Physics of Lacrosse

            The speed a lacrosse ball is shot is dependent on the weight of the ball, the weight of the stick and the length of the point of rotation. For a lacrosse ball with a weight of .150kg and a lacrosse stick with the weight of 1.0 kg and 0.76 meters in length the velocity of the ball when it leaves the stick will change based on the positioning of your hands on the stick. The positioning of your hands on the stick will alter the point of rotation of the stick causing a change in inertia and a change in kinetic energy of the ball. The kinetic energy equation states that ΔKE=-ΔPE+W_NC meaning the change in kinetic energy is equal to the change in potential energy plus the work of non-conservative forces. By ignoring the work or friction and air resistance and determining that there is no potential energy in the system we can state that ΔKE=0. The kinetic energy of the system is equal to the translational kinetic energy and the rotational kinetic energy. Therefore, ΔKE=½mv²+ ½Iw²=0. Therefore, the rotational kinetic energy of the system will affect the translational kinetic energy of the ball after it is thrown. The rotational kinetic energy is based on the inertia of the system and the rotational velocity. The inertia of a long uniform rod can vary based on the axis of rotation. If the axis of rotation of a long uniform rod is through the center then I= 1/12ml², but if the axis of rotation is through the end then I= 1/3ml². If the mass, length of the rod and the angular velocity of the system all remain constant then the linear velocity of the ball as it were thrown would depend on the inertia of the system. Therefore, the long uniform rod with the axis of rotation in the end will produce a larger inertia than if the axis of rotation was in the middle making the linear velocity larger for the long uniform rod with the axis of rotation at the end. The rotational kinetic energy is converted into translational kinetic energy so a larger rotational kinetic energy will create a larger translation kinetic energy, and therefore, a larger linear velocity. In lacrosse it is more beneficial to put your bottom hand at the bottom most part of the stick and use that point as an axis of rotation to produce the fasted shot or pass. Based on the kinetic energy equation and the inertia equation for a long uniform rod using the bottom of the stick as an axis of rotation would produce the fastest shot.