Detectors trained on closed-set annotations can miss rare moving objects outside the training taxonomy. Automotive radar provides category-independent Doppler motion cues and is less affected by adverse illumination and weather, but sparse, noisy returns hinder class-aware 3D box detection. Surface location and velocity remain useful for motion reasoning and collision avoidance when full box geometry is difficult to recover. We present the Physics-Aware Radar Transformer (PART), a fully sparse radar-only detector that predicts existence confidence, a representative surface point, and 2D ground-plane velocity for each moving-object hypothesis. Doppler-Aware Query Initialization (DAQI) replaces scene-independent learned queries with input-dependent proposals by clustering radar returns in position and velocity, easing query-object assignment in sparse scenes. Physics-Guided Cross-Attention (PGCA) incorporates radial-Doppler consistency and radar cross section (RCS) into query-point association. Uncertainty-aware supervision randomly masks ground-truth objects and assigns soft existence targets to ambiguous radar-supported queries, reducing reliance on exhaustive annotations. With only 1.1 million parameters, PART achieves a class-agnostic average precision (CA-AP) of 0.8827, a mean average surface translation error (mASTE) of 0.3188 m, and a mean average velocity error (mAVE) of 0.8084 m/s on nuScenes. It attains 0.9203 recall on rare and safety-relevant categories excluded from the standard evaluation and remains effective at night, in rain, and under severe occlusion. Inspection of apparent false positives shows that some predictions correspond to moving objects absent from the nuScenes annotations. Code and pretrained model weights will be publicly available at https://github.com/sunyinghao-uestc/PART.

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