We consider 2D viscous incompressible flows in a disk with rotating boundary. We assume that the angular velocity is BV in time, which includes impulsively started rotations. We study the vanishing viscosity limit and prove that for circularly symmetric initial data the solution of the Navier-Stokes equations converges strongly in $L^{\infty}([0,T],L^2)$ to the corresponding stationary solution of the Euler equations. This result generalizes work of Matsui, Bona and Wu, and is related to work of Wang. In particular, we do not assume boundary compatibility of the initial data. Our proof relies on a symmetry reduction of the equations and semigroup methods for the reduced problem. This is joint work with Milton Lopes and Helena Nussenzveig Lopes.