When I am browsing through my rotational dynamics chapter, I raise myself a question on the direction of frictional force under all kinds of possible circumstances: 1. Pure rolling For pure rolling, the frictional force will always be 0; 2. Non-pure rolling For this situation, I will analyse with a model: A rolling ball lying on a level ground. And to simplify my listing, I will ignore some situations if they are similar to each other. 2.1 ω anti-clockwise v left (1) ωR<v Frictional force will tend to slow V down and increase ω, hence it is to the right; (2) ωR>v Frictional force will tend to increase V up and slow ω down. Hence it is to the left; 2.2 ω anti-clockwise v right At first, the frictional force will be to the left(Slow down both ω and v) But later, I think two situations may occur: ω is not sufficiently large but v is sufficiently large, ω will be decreased to 0. And continuously, frictional force will be to the left to increase ω clockwisely until pure rolling occurs. v is not sufficiently large but ω is sufficiently large, v will be decreased to 0. And after that, frictional force will be to the left to increase v leftwards until pure rolling occurs. If ω and v just happen to be such nice that it will be decreased to 0 at the same time, the object will just stop then. My idea in analyzing the frictional force is that: Non-pure rolling will always tend to transit itself into pure-rolling condition. Thank you for spending time on reading this but could you please tell me whether my analysis is correct?