We show that an element w of a finite Weyl group W is rationally smooth if and only if the hyperplane arrangement I(w) associated to the inversion set of w is inductively free, and the product (d1 +1) · · · (dl +1) of the coexponents d1, . . . , dl is equal to the size of the Bruhat interval [e, w]. We also use Peterson translation of coconvex sets to give a Shapiro-Steinberg-Kostant rule for t...