Chapter 4.3, Problem 40E

Four equally massive particles can be made to rotate, equally spaced, around a circle of radius r. This is physically possible provided the radius and period T of the rotation are chosen so that the following action function is at its global minimum:

$A(r)=\frac{r^2}{T}+\frac{T}{r},r>0.$

1. (a) Find the radius r at which A(r) has a global minimum.
2. (b) If the period of the rotation is doubled, determine whether the radius of the rotation increases or decreases, and by approximately what percentage.