A protective helmet for repetitive impact applications, the helmet comprising a hard impact-resistant outer shell, a head-follower head cap which surrounds at least a portion of the cranial part of a wearer's head, wherein the outer shell surrounds at least a portion of the head cap, the head cap being a partial surface of similar shape to the outer shell, an adjustable chin strap assembly having an attachment/detachment device for securing it to the head cap enabling a wearer to secure and unsecure the helmet to his head, wherein the attachment/detachment device is attached to the head cap but not to the outer shell, a liner between the head cap and outer shell, the liner being attached to both the head cap and the outer shell and exhibiting energy absorbing linear compliance and energy absorbing angular compliance, characterized in that the liner being comprised of a plurality of long, narrow, side-by-side, radially-oriented, viscoelastic open-cell foam columns, the columns being well adhered at each end to the outer surface of the head cap and inner surface of the outer shell, the columns span and nearly fill the available space between the outer surface of the head cap and the inner surface of the outer shell forming mating surfaces between the columns such that during a centered impact, namely an impact whose velocity vector of the impacting helmet minus the velocity vector of the impacted helmet just prior to the impact is directed toward the center of the helmet, both the outer shell and the head cap are configured to move away from their initial position in the inertial frame, in the direction of the impact, with the outer shell moving about twice as much as the head cap, the compliant liner columns symmetrically absorbing the difference, wherein the columns in a quadrant (C-D) of 90° degrees near to the impact are configured to be mostly compressed and the columns in a quadrant (A-B) of 90° degrees opposite the impact are configured to be mostly stretched, and the columns in the other two quadrants (B-C, D-A) of 90° degrees are configured to be mostly deformed into S curves, wherein in said two other quadrants (B-C, D-A) all of the stretching convex surfaces are configured to rub against all of the adjacent compressing concave surfaces for greater energy absorption, and during an off-center impact, namely an impact whose velocity vector of the impacting helmet minus the velocity vector of the impacted helmet just prior to the impact is not directed toward the center of the helmet, both the outer shell and the head cap are configured to move away from their initial position in the inertial frame, substantially in the direction from the point of impact toward the center of the helmet, with the outer shell moving about twice as much as the head cap, the compliant liner columns absorbing un-symmetrically the difference, wherein the outer shell is configured to rotate in an horizontal plane because of the off-center nature of the impact, wherein the columns in the quadrant (C-D) of 90° degrees near to the impact are configured to be mostly compressed and the columns in a quadrant (A-B) of 90° degrees opposite the impact are configured to be mostly stretched, and all the columns are configured to be mostly deformed into S curves, wherein for all the columns all of the stretching convex surfaces are configured to rub against all of the adjacent compressing concave surfaces for greater energy absorption, and after an impact the liner causes the outer shell to automatically return to its initial pre-impact start position relative to the head cap and the head.