  We wish to measure the cool star rotation period distribution for the
Pleiades-age rich open cluster NGC 2516 and use it to determine whether
cluster-to-cluster variations exist in otherwise identical open clusters. We
obtained 42 d-long time-series CCD photometry of NGC 2516 using the Yale 1 m
telescope at CTIO and performed a number of related analyses, including
PSF-based time-series photometry. Our data are complemented with additional
information from several photometric datasets, literature radial velocities,
and Gaia DR2 astrometry. All available data are used to construct an integrated
membership list for NGC 2516, containing 844 stars in our 1deg FoV. We derived
308 rotation periods for late-F to mid-M cluster members from our photometry.
We identified an additional 247 periodic M dwarf stars from a prior study as
cluster members, and used these to construct a 555-star rotation period
distribution for NGC 2516. We find a group of slowly rotating M dwarfs
(10d<P<23d), forming a branch in the colour-period diagram which we call the
'extended slow rotator sequence'. This, and other features of the rotational
distribution can also be found in the Pleiades, making the colour-period
diagrams of the two clusters nearly indistinguishable. We demonstrate the
existence of a representative ZAMS rotational distribution and provide a simple
colour-independent way to represent it. We perform a detailed comparison of the
NGC 2516 rotation period data with a number of recent rotational evolution
models. Using X-ray data from the literature, we also construct the first
rotation-activity diagram for solar-type stars in NGC 2516. The two clusters
NGC 2516 and Pleiades can be considered twins in terms of stellar rotation and
related properties, suggesting that otherwise identical open clusters also have
intrinsically similar cool star rotation and activity distributions. (Abridged)
