A two-dimensional model for computing contacts and motions of granular particles of different shapes, sizes and material properties is presented. The primary aim of this model is to achieve a high degree of computational efficiency, to allow simulations to be performed very rapidly on a modest sequential machine. The important features of the model are (i) a polar representation of particle shape, (ii) a simple algorithm for contact detection, (iii) a binary collision model using momentum exchange as the describing feature, (iv) energetic coefficients of restitution selected pseudo-randomly, (v) a Coulomb friction approximation to describe slip at impact, and (vi) an optimized move-update algorithm. Results in satisfactory agreement with analytical solutions and existing, less efficient computer simulations are presented.