Source-free test-time adaptation (TTA) is appealing for mobile and wearable sensing because it enables on-device personalization from unlabeled test streams without centralizing private data. However, sensor-based human activity recognition (HAR) poses challenges that are less pronounced in standard vision benchmarks: behavioral inertial streams are temporally correlated and often exhibit within-session shifts caused by sensor rotation, placement change, and sampling-rate drift. Under this streaming non-i.i.d. setting, widely used vision-style TTA objectives can become unstable, leading to overconfident errors, representation collapse, and catastrophic forgetting. We propose PI-TTA, a lightweight source-free adaptation framework that stabilizes online updates through three physics-consistent constraints: gravity consistency, short-horizon temporal continuity, and spectral stability. PI-TTA updates the same small parameter subset as strong source-free baselines and incurs only modest overhead, making it suitable for on-device deployment. Experiments on USCHAD, PAMAP2, and mHealth under long-sequence stress tests and factorized shift protocols show that PI-TTA mitigates the severe degradation observed in confidence-driven baselines and preserves stable adaptation under sustained streaming conditions. It improves long-sequence accuracy by up to 9.13% and reduces physical-violation rates by 27.5%, 24.1%, and 45.4% on USCHAD, PAMAP2, and mHealth, respectively. These results demonstrate that physics-informed adaptation can improve accuracy, stability, and deployment reliability for real-world mobile sensing systems.