Rolling Resistance

So what, you may ask, is rolling resistance and what does it have to do with friction? Well rolling resistance is the resistance exerted by a surface that an object is being rolled on and is caused by the deformation of that surface. For instance, both a train wheel movin on a track and a tractor wheel rolling on the dirt have a resistance to their rolling that is caused by the deformation of the surface they roll on. One should note that the amount of deformation also plays a roll in how much resistance a rolling object encounters. generally, the more deformation the more resistance that is caused. The picture below shows an ideal situation in which there is no deformation to the surface. "μ_kN=F_friction".

This next picture illustrates what actually happens when an object begins to feel a force that intends to push it in a certain direction. There is a distribution of different normal forces acting on the object which all sum to on normal force that will be acting at an angle to the center of gravity of the object.

It can be analyzed that P is approximately equal to W*a/r for a cylinder that is moving at a constant velocity. Therefore one would have to apply a force to the cylinder approximately equal to P in order for the cylinder to move at a constant velocity and to not slow down.