The effect of inertial normal force on the rolling friction of a soft sphere on a hard plane

Previously, in the rolling-friction analysis, the normal compression force was assumed to be independent of the rolling speed. In this study, it is found that the normal compression force of a soft sphere on a hard plane depends on its rolling speed as the inertial force is taken into consideration. A new expression of the rolling frictional torque, which is not proportional to the apparent normal force as the previous one is derived. It is shown that the relation between rolling frictional torque and rolling speed is nonlinear as the inertial force is considered