Shock and vibration isolation are a critical need in helmets, which are widely used to protect athletes, workers, soldiers, and astronauts. Passive vibration isolation systems are a good option when mass and volume should be minimized and when the experienced loadings can be predicted. However, it is frequently challenging to find materials and structures which exhibit the optimal vibration and impact isolation properties for an application. As a case study illustrating a novel design paradigm for rotational shock absorption, a family of optimal solutions for the physical properties of American football helmets is presented. Lumped parameter Simulink models simulate a variety of impacts to a helmeted head. These models were optimized to minimize the Head Injury Criterion (HIC) and Helmet Performance Score (HPS) metrics and determine the optimal values of rotational and translational stiffness and damping between the head and helmet. The optimization of the 1-dimensional simulations was validated with an analytical solution to the optimization problem. The 3-dimensional simulation suggested that a helmet optimized considering both rotational and translational accelerations could improve the Helmet Performance Score by 48% or more as compared to translational accelerations only. The optimal stiffness and damping computed from the models was used to drive the design of multimaterial shock absorbing elements. A custom impact testing machine was used to test the mechanical properties of prototype isolators. A 3D printed TPU shock absorber was designed within 2.2% of the target optimal stiffness;​ however, no materials were found that could provide enough damping. This research illustrates a new design paradigm for independent tuning of rotational energy storage and dissipation that can be translated to a variety of applications.