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The initial distribution of spin rates of massive stars is a fingerprint oftheir elusive formation process. It also sets a key initial condition forstellar evolution and is thus an important ingredient in stellar populationsynthesis. So far, most studies have focused on single stars. Most O stars arehowever found in multiple systems. By establishing the spin-rate distributionof a sizeable sample of O-type spectroscopic binaries and by comparing thedistributions of binary sub-populations with one another as well as with thatof presumed single stars in the same region, we aim to constrain the initialspin distribution of O stars in binaries, and to identify signatures of thephysical mechanisms that affect the evolution of the massive stars spin rates.We use ground-based optical spectroscopy obtained in the framework of theVLT-FLAMES Tarantula Survey (VFTS) to establish the projected equatorialrotational velocities (\vrot) for components of 114 spectroscopic binaries in30 Doradus. The \vrot\ values are derived from the full-width at half-maximum(FWHM) of a set of spectral lines, using a FWHM vs. \vrot\ calibration that wederive based on previous line analysis methods applied to single O-type starsin the VFTS sample. The overall \vrot\ distribution of the primary starsresembles that of single O-type stars in the VFTS, featuring a low-velocitypeak (at $\vrot < 200$ kms) and a shoulder at intermediate velocities ($200 <\vrot < 300$ kms). The distributions of binaries and single stars howeverdiffer in two ways. First, the main peak at $\vrot \sim$100 kms is broader andslightly shifted toward higher spin rates in the binary distribution comparedto that of the presumed-single stars. Second, the \vrot distribution ofprimaries lacks a significant population of stars spinning faster than 300 kmswhile such a population is clearly present in the single star sample.

The VLT-FLAMES Tarantula Survey XXI. Stellar spin rates of O-type spectroscopic binaries