Organo-halide lead perovskites are revolutionizing the photovoltaic scenario, with efficiencies exceeding 15%. The orientational dynamics disorder of the methylammonium cations (MA) is one of the most peculiar features of these materials. Here, we perform ab initio molecular dynamics simulations and IR spectroscopic measurements on lead halide hybrid perovskites to elucidate the rotational motion of the MA cations in these systems and its effects on the structural and electronic properties of hybrid perovskites. In the investigated time frame, the MA cations are found to rotate within the inorganic framework on a timescale of a few ps. A variation of ±0.1 to 0.2 eV of the electronic properties with the ion dynamics is found, which increases upon increasing the temperature.