Radar sensing applications for assisting communication have attracted interest thanks to their potential in dynamic environments. A particularly interesting problem for this approach appears in the vehicle-to-vehicle (V2V) millimeter wave and terahertz communication scenarios, where the narrow beams change with the movement of both vehicles. To address this problem, in this work, we develop a radar-aided beam-tracking scheme, where a single initial beam and a set of radar measurements over a period of time are utilized to predict the beams after this time duration. Within this framework, we develop two approaches with the combination of various degrees of radar signal processing and machine learning. To evaluate the feasibility of the solutions in a realistic scenario, we test their performance on a real-world V2V dataset. Our results indicated the importance of high angular resolution radar for this task and affirmed the potential of using radar for the V2V beam management problems.