The roller-reamer tool is typically installed in an oil and gas well bottom hole drilling assembly (BHA) to ream or smoothen out rough, gouging and scored wellbore surfaces left from the drill bit cutting action. The rotational dynamics of the roller-reamer functionally combines reaming and stabilizing action as it is constrained to rotate in circular wellbores. The relative velocity method developed for dynamics analysis of planetary gears is first used to obtain the Newtonian velocity and acceleration equations, then with use of the Extended Hamilton’s principle, derive Lagrange equations of motion. Published works of dynamics simulations from numerical models typically idealize drillstrings as series of connected non-linear Euler-Bernoulli beam elements representing various components of a drillstring, for instance, stabilizers and roller reamers are modeled as point contacts. This idealization and lumped parameter model approximations of potential sources of dynamics dysfunction such as roller-reamers mask understanding of their behavior and opportunities for design improvements and further application optimization. Of particular interest in this work is comparison between the torque magnitudes generated by the drilling stabilizer and the roller-reamer. Phase portraits of angular velocity versus displacement — proxy for torque generated — from numerical simulations for torque-free, precession modes in oversized wellbores and applied external load states, offer insights into downhole operating dynamics of an essential component of oil and gas well bottom hole assembly (BHA) drilling assemblies.