  Small objects floating on a fluid have a tendency to aggregate due to
capillary forces. This effect has been used, with the help of a magnetic
induction field, to assemble submillimeter metallic spheres into a variety of
structures, whose shape and size can be tuned. Under time-varying fields, these
assemblies can propel themselves due to a breaking of time reversal symmetry in
their adopted shapes. In this article, we study the influence of an in-plane
rotation of the magnetic field on these structures. Various rotational modes
have been observed with different underlying mechanisms. The magnetic
properties of the particles cause them to rotate individually. Dipole-dipole
interactions in the assembly can cause the whole structure to align with the
field. Finally, non-reciprocal deformations can power the rotation of the
assembly. Symmetry plays an important role in the dynamics, as well as the
frequency and amplitude of the applied field. Understanding the interplay of
these effects is essential, both to explain previous observations and to
develop new functions for these assemblies.
