The paradox of the tight spiral pass in American football: A simple resolution
An American football is a rotationally symmetric object, which, when well-thrown, spins rapidly around its symmetry axis. In the absence of aerodynamic effects, the football would be a torque-free gyroscope and the symmetry/spin axis would remain pointing in a fixed direction in space as the football moved on its parabolic path. When a pass is well-thrown through the atmosphere, however, the symmetry axis remains—at least approximately—tangent to the path of motion. The rotation of the symmetry axis must be due to aerodynamic torque; yet, that torque, at first glance, would seem to have precisely the opposite effect. In this work, we explain the action of aerodynamics on the ball's orientation at second glance.
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