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On June 3, 1997, Tournoi de France, Roberto Carlos left the Football world amazed with a still
remembered legendary free kick of this game internationally, being the most famous goal of
Carlos’ career. Goalkeeper Fabien Barthez was almost clueless as the ball seemed to be heading
to the corner flag. But the ball curved unpredictably for many only to hit the net. This paper
reviews a few research papers and articles to study Physics behind Soccer.
2. Forces on a Soccer ball
Following forces decide the motion of a football on kicking, as per NASA official website:
Figure 1: Forces on a football (Source: NASA)
➔ Weight: Center of gravity is located at the exact center of the soccer ball and weight is
always directed towards the center of the earth. It depends on the mass of the ball and it is
determined using Newton’s law of gravitation.
➔ Drag: Drag is the resistance to the ball due to air and always opposes the motion of the
ball. Magnitude depends on the physical design of the object, velocity^2 of the object,
and dynamics of the medium like density and viscosity.
➔ Lift: This aerodynamic force acts perpendicular to the direction of football’s flight. This
property is core physics of airplanes in the sky. It’s mostly affected by speed of rotation
for a soccer ball.
3. Swing of Ball due to Magnus Force
Mohammad Ahmad created a model in their paper to accurately simulate the curved trajectory of
the ball for the famous free Kick by Carlos using the Mathematica tool. Author analyzed through
the model simulation (with a few assumptions) that Roberto Carlo...
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