Whether in robotics or even in space vehicles, reaction wheels, characterized by a rotating disk coupled to an inertia flywheel, act as actuators that confers a non-linear and under-acting behavior to the response. This particularity in the response allows several applications within mechatronic systems, such as in the balance control of a robot. This work presents the numerical-computational modeling and simulation of a system with reaction wheels and, finally, its project. The model developed is based on the Newton-Euler methodology for modeling mechanical systems whose equations of motion were computationally simulated, enabling the design of all system components. With the results obtained, the validity of the model built in this work was confirmed. That way, it is expected to get more clarity about this matter in order to enable different applications not yet explored.