  A cluster intermediate in age between the Pleiades (150 Myr) and the Hyades
(600 Myr) is needed to probe the rotational evolution, especially the
transition between fast and slow rotation that occurs between the two ages. We
study the rich 300 Myr-old open cluster NGC 3532 to provide constraints on
angular momentum loss. Measuring the rotation periods builds on our prior work
of providing spectroscopic membership information for the cluster, and it
supports the chromospheric activity measurements of cluster stars that we
provide in a companion paper. Using 42 d-long photometric time series
observations, we measured rotation periods for members of NGC 3532 and compared
them with the predictions of angular momentum evolution models. We directly
measured 176 photometric rotation periods for the cluster members. An
additional 113 photometric rotation periods were identified using activity
information resulting in a total sample containing 279 rotation periods for
FGKM stars in NGC 3532. The colour-period diagram constructed from this rich
data set shows a well-populated and structured slow rotator sequence, and a
fast rotator sequence evolved beyond zero-age main sequence age whose stars are
in transition from fast to slow rotation. We also identify an extended slow
rotator sequence, apparently the analogue of the one we previously identified
in NGC 2516. We compare our period distribution to rotational isochrones in
colour-period space and find that all considered models have certain
shortcomings. Using more detailed spin-down models, we evolve the rotation
periods of the younger NGC 2516 forward in time and find that the spindown of
the models is too aggressive with respect to the slow rotators. In contrast,
stars on the evolved fast rotator sequence are not spun down strongly enough by
these models. Our observations suggest a shorter crossing time for the
rotational gap. (Abridged)
