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 (\(t\overline{t} \rightarrow W W b \overline{b}\rightarrow l \nu j_1 j_2 b \overline{b}\)) and dileptonic (\(t\overline{t} \rightarrow W W b \overline{b}\rightarrow l \nu l \nu b \overline{b}\)) \(t\bar{t}\) 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 (F0) can be measured with a 2% accuracy and the right-handed component (FR, which is zero in the Standard Model) with a 1\(\%\) precision with 10 fb-1. Even though the top quarks in \(t\bar{t}\) 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 \(t\bar{t}\) production.