## Football Field Goal Physics

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# Football 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 = (1/2)mv2, where m is the kicker's mass (around 215 lb [97.5 kg]) and v is the velocity of the kicker's straight-line (linear) running motion (usually about 15 ft [4.6 m]) per second immediately before the collision). The physics of the kick also involves rotational kinetic energy: KErot equals (1/2)Iω2. Like momentum, the kinetic energy of the ball and kicker before the collision is equal to the kinetic energy of the ball and kicker after the collision.

A football is at rest before being hit by the kicker's foot; therefore, its kinetic energy is zero. The kicker runs forward with straight motion so linear kinetic energy is used before the collision. The football's path immediately after it is hit by the foot involves simple straight-line motion; thus, the ball's kinetic energy is linear. The kinetic energy of the kicker's leg is the most complicated form of kinetic energy because it involves rotational kinetic energy of the kicker's leg rotating about its hip joint and linear kinetic energy as the kicker's leg travels with the kicker as he continues to run in straight-line motion after the collision.

Although other appropriate numbers can be used to calculate various parameters of the field goal kick, if the above numbers are inserted into appropriate equations, the football's speed immediately after being kicked is about 126 ft (38.4 m) per second, or 93 mi (150 km) per hour.