We investigate the translational and rotational relaxation dynamics of a crowded two-dimensional system of monodisperse Penrose kites, in which crystallization, quasi-crystallization, and nematic ordering are suppressed, from low to high area fractions along the metastable ergodic fluid branch. First, we demonstrate a decoupling between both the translational and the rotational diffusion coefficients and the relaxation time: the diffusivities are not inversely proportional to the relaxation time, neither in the low-density normal liquid regime nor in the high-density supercooled regime. Our simulations reveal that this inverse proportionality breaks in the normal liquid regime due to the Mermin-Wagner long-wavelength fluctuations and in the supercooled regime due to the dynamical heterogeneities. We then show that dynamical heterogeneities are mainly spatial for translational degrees of freedom and temporal for rotational ones, that there is no correlation between the particles with the largest translational and rotational displacements, and that different dynamical length scales characterize the translational and the rotational motion. Hence, despite the translational and the rotational glass-transition densities coincide, according to a mode-coupling fit, translations and rotations appear to decorrelate via different dynamical processes.
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