<p>A novel general drag formula is derived for the unsteady motion of a rigid body of revolution immersed in a porous medium saturated with an incompressible micropolar fluid. The analysis is formulated within the framework of the time-dependent Brinkman micropolar model and yields an exact expression for the hydrodynamic drag in the Laplace transform domain. Unlike existing results, which are largely restricted to steady flows or specific geometries, the present formulation is valid for transient creeping flows, is independent of the body shape, and is applicable to micropolar fluids permeating porous media. Fluid motion within the porous matrix is initiated by the sudden application of a steady body force, thereby capturing the transient response of the system. The applicability of the developed drag formula is demonstrated through the transient motion of a spherical colloidal particle in an unbounded Brinkman micropolar medium. Closed-form expressions for the Laplace-domain drag force is obtained. The results reveal the combined influence of micropolar material parameters and porous medium permeability on the unsteady hydrodynamic resistance experienced by the particle. In the limiting cases, the analysis reduces to previously reported solutions for Newtonian fluids and non-porous media, thereby validating the proposed theory. The present study provides insight into particle mobility in polymer gels and related porous, soft materials, with potential implications for controlled drug delivery and the design of biocompatible materials.</p>