Terrain traversability in unstructured off-road autonomy has traditionally relied on semantic classification, resource-intensive dynamics models, or purely geometry-based methods to predict vehicle-terrain interactions. While inconsequential at low speeds, uneven terrain subjects our full-scale system to safety-critical challenges at operating speeds of 7--10 m/s. This study focuses particularly on uneven terrain such as hills, banks, and ditches. These common high-risk geometries are capable of disabling the vehicle and causing severe passenger injuries if poorly traversed. We introduce a physics-based framework for identifying traversability constraints on terrain dynamics. Using this framework, we derive two fundamental constraints, each with a focus on mitigating rollover and ditch-crossing failures while being fully parallelizable in the sample-based Model Predictive Control (MPC) framework. In addition, we present the design of our planning and control system, which implements our parallelized constraints in MPC and utilizes a low-level controller to meet the demands of our aggressive driving without prior information about the environment and its dynamics. Through real-world experimentation and traversal of hills and ditches, we demonstrate that our approach captures fundamental elements of safe and aggressive autonomy over uneven terrain. Our approach improves upon geometry-based methods by completing comprehensive off-road courses up to 22% faster while maintaining safe operation.