We show that the rotation in isospace of a chiral soliton induces nonlinear distortions of the chiral field leading to a band cutoff phenomenon. In models in which quarks are coupled to the chiral field, this band cutoff is caused by the alignment of the quark isospins about the rotation axis, which induces a corresponding change in the symmetry of the chiral field. We present a simple model in which these nonperturbative effects can be calculated analytically. The same model allows us to analyze the effects of classical radiation of pions by a rotating source. We apply it to the N-..delta.. system, and we find a consistent description for a reasonable choice of parameters which leads to a band cutoff at a spin-isospin close to I = T = (3/2.