A bearing system for a spin-stabilized projectile including bearing configurations that permit selective relative rotation between a spindle and a body portion and which facilitate automatic centering of the spindle. Each bearing configuration includes a conical bearing surface rotatable with respect to a corresponding conical body surface. One bearing configuration is in a forward portion of the body portion and selectively engages a first body surface upon the projectile experiencing set-back forces to direct forces away from bearing elements, and another bearing configuration is in a rearward portion of the body portion and engages a second body surface upon the projectile experiencing set-forward forces to direct forces away from the bearing elements. Biasing elements work in cooperation with the bearing configurations to automatically maintain the spindle centered with respect to the body portion during pre-launch and in-flight and to re-center the spindle after set-back, balloting and/or set-forward phases.