The Shear-Slip Mesh Update Method (SSMUM) was developed for computation of flow problems with mechanical components undergoing fast translations or rotations. It complements the Deforming-Spatial-Domain/Stabilized Space-Time (DSD/SST) formulation, developed earlier for flow problems with moving boundaries and interfaces, including flows with moving mechanical components. Here, we provide an overview of the DSD/SST formulation and SSMUM, and show how this combined approach, with efficient parallel implementation, is applied to 3D computation of complex flow problems with fast-rotating mechanical components, such as flow around a helicopter with its rotor in motion.