We investigate the finite-size effect due to the conservation of the total angular momentum L in a hard-disk mixture confined to a hard circular cavity. The study is made by means of molecular dynamics simulations in the microcanonical ensemble. Given the geometry of the cavity and the nature of interparticle interactions, L is conserved if the cavity hard wall is smooth, that is, if one considers particle-wall specular collisions. Conversely, L fluctuates about its mean value for a rough hard wall for which the (energy-conserving) collisions are not specular. The size effect due to the conservation of L becomes apparent in several situations where the two types of wall lead to density profiles that are significantly different. The rough-wall results are related to the smooth-wall ones by means of a series expansion in terms of the fluctuations in the total angular momentum. (C) 2003 American Institute of Physics.