Local coordinate system for planar motion on a curve.

Two different positions are shown for distances s and s + ds along the curve.

At each position s, unit vector u < sub > n </ sub > points along the outward normal to the curve and unit vector u < sub > t </ sub > is tangential to the path.

The radius of curvature of the path is ρ as found from the rate of rotation of the tangent to the curve with respect to arc length, and is the radius of the osculating circle at position s. The unit circle on the left shows the rotation of the unit vectors with s.