This paper introduces a radar-based solution for noncontact detection of mass imbalance in rotational machinery systems. The approach uses a low-cost 24 GHz continuous-wave radar to acquire baseband in-phase and quadrature signals, from which amplitude, phase, and instantaneous frequency are derived. Based on these complementary domains, a multi-domain hybrid feature representation is created. It combines one-dimensional statistical descriptors from each domain with cross-domain geometric features taken from the joint trajectory in amplitude, phase, and frequency space. This approach results in a compact 50-dimensional feature vector. The features are evaluated on a radar dataset created from 1,802 recordings collected under four imbalance levels and multiple operating conditions. Employing a support vector machine classifier, the proposed approach achieves a test accuracy of 98.06%, a Macro-F1 score of 97.99%, and a Matthews Correlation Coefficient of 97.01%. For comparison, several state-of-the-art feature extraction schemes are implemented, including power spectral density, empirical mode decomposition, Hilbert-Huang transform, and wavelet packet decomposition features. Using identical classifier pipelines, these baselines achieve test accuracies in the 85-90% range. Computational analysis further indicates that the proposed method maintains real-time feasibility with only modest feature-extraction overhead compared to the most demanding baselines. These results demonstrate that the proposed multi-domain feature extraction scheme provides a more discriminative and robust representation for imbalance diagnosis than conventional single-domain or purely time-frequency approaches.