Kicking a Ball

    The first thing to consider when bending a soccer shot is kicking the ball.  Two important concepts that help in understanding this action are Newton's third law and the conservation of energy.  Newton's third law states that for every action there is an equal and opposite reaction.  The conservation of energy states that energy may neither be created nor destroyed.
    As you are swinging your leg to kick the ball you are building up kinetic energy in your leg till the moment of impact.  This energy is then transferred to the ball which flies off in whatever direction you hit it.
     At the point of impact the energy from your leg can be calculated using the formula for kinetic energy, K = 1/2mv². The kinetic energy is equal to half the mass of your leg times the velocity of your leg squared.  To determine the velocity of the ball plug in the mass of the ball and the kinetic energy of your leg into the equation above.  Take into account that some energy is lost through heat and friction and so this is just a good estimate.

Curving a ball
(Bend it like Beckam!)

 The first step to curving the ball is to strike it slightly off center which causes it to spin horizontally in midair.  From here two important physics concepts come into play, Bernoulli's principle and the "Magnus effect".
 
Bernoulli's principle states that as the velocity of a fluid (air) increases, the pressure exerted by that fluid (air) decreases.  As the ball moves forward, air flows by it on all sides.  When the ball is spinning, air travels faster on the side of the ball that is moving in the same direction as the airflow.  This reduces the pressure on that side of the ball. The inverse occurs on the opposite side with the ball spinning against the air flow and pressure being greater (see below).

(http://physicsworld.com/cws/article/print/1998/jun/01/the-physics-of-football)

When this occurs there is an imbalance in the pressure exerted on the two sides of the ball and the ball deflects or curves to the side with less pressure.   This is the know as the "Magnus effect"

Having the ball curve at the right time

    At this point we know how a ball curves, but how does it curve at the right time? This comes down to the velocity of the ball and the air drag on the ball.  The air drag is the force that air applies to the ball as it flies through the air.  The drag force formula is  F_D = 1/2rv²AC_D ( F_D: drag force, r: density of the ball, v² : velocity of the ball squared, A: cross sectional area of the ball, C_D: drag coefficient of the ball). 
    "The drag force, F_D , on a ball increases with the square of velocity, v, assuming that the density, r, of the ball and it's cross-sectional area, A, remain unchanged... It appears, however, that the 'drag coefficient' ,C_D , also depends on the velocity of the ball.  For example, if we plot the drag coefficient against Reynold's number – a non-dimensional parameter equal to rv D /μ, where D is the diameter of the ball and μ is the kinematic viscosity of the air – we find that the drag coefficient drops suddenly when the airflow at the surface of the ball changes from being smooth and laminar to being turbulent (see below). 

When the airflow is laminar and the drag coefficient is high, the boundary layer of air on the surface of the ball 'separates' relatively early as it flows over the ball, producing vortices in its wake. However, when the airflow is turbulent, the boundary layer sticks to the ball for longer. This produces late separation and a small drag." (Asal 1998) 

The graph below is a comparison of drag force with ball speed.  At high speeds, the drag force drops and thus the struck ball does not curve.  It is only when the ball slows down does the "Magnus effect" take over and the ball starts curving.  So the next time you see a curved shot on goal that doesn't drop in, the player either didn't put enough spin on it, or they struck it too hard.