When a small rubber roller spins against a large one, how do they move in relation to each other?

When a small rubber roller spins against a large roller, the small roller will indeed spin in the opposite direction to the large roller. This happens because of the nature of rolling motion and the interaction between the two surfaces. When one roller makes contact with the other, the point of contact on both rollers must move at the same speed to avoid slipping. Given that the small roller has a smaller circumference than the large roller, it must rotate more to cover the same distance that the larger roller does in one complete revolution.

As a result, for every rotation of the large roller, the small roller completes more than one rotation, leading to them spinning at different speeds. This differential in speed contributes to the opposite direction of the spins; when one roller's surface moves upwards, the other’s surface must move downwards at the point of contact to maintain that no slipping occurs. Thus, the interaction between the sizes and rotational speeds of the two rollers results in them spinning in opposite directions at different speeds.