An apparatus for balancing a statically unbalanced system, particularly useful in balancing X-ray and mammography systems having an X-ray source and detector mounted to a rotational arm, includes a spring mechanism which synchronizes the activation of the spring mechanism with the rotation of the arm of the mammography system. The balancing system reduces the amount of torque necessary to rotate the arm and decreases the overall inertia of the system by eliminating the need for counterweights to maintain balance of the system.