When mass is transferred between the two components in a close binary system, the matter falling towards the secondary star can gain a considerable amount of angular momentum. Eventually a ring or disk around this star is formed. The star can increase its angular momentum by accreting part (or the whole) of this matter. We have examined the ensuing changes in rotational velocity of the mass-accreting star. A simplified calculation (assuming accretion from a ring, rigid rotation of the star, and taking the stellar radius as well as its radius of gyration constant) shows that the star reaches its break-up velocity after increasing its original mass by only a few percent.