Restricting cohomology classes to disk and segment configuration spaces

The configuration space of n labeled disks of radius r inside the unit disk is denoted Confn,r(D2). We study how the cohomology of this space depends on r. In particular, given a cohomology class of Confn,0(D2), for which r does its restriction to Confn,r(D2) vanish? A related question: given the configuration space Segn,r(D2) of n labeled, oriented segments of length r, it has a map to (S1)n that records the direction of each segment. For which r does this angle map have a continuous section? The paper consists of a collection of partial results, and it contains many questions and conjectures.