  In this paper, we continue our study on the evolution of black holes (BHs)
that receive velocity kicks at the origin of their host star cluster potential.
We now focus on BHs in rotating clusters that receive a range of kick
velocities in different directions with respect to the rotation axis. We
perform N-body simulations to calculate the trajectories of the kicked BHs and
develop an analytic framework to study their motion as a function of the host
cluster and the kick itself. Our simulations indicate that for a BH that is
kicked outside of the cluster's core, as its orbit decays in a rotating cluster
the BH will quickly gain angular momentum as it interacts with stars with high
rotational frequencies. Once the BH decays to the point where its orbital
frequency equals that of local stars, its orbit will be circular and dynamical
friction becomes ineffective since local stars will have low relative
velocities. After circularization, the BH's orbit decays on a longer timescale
than if the host cluster was not rotating. Hence BHs in rotating clusters will
have longer orbital decay times. The timescale for orbit circularization
depends strongly on the cluster's rotation rate and the initial kick velocity,
with kicked BHs in slowly rotating clusters being able to decay into the core
before circularization occurs. The implication of the circularization phase is
that the probability of a BH undergoing a tidal capture event increases,
possibly aiding in the formation of binaries and high-mass BHs.
