Question

When we hit the cue ball off-center to impart spin, we still don't know exactly how the tip and ball interact during the tip-ball contact. There are models and papers on this subject already. Dr.Dave did one analysis assuming the tip and the impact point remain static during the entire contact period.

However, what I find confusing for this assumption is that, if the tip and impact point remain static throughout the impact, that means the impact point on the ball, at rest right before impact, needs to have an instantaneous jump in velocity, in the direction tangential to the normal direction (connecting impact point to the center of ball). This is because the tip approaches the impact point with some velocity, and this velocity can be decomposed into the direction normal to the ball, and tangential to the ball at impact point.

That being said, is it true that there has to be some slipping between the tip and the ball at the very beginning of the impact, in order for the ball surface to catch up to the tip, and for the tip to decelerate? This conclusion comes from another paper Motions of a billiard ball after a cue stroke on page 5, right after the sentence Let us explain the collision process in the order of time.

Answer 1

When hitting the cue ball off-center, the interaction between the tip and the ball is still not fully understood. It is possible that there is some slipping between the tip and the ball at the beginning of impact.

Step-by-step explanation:

When hitting the cue ball off-center to impart spin, the interaction between the tip and the ball during the tip-ball contact is still not fully understood. However, there are models and papers that have analyzed this subject. One analysis assumes that the tip and the impact point remain static during the entire contact period, but this raises questions about the velocity of the impact point.

It is true that there may be some slipping between the tip and the ball at the very beginning of the impact in order for the ball surface to catch up to the tip and for the tip to decelerate. This conclusion comes from another paper on the motions of a billiard ball after a cue stroke.

Overall, the precise details of the interaction between the tip and the ball during spin imparting are still an area of ongoing research.