Stringent tests on top quark production and decay mechanisms are provided by the measurement of the top quark and W boson polarization. This paper presents a detailed study of these two measurements with the ATLAS detector, in the semileptonic (ttbar -> W W b bbar -> l nu j1 j2 b bbar) and dileptonic (ttbar -> W W b bbar -> l nu l nu b bbar) ttbar channels. It is based on leading-order Monte Carlo generators and on a fast simulation of the detector. A particular attention is paid to the systematic uncertainties, which dominate the statistical errors after one LHC year at low luminosity (10 fb^{-1}), and to the background estimate. Combining results from both channel studies, the longitudinal component of the W polarization (F_0) can be measured with a 2% accuracy and the right-handed component (F_R) with a 1% precision with 10 fb^{-1}. Even though the top quarks in ttbar pairs are not polarized, a large asymmetry is expected within the Standard Model in the like-spin versus unlike-spin pair production. A 4% precision on this asymmetry measurement is possible with 10 fb^{-1}, after combining results from both channel studies. These promising results are converted in a sensitivity to new physics, such as tWb anomalous couplings, top decay to charged Higgs boson, or new s-channels (heavy resonance, gravitons) in ttbar production.
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