Chapter 6.3, Problem 17P

Expand the triple product for $a=\omega \times (\omega \times r)$ given in the discussion of Figure 3.8. If $r$ is perpendicular to $\omega$ (Problem 16), show thata $=-{\omega }^{2}r,$ and so find the elementary result that the acceleration is toward the center of the circle and of magnitude $v^2/r$.