Chapter 14.5, Problem 82E

Alternative derivation of the curvature Derive the computational formula for curvature using the following steps.

1. a. Use the tangential and normal components of the acceleration to show that v × a = κ|v|³B. (Note that T × T = 0.)
2. b. Solve the equation in part (a) for κ and conclude that $\kappa =\frac{|v\times a|}{\left|v^3\right|}$, as shown in the text.