We investigate, both analytically and numerically, the quantum dynamics of a planar (2D) rigid rotor subject to suddenly switched-on or switched-off concurrent orienting and aligning interactions. We find that the time-evolution of the post-switch populations as well as of the expectation values of orientation and alignment reflects the spectral properties and the eigensurface topology of the planar pendulum eigenproblem established in our earlier work [Frontiers in Physics 2, 37 (2014); Eur. Phys. J. D 71, 149 (2017)]. This finding opens the possibility to examine the topological properties of the eigensurfaces experimentally as well as provides the means to make use of these properties for controlling the rotor dynamics in the laboratory.