In studying traumatic brain injury (TBI), it has been long hypothesized that the head is more vulnerable to injury from impacts in certain directions or locations, as the relationship between impact force and the resulting neurological outcome is complex and can vary significantly between individual cases. Many studies have identified head angular acceleration to be the putative cause of brain trauma, but it is not well understood how impact location can affect the resulting head kinematics and tissue strain. Here, we identify the susceptibility of the head to accelerations and brain strain from normal forces at contact points across the surface of the skull and jaw using a three-dimensional, 20-degree-of-freedom rigid-body head and cervical spine model. We find that head angular acceleration and brain tissue strain resulting from an input force can vary by orders of magnitude based on impact location on the skull, with the mandible as the most vulnerable region. Conversely, head linear acceleration is not sensitive to contact location. Using these analyses, we present an optimization scheme to distribute helmet padding thickness to minimize angular acceleration, resulting in a reduction of angular acceleration by an estimated 25% at the most vulnerable contact point compared to uniform thickness padding. This work gives intuition behind the relationship between input force and resulting brain injury risk, and presents a framework for developing and evaluating novel head protection gear.