Field Goal Physics

Kicking a field goal in football involves accuracy, distance, and height. Although the contact of the kicker's foot with the football is the visible result, the mechanism to complete this task involves physics.

When preparing to kick a stationary football for a field goal, the kicker will approach the ball as he increases his velocity (v). When in front of the ball, the kicker will place his non-kicking foot firmly on the turf to establish a solid base. By swinging his hips around the hip joint, the kicker brings the kicking leg forward in a smooth arc with a small bend at the knee. As the foot contacts the ball, the kicking leg snaps straight so the whip-like motion of the kicking leg increases the angular velocity (ω) of the leg to about 20 radians per second (60 ft [18.2 m] per second). The resulting collision launches the football so it (hopefully) sails through the goalposts.

The principles of conservation of angular momentum and conservation of kinetic energy are involved in kicking a field goal. When momentum and kinetic energy are conserved, as they are approximately conserved when kicking a football, there is no loss in momentum and energy before or after the collision. Therefore, initial momentum and energy before the collision is equal to final momentum and energy after the collision.

The physics of kicking a field goal involves angular momentum: L equals Iω, where I equals moment of inertia and o equals angular velocity. The moment of inertia equals mass times the length of the axis of rotation that passes through the kicker's hip joint, where leg mass is about 35 lb (16 kg) for an average kicker, ball mass is 0.91 lb (0.413 kg), and axis length is about 3 ft (0.9 m). For the collision, the equation for the conservation of angular momentum involves the momentum of the kicker's leg and ball before the collision equaling the momentum of the leg and ball after the collision.

Kicking a field goal also involves linear kinetic energy: KElin =...