In the sport of hammer throwing, athletes need to make the most of many rules of physics in order to achieve the best results. Angular velocity and throw accuracy must be well calibrated to send the hammer too far. Let’s analyze this wonderful sport from a physical and athletic point of view. Hammer throwing is a very difficult Olympic discipline. Athletes must quickly rotate the tool to manage to hold it until the moment it, after release, flies off the safety nets as far as possible. Whoever throws it more wins. There are at least three requirements to maximize launch: firing at an angle of approximately 45 degrees; rotate the body as quickly as possible; Keep arms fully extended when going outside. These are the compromises that athletes reach after years of training. The hammer is the tool used and should be thrown as far as possible. It must be certified and compliant. It consists of three distinct parts: the metal head is shaped like a ball; steel wire cable; handle. For absolute categories, the total weight should be from 7,260 kg to 7.285 kg, the diameter of the head should be between 11 cm and 13 cm and the distance between the head and handle between 117.5 cm and 121.5 cm (for men). For women, the total weight of the hammer should range from 4 kg to 1 kg, the diameter of the head should be between 9.5 cm and 11 cm, and the distance between the head and handle should be between 116 cm and 119.5 cm. Firing When the hammer is thrown, the athlete produces energy and transfers it to the tool. A lot of skill is needed to achieve the maximum result. All parts of the body are involved in this difficult work. An athlete’s ability is to try to align them and extract maximum energy from them. The final throw distance, which is intended to be the final action of the system, is determined primarily by the following variables: the height of the hammer at the exit; exit angle; height of the center of gravity of the tool at the time of release; angular velocity at the exit; aerodynamic elements of the instrument; properties of liquid (air); The possibility of wind. The general formula for the range is as follows: where: “v” is the speed with which the hammer is thrown; “g” is the gravitational acceleration, on planet Earth it is 9.81 m/s^2; Theta is the angle at which the hammer is thrown. The exit height depends on the height of the athlete. It is clear that the higher this height, the greater the tool range, because the traced parabola will be wider. The best theoretical angle of launch is 44-45 degrees but scientists note that the best results are obtained with an exit angle between 38 degrees and 43 degrees. Exit speed has a decisive influence and athletes’ technique focuses on this. Their purpose, in fact, is to impose a large centrifugal force on the hammer, also depending on its mass. Finally, the density of air, considered to be the fluid in which the hammer travels, is not particularly relevant, and a hammer throw performed in absolute vacuum would lengthen the parabola by a few centimeters. Wind also has little effect on launch quality and a wind speed of 2 m/s will vary in the range by +/- 0.5 m. The diagram in Figure 1 shows the parabola of a hammer throw with the following initial characteristics: Hammer mass: 7.26 kg; Density: 471.8 kg/m^2; Output speed: 26m/s; exit angle: 45 degrees; Height at the exit: 155 cm above the ground. Figure 1: A parabola plotted with a hammer throw The graphs in Figure 2 show some results at different sizes, during firing. In such conditions, the hammer travels a distance of about 70 meters and reaches a peak height of about 18.45 meters, at which the absolute speed of the object is minimal. It then begins to accelerate due to the fall associated with the force of gravity, and reaches a maximum speed of about 26.4 m/s immediately before hitting the ground. The maximum kinetic energy in the tool is 2532 J just before impact with the ground. Figure 2: Physical Parameters in Hammer Throw The previous formula shows that tool speed is the most important variable for the maximum range. The hammer throw velocity is generated by the rotation of two blocks, the player’s block and the tool’s block. He exerts all his energies to reach the maximum angular velocity. Complex movement constitutes a human tool system that can be carefully studied to maximize the result. The latter is highly dependent on the different centers of gravity of the different components. The orbit of the tool’s center of gravity must be extremely smooth and fast. These are the same mechanisms as the slingshot, an ancient weapon used by primitive men who made stone very quickly with a rope, eventually throwing it at prey or the enemy. The orbit of the tool’s center of gravity is characterized by amplitude, inclination, and torsion. Capacitance is the radius comprising the center of gravity of the entire system and the center of gravity of the hammer. It is constantly changing and unpredictable in any way. As the hammer rotates, its speed increases more and more. By convention, each 360 degree orbit lies on an “orbit plane” but is actually not a 2D plane but a 3D plane, where the altitude also changes continuously and unpredictably. Centrifugal force and gravity: The trajectory of the hammer is determined by two forces: centrifugal force, which tends to move the hammer away from the center of rotation and centripetal force (exerted by the arms) which pulls the mass in the opposite direction. (See Figure 3). The centrifugal force, during the movement of revolution, is defined as follows: where: “m” is the mass of the body; Omega2 is the angular velocity; “r” is the distance from the axis of rotation (radius). Given the circular motion of the system, to obtain the maximum angular momentum it is necessary to apply the maximum possible eccentric force. Athletes spin themselves primarily to throw the hammer as fast as they can. when it is released. The radius of the athlete’s arm and hammer is approximately two metres. In an average performance of 4 laps, the metal ball covers an area of about 50 metres, mostly subject to acceleration. This technical gesture includes the concept of “angular momentum” and is defined by the following formula: where: “p” is the momentum vector; “m” is the mass of the body; “v” is the velocity vector of the body. The ability of an athlete to quickly make several revolutions on himself, without losing his balance and falling. On average performance, for example, athletes are able to complete 3.5 laps in about 1.7 seconds. Approx. 1 lap every 0.48 seconds. Every time the body makes a revolution, the hammer increases its speed. The number of roles depends on the person and his physical capabilities. There are no rules in this regard. In terms of centripetal acceleration, a larger radius corresponds to a farther shot. In other words, a bowler whose arms are longer when extended will have a small advantage over other competitors. Figure 3: Hammer rotation speed is highly limited to its range. The ball is then made to spin on a circular path at the end of the string. After turning the tool several times, the shooter releases his fist on the chain and the “hammer” is thrown away. Since the hammer is moving in a horizontal plane, the force of gravity is horizontal. The vertical component of the chain tension (directed upwards) is balanced by the weight of the hammer (directed down). On the Internet there are many tools for simulating the movement of a parabola (see Figure 4). It is a small application built with Geogebra and its use is very simple and intuitive. It is enough to determine: the height from the ground from which the launch is carried out; the initial velocity of the mass; launch angle. The tool is based on the video clip that calculates the parabola with the information provided and also tracks the relative animation. Figure 4: Online simulation of parabola motion Conclusions Fast-rotating objects absorb huge amounts of energy. Consider, for example, work tools, most of which are based on a rotary system. Many sports of this type, in addition to being great, involve a great deal of risk, especially for people in the vicinity of performance athletes. Precisely for this reason, they are surrounded by special protection networks. Technology and science are increasingly helping athletes understand and study their artistic gestures. World scores and records are increasing more and more, not because humans are getting stronger but because physics helps to achieve maximum results. Just think that the best throws in the 60s did not reach 70 metres, today they exceed 85 metres. .

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