Our research team is developing a UAV with a passive rotating spherical shell whose purpose of inspecting bridge. The UAV with a passive rotating spherical shell can avoid crashes caused by contact with some objects. This UAV have been successful in inspecting under some bridges. But for now, there is no optimal controller that can be applied to this UAV. This is because of the existence of the passive rotating spherical shell. So, the dynamics of this UAV is different from general UAVs. In this study, we propose a new dynamic model and controllers for a UAV with a passive rotating spherical shell. The new dynamic model is considering the moment of inertia of the spherical shell. Because the moment of inertia is unknown, the new controller is used adaptive control via backstepping to estimate it. We conducted an experiment using simulation and confirm that a controller could be used for actual usage.