In liquids, a substantial portion of the polarizability anisotropy is interaction induced and its time correlation function (TCF), observable in depolarized light scattering, optical Kerr effect (OKE) and other experiments, decays through translational as well as rotational mechanisms. In this work we develop methods, based on instantaneous normal mode (INM) analysis and on a theory due to W. A. Steele [Mol. Phys. 61, 1031 (1987)], to identify the contributions of rotation, translation, and their cross correlations to polarizability anisotropy dynamics. The Steele theory is also used to extend the analysis of the dynamical origin of solvation response beyond the short-time regime. We use this methodology to investigate the contributions of rotation and translation to the OKE response of acetonitrile at room temperature and to compare it to electrostatic solvation dynamics in this liquid. We find that rotation is the largest contributor to polarizability anisotropy dynamics, but that the translational and translation-rotation cross correlation components are important at all times relevant to the rise and decay of the OKE signal. The polarizability anisotropy INM spectrum of acetonitrile is quite similar to the corresponding electrostatic solvation spectrum determined earlier [B. M. Ladanyi and R. M. Stratt, J. Phys. Chem. 99, 2502 (1995)]. This similarity extends to the polarizability anisotropy and solvation energy velocity TCFs and their decomposition into rotational, translational, and their cross-correlation components. The implication of these results to the use of the OKE spectral density to predict the solvation response in acetonitrile and in other liquids is discussed.