An alternative definition gives the curvature of a sufficiently differentiable plane curve to be |df/ds|, where ϕ is the angle between T and i (Figure 13.37a). Figure 13.37b shows the distance s measured counterclockwise around the circle x² + y² = a² from the point (a, 0) to a point P, along with the angle ϕ at P. 

Calculate the circle’s curvature using the alternative definition.

Transcribed Image Text:

y 0 T J i x² + y² = a² y 0 a (a) T FIGURE 13.37 0 P S (b) →X X s = 0 at (a,0)