Definition:Turning Angle

Definition
Let $C$ be a curve.

The turning angle $\psi$ of $C$ at a point $P$ is defined by the differential equation:
 * $\rho = \dfrac {\mathrm d \psi} {\mathrm d s}$

where:
 * $\rho$ is the radius of curvature at $P$
 * $\dfrac {\mathrm d \psi} {\mathrm d s}$ is the derivative of $\psi$ the arc length $s$.

That is, the turning angle is a measure of how sharply a curve changes direction.

The turning angle is an intrinsic property of $C$.

Also known as
The turning angle is known in some sources as its tangential angle.

Also see

 * Definition:Whewell Equation