Please could someone help with some physics about resistive forces that would slow a ball down which is rolling across a floor. I have found conflicting bits of information about the effect friction has. If the ball grips the floor am I correct in thinking that there is no kinetic friction since the surfaces do not move relative to each other? There would be static friction of course but in terms of slowing the ball down would there be no frictional loses between the floor and the ball. My reasoning is that work done against the balls motion would be the frictional force multiplied by the distance it acts across but there is no kinetic frictional and static friction cannot do any work by definition as it is static? Is that right? Some bits of information I have found said friction does oppose the motion but I don't see how it can if the ball is not slipping as its rolling?
You are correct that the ball is not moving with respect to the floor, so we don't have to worry about kinetic friction at this interface.
But since the energy loss there is so low, other areas of energy loss become significant. Small sources of loss need to be investigated to understand the picture. As you say, air resistance might show up as a big part.
The other major area of loss comes from the fact that neither the floor nor the ball are completely rigid or completely smooth. This allows both to flex during the roll. Some of this flex will be inelastic. The rebound of the material will be incomplete, slowing the ball. Areas where the interface isn't completely smooth will cause the two surfaces to strike and vibrate. The vibration dissipates as heat and sound, not motion. If you can hear the ball rolling, then you know some of the energy is being lost to generate the sound waves.
The sum effect of all these losses is commonly known as "rolling friction" or "rolling resistance", even though the source is somewhat different than the common physics usage of static and kinetic friction.
If the ball and the surface on which it rolls were completely smooth, there would be no static friction. But the ball would not roll; it would slip.
In reality, ball and surface are rough, but this jiggles the ball as it is rolls. The jiggling caused by surface roughness is just above the threshold between static and kinetic friction. This threshold is the coefficient of static friction, which is the amount of force that resists friction divided by the normal force perpendicular to the rolling surfaces. However, as the point of contact between ball and surface is always static, the only mechanical friction you need consider in a rolling ball is kinetic friction.
Kinetic friction in a rolling ball is caused by the jiggling of the ball's rough surface against the floor's rough surface. The coefficient of kinetic friction is always less than the coefficient of static friction, because it takes less force to keep an object moving than to overcome its motionless inertia. However, as a ball rolls rather than slides, kinetic friction will not be very considerable.
The softer the ball, the more it will deform while rolling, and the greater the surface contact between ball and floor, providing more opportunity for kinetic friction. In addition, deformation of the ball is a use of energy and will create drag.
In addition to mechanical friction, there is molecular attraction between the ball's material and the surface material.
Generally, the coefficient of rolling friction is determined experimentally for two materials. You can calculate resistive force by multiplying the coefficient of rolling friction by the weight of the rolling object (the normal force).
If one gets down to analyzing this problem I suspect it's very complicated and you probably have different regimes of motion with regards to energy transfer - and relative to the speed or rather the momentum of the ball and the normal force dependent on the gravity and weight of the ball. The ball has a forward linear momentum, but since friction grabs the surface it imparts a torque and so the ball also stores angular momentum. One can pose the problem as thought experiment and say that the friction is all 'static' but the reality is things are very messy - there is both grabbing and slipping and heat is always being lost to the floor as the ball rolls. That's what ultimately slows it down if you disregard wind resistance (drag).
I once worked with a very clever engineer that invented a gear reducer that had no teeth. The idea was to eliminate backlash and have infinite resolution of motion. The design was similar to a planetary gear arrangement, but instead of gears he used precision round and highly polished ball bearings that contacted one another with an extremely high preload. Theoretically it should have worked based on the assumption that all the friction would be static (assuming sufficient preload). But the invention failed. He could never fully eliminate sliding friction and the period of sliding/static events were random, and never repeatable.