  Spherically symmetric static fluid sources are endowed with rotation and
embedded in Kerr empty space-time up to an including quadratic terms in an
angular velocity parameter using Darmois junction conditions. Einstein's
equation's for the system are developed in terms of linear ordinary
differential equations. The boundary of the rotating source is expressed
explicitly in terms of sinusoidal functions of the polar angle which differ
somewhat according to whether an equation of state exists between internal
density and supporting pressure.
