Chapter 11, Problem 102P

(a)

To determine

ToShow: The difference in speed between its outermost and innermost portions, $\Delta v$ , is given by the approximate expression by

  $\begin{array}{l}\Delta v=v_{out}-v_{in}\\ \Delta v\approx v_{avg}\frac{\Delta r}{R}\end{array}$

(b)

To determine

ToShow: $\Delta v\approx -\frac{1}{2}\left(v_{avg}\frac{\Delta r}{R}\right)$ if the ring is composed of many small chunks.