Like any other sport, basketball is also based on many concepts of physics and mathematics. Their study allows to maximize and improve the performance of athletes in order to win matches. In this article, we will examine some particular phenomena that deserve in-depth study with related note on physics. Here are other articles on the physics of sports. Basketball is more complex than it looks Basketball is full of technical moves, jumps, shots, parabolas, forces and other events that lead to the basic concepts of physics and mathematics. The dominant theme, of course, is the force of gravity. A game of basketball that is played on another planet, and in general in a different system of reference, will surely mean a very different reaction from players with very poor or different performances. This fact occurs because the human body, along with muscles and other organs, is not used to interacting with various forces that act from the outside. The human body is very flexible, reactive and learns new working conditions almost instantly, so a few courses are enough for players to play in different planetary conditions. Today, teams are increasingly matching the concepts of the real game with those of physics and mathematics and with the help of the best software available it is possible to significantly increase the performance of the basketball team. Many engineers carefully monitor the individual movements of each player in order to understand invisible nuances, observe behaviors and study possible reactions for improvement through complex mathematical formulas. Only in this way can the wonderful performances of the best basketball players in the world be explained. Thanks to the adoption of certain mathematical and physical algorithms, it is practically possible to arrive at and implement near-perfect movements. Moreover, thanks to the use of special robots to shoot the ball accurately, it is possible to simulate movements, shots and throws with greater safety, strength and accuracy. These machines are the product of highly sophisticated and sophisticated studies that exploit the knowledge gained in mathematics and physics to apply any corrections to each player’s movements. In fact, the analysis is not done cumulatively for the entire team but is customized for each player, with very specific playing characteristics and times. Balance the ball on the finger Many basketball players like to spin the ball with their fingers. It is a kind of juggling move that can be learned in a few days (see Figure 1). To make the ball spin balanced on your fingers, it must rotate rapidly around its vertical axis with the equator parallel to the ground. As long as the ball is spinning quickly, the balance is more stable and the exercise lasts several seconds. The ball cannot balance if the spin ends, just like the vertical balance of a bicycle. It is really interesting to calculate the rotational kinetic energy of an object. A body rotating with an angular velocity ω about a fixed axis has rotational kinetic energy, according to the laws of rotational motion. Each point in the body has its own kinetic energy which is equal to: Since kinetic energy is a scalar quantity, the individual energies of each point can be added to get the total energy: ie: At the end: each particle has its tangential velocity, but they all have the same angular velocity. Remember that the tangential velocity is related to the angular velocity by the relation: thus, the sum corresponds to the moment of inertia of a system of particles, and is measured in joules (J) and depends on the axis of rotation. Alternatively, the moment of inertia of the body can be calculated by dividing it into elements of small size, each of which has a mass m (i). In Figure 2, the relationships between translational motion and rotational motion can be observed. Figure 2: Relationships between translation and rotational motion Why does a basketball balance on a finger when it rotates? The sphere behaves like a gyroscope, i.e. an object that can rotate symmetrically with respect to one of its axes. When the gyroscope rotates, it acquires a large inertial force. In particular: during rotation, the axis of rotation tends to maintain the starting direction, in the case of a ball, the vertical one; If a force is applied to the axle to make it deviate, this must be much greater than the force necessary if the body is stationary; The faster the rotation, the greater the force to be used. Therefore the ball remains standing due to the gyroscopic effect (see diagram in Figure 3). When it rotates in an oblique direction it does not fall because, thanks to this effect, a force appears that generates a conical motion of its axis of rotation (precipitation). But when the rotational speed is less than a certain value, the force of the weight prevails and the ball falls. In other words, when the ball is stationary, the force of gravity (acting downward) is able to overcome the constraint reaction (acting upward) causing it to fall to the side. During rotation, angular momentum is created that balances the system and allows the ball to remain vertical. Figure 3: The ball remains in equilibrium thanks to the movement of the parabola (or the movement of the projectile) Basketball is probably one of the sports in which the parabola movement is more pronounced and more frequent during the stages of the game. The player must try to throw the ball into a basket that is placed at a level much higher than him. The trajectory of the ball is a function of two motions, namely, the uniformly oblique velocity motion, to make the ball rise, and the uniformly accelerating downward motion caused by the Earth’s gravitational force. When a basketball player throws the ball toward the basket, it follows an equivalent trajectory. To increase the probability of scoring a point, it is necessary to raise the top of the parabola much higher than the basket (which is located at a height of 3.05 m), which will increase the shooting angle and give greater strength. Many players take advantage of this principle, and with proper training, they are able to raise the top of the shot to more than 5 meters, and score many points. In the field goal shot, there are two opposing and incompatible variables: maximum throw height (peak); Take control of the shot. Unfortunately, raising the plate makes it difficult to control the shot, so most basketball players prefer to keep the tip low and have more control. Few players in the world are able to maximize the two parameters together. When the ball reaches the top of the parabola, it has potential energy (determined by the force of gravity), which increases with height. During a fall, the potential energy is converted into kinetic energy, which is used in two opposite cases: if the ball hits the edge of the basket or the backboard, it bounces; If the basket is scored, the energy is dissipated by friction with the grid. Figure 4 shows a shot taken from the center of the field that entered the basket. The peak of the proverb is very high. There are two interesting aspects: the ideal peak is very high; The range of the shot is very large. These two goals are achieved by giving the ball a lot of energy and this is the result of the player’s great technique, accuracy, muscle and strength. Using only these components, the ball can be thrown from a distance and with high control. Figure 4: Ball long range from a popular basketball game An important aspect of a parabolic shot is range, that is, the distance from the starting point of an object thrown in an upward slanting direction, from the point where it returns to the ground. The parabolic path is symmetric with respect to the vertical axis passing through the vertex and the length L of the band is twice the parametric of the vertex (see Fig. 5). The value of the range is equivalent to: Moreover, it is known from physics that the maximum range occurs when the launch angle is equal to 45 degrees with zero initial height. For basketball, this rule is only partially applied, since players are not only looking for the greatest distance in their throws, but also for the greatest possible accuracy. Maximum range is the maximum length that can be obtained when throwing an object. It largely depends on the angle of launch: as the angle increases, the range increases until it reaches its maximum value, and then decreases when the launch angle increases again. Figure 5: The range depends largely on the angle of the shot In Fig. 6 you can see a graph of the different ranges reached with a shot made with an initial height of 2 m above the ground and an initial velocity of 10 m/s. Figure 6: Range graph at different launch angles Conclusions As usual, the concepts behind basketball physics need further analysis. Sport is full of physical and sporting events and coaches and players are increasingly learning to observe and study them, thanks to the adoption of sophisticated computers and artificial intelligence software. It is believed that one day autonomous robots will play basketball so perfectly that no human player will be able to compete with them. .