We study the effects of the cluster environment on galactic morphology by defining a dimensionless angular momentum parameter ld, to obtain a quantitative and objective measure of galaxy type. The use of this physical parameter allows us to take the study of morphological transformations in clusters beyond the measurements of merely qualitative parameters, e.g. S/E ratios, to a more physical footing. To this end, we employ an extensive SDSS sample, with galaxies associated with Abell galaxy clusters. The sample contains 93 relaxed Abell clusters and over 34,000 individual galaxies. We find that the median ld value tends to decrease as we approach the cluster center, with different dependences according to the mass of the galaxies and the hosting cluster; low and intermediate mass galaxies showing a strong dependence, while massive galaxies seems to show, at all radii, low ld values. By analysing trends in ld as functions of the nearest galactic neighbour environment, clustercentric radius and velocity dispersion of clusters, we can identify clearly the leading physical processes at work. We find that in massive clusters (s > 700 km/s), the interaction with the cluster central region dominates, whilst in smaller clusters galaxy-galaxy interactions are chiefly responsible for driving galactic morphological transformations.