Thanks for the clarification, Mike.Hey Jim,
No, I wasn't really trying to get into that. I agreed with PJ's analogy about a barrell rolling on its edge. My contention :smile: is that an object ball will pick up a small amount of speed from the extreme side spin of the cue ball on a thin cut.
For what it's worth, I don't there's much doubt that, all else being equal, the throw component adds to an object ball's speed, but extremely little.
Let's say you execute a cut shot with just the right amount of outside english to eliminate throw (or maybe put some spit on the contact area). The object ball takes off with a certain speed. You then do the same shot again, but change the amount of outside english so that there is some throw. As Patrick pointed out, the friction acts perpendicular to the direction of the object ball in the first shot. Nevertheless, it now has an additional velocity component which adds, vectorally (Pythagorean addition in this case) to its total velocity. That is, it'll have more speed along its new direction of travel. We're assuming the original forward speed component (the one in the first shot) isn't affected by the friction. This is probably near enough true, but it is an assumption. As indicated earlier, though, it's next to nothing. With 5 degrees of throw, it works out to about a 0.3% increase.
However, if you produced the throw by increasing the outside english, then compensated by hitting the OB thicker to drive it in the same direction as the first shot, then its speed will also be increased because of the thicker hit, as a few posters have pointed out. This particular addition to its velocity is greater at larger cut angles for the same throw compensation (it's almost nothing at very modest cut angles).
In a sense, yes. Let's say you cut a ball 83 degrees without any throw (or very little). Then you repeat the shot with lots of outside english, attempting to send the OB in the same direction. And say you expect about 3 degrees of throw (and possibly get it), so you hit it thicker, equivalent to an 80-degree cut. Because of that second addition to the OB's speed mentioned above, its speed will be increased by a whopping 40% (given the same cueball speed, of course)! Since travel distance is proportional to the square of a ball's speed, it should go about twice as far (1.4 x 1.4 = 1.96). The throw itself contributes virtually nil, as per above.This small transfer of speed is possibly proportional to the decreasing amount of force from the impulse of the cue ball and object ball. I seem to see it most when I cut balls 80+ degrees.
Comparing this to a 30-degree versus a 33-degree cut, the increase is a mere 3%. The moral is that OB speed is extremely sensitive to changes in contact point at really severe cuts.
I started by saying "in a sense," because it's actually 'how' the impulse drops off with cut angle (cosine of the cut angle), not merely that it drops off.
Jim