Physical AI is moving from research into industrial deployment at scale. The International Federation of Robotics reports more than four million industrial robots in operation globally, and recent national strategy documents identify Physical AI as a priority area for the coming decade. Three discipline traditions inform the safety of such systems: AI Safety, Functional Safety, and Robot Safety. None of them, individually or collectively, addresses the failure modes that arise when machine-learning components drive physical actuators with assurance levels comparable to legacy automation. This paper introduces Physical AI Safety as a distinct discipline. It is the discipline of designing, verifying, and operating Physical AI systems such that the probability of physical harm is bounded to levels equivalent to or lower than those of comparable legacy automation under existing functional safety frameworks. The paper presents a four-layer reference model — the Physical AI Safety Stack — that spans AI decision, software safety monitoring, hardware safety constraint, and actuators. It enumerates a taxonomy of six failure modes specific to Physical AI: hallucinated commands, distributional shift, common-cause software failure, adversarial input, sensor-based deception, and emergent multi-agent failure. A research agenda of ten open problems follows. The category exists; the term does not yet. This paper proposes both, and invites the academic community, standards bodies, and regulators to adopt them.