This Past Sunday we played a match against Louisville in the NCAA Sweet 16. Towards the latter stages of the second half, I received a long pass in the box, settled the ball and shot it. The ball traveled with a tremendous amount of velocity but went just wide into the side netting. When watching the replay, I realized that the ball was knuckling after I hit it. When a soccer ball knuckles it travels throughout the air without any rotation. I then wanted to know how much faster a knuckling shot traveled than a shot that has spin on it if both have the same kinetic energy
A standard soccer ball has a radius of 11 cm.
A soccer ball is a uniform sphere, so it's moment of inertia is 2/5 MR^2
The mass of a standard soccer ball is .42 kg
I am assuming I shot the ball with a velocity of 26 m/s
The knuckling shot has a kinetic energy of (1/2)MV^2, because there is no rotational kinetic energy:
(1/2) (.42 kg)(26 m/s)^2 = 140 J
Thus if both balls have the same kinetic energy of 140J, we can solve for the velocity of the rotating ball. We will assume that the ball is rotating with an angular speed of 5 rev/s
25rev/s = 157 rad/s
The Kinetic Energy for an object that is both translating and rotating is (1/2)MV^2 + (1/2)Iw^2
(1/2)(.42kg)(v)^2 + (1/2)(2/5)(31 rad/s)(.42kg)(.11m)^2 = 140J
v= 25.8 m/s
It turns out that a knuckling ball will not travel much faster than a ball that is shot with rotation if both shots have the same amount of kinetic energy. The amount of energy that is contributed from rotation is minuscule in comparison to the total amount of energy that the ball has.