In order to provide additional constraints to current models of angular momentum evolution of solar-type stars, we have conducted a period-determination program in the Alpha Perseus cluster. We have selected a sample of 22 Alpha Persei G and K dwarfs on the basis of their seemingly slow rotation rate (vsini<=10km/s). We searched for periodic modulation induced by stellar spots by performing a photometric CCD monitoring campaign in the V band over a baseline of 14days. We detected 10 periods ranging from 1.3 to 7.1days. A period was found for 7 out of the 10K stars of our sample but for only 3 out of the 12 G and F stars. This bias is due to the existence of a clear relationship between spectral type and the amplitude of modulation by spots. We show that our study is not biased against the detection of very slow rotators and conclude to the existence of a lower limit of about 6km/s for the rotational velocity of Alpha Per G and K dwarfs. A significant fraction of solar-type stars in young clusters thus appear to have equatorial velocities distributed in a very narrow range between about 6 and 10km/s, a result which poses a severe constraint to current models of angular momentum evolution.