Answer: All that is necessary to create lift is to turn a flow of air. The airfoil of a wing turns a flow, and so does a rotating cylinder. A spinning ball also turns a flow and generates an aerodynamic lift force.
The details of how a spinning ball creates lift are fairly complex. Next to any surface, the molecules of the air stick to the surface, as discussed in the properties of air slide. This thin layer of molecules entrains or pulls the surrounding flow of air. For a spinning ball the external flow is pulled in the direction of the spin. If the ball is not translating, we have a spinning, vortex-like flow set up around the spinning ball, neglecting three-dimensional and viscous effects in the outer flow. If the ball is translating through the air at some velocity, then on one side of the ball the entrained flow opposes the free stream flow, while on the other side of the ball, the entrained and free stream flows are in the same direction. Adding the components of velocity for the entrained flow to the free stream flow, on one side of the ball the net velocity is less than free stream; while on the other, the net velocity is greater than free stream. The flow is then turned by the spinning ball, and a force is generated. Because of the change to the velocity field, the pressure field is also altered around the ball. The magnitude of the force can be computed by integrating the surface pressure times the area around the ball. The direction of the force is perpendicular (at a right angle) to the flow direction and perpendicular to the axis of rotation of the ball.
On the figure at the left, we show the geometry of the spinning ball. A ball of radius b rotates at speed s measured in revolutions per second. A black dashed line indicates the axis of rotation of the ball, and the ball rotates clock-wise, when viewed along the axis from the lower left. The ball has been sliced into a large number of grey-colored sections along the axis of rotation. The air with velocity V and density rho strikes the ball from the upper left. The resulting lift force L is perpendicular to the air velocity and the axis of rotation.
To determine the ideal lift force on the ball, we consider the spinning ball to be composed of an infinite number of very small, grey-colored, rotating cylinders. Adding up (integrating) the lift of all of the cylinders along the axis gives the ideal lift of the ball.
The Kutta-Joukowski lift theorem for a single cylinder states the lift per unit length L is equal to the density rho of the air times the strength of the rotation Gamma times the velocity V of the air.
