Unlike the Ballista the Mangonel does not release its energy in a linear fashion. The arm makes an arc (part of a circle) with radius equal the arm length. Therefore the Potential Energy is transferred in the Rotational Kinetic Energy. The w stands for the angular velocity and r for the length of the arm. I is the moment of inertial as the arm is a rod and its rotating on its end, I=1/3mr2