The Pool Table/Cueball Problem

As an interjection to the 15-Mar-2005 report, I’d just like to add one or two things - firstly, here in the UK, the cueball is almost always smaller than the object balls, as opposed to being bigger. Also, in situations with magnetic pool balls (and while I don’t profess to be anywhere near professional, I play pool to a fairly high standard) a lot of strange reactions concerning ‘kicks’ occur - a lot of research has gone into kicks on a snooker table and not much seems to be known about them by all accounts, but in my experience, more kicks occur with magnetic cueballs. A kick is frustrating thing, and it’s a rather vague term for any number of things that happens between cueball and object ball, from either or both balls jumping off the bed of the table upon contact and balls seemingly defying the laws of logic and physics in their trajectories after contact.

As you will already know, assuming that there is no friction on a table, balls after contact will move away from that point of impact at a 90 degree angle, which is what should happen with a stun shot (English terminology, I know you Americans call it something else but I forget what). However, in some kick occurrences both cue ball and object ball straighten up considerably before the friction of the table kicks in (at which point the balls straighten up further, obviously), resulting in a much more acute angle than the expected 90.

Just my two pence.

BristolBoy. Welcome to the boards. And thanks for your post.

When you discuss a previous column, it’s good to provide a link which will help other readers see what you’re talking about. You’ll know next time.

I’m not sure what you mean by this. Consider one ball striking another straight-on. The point of contact of the balls is directly in the line of the motion, and both balls will move along that line, by conservation of momentum. Where is your right angle?

The straight-on case is a special one. Otherwise, when the cue ball hits an object ball, the cue ball will move on a path that’s 90 degrees off the path of the object ball, at least until the spin of the cue ball takes over and alters its course. If you hit the cue ball with a little backspin so that, at the time of impact, it is not spinning at all, you’ll see the 90-degree effect.

In the case of the straight-on shot, you can say that its path is 90 degrees off, but its speed is zero. It sounds like a bogus solution, but if you take the limit as you approach a straight-on shot with smaller and smaller angles, the cue ball rebound path approaches 90 degrees and its velocity approaches zero.

Okay, you meant the paths of the balls immediately after the collision are perpendicular. Now that that’s cleared up, a quick bit of algebra shows that your assertion can only be correct if the masses of the balls are equal. As Una’s report states, many coin-op tables have cue balls of a different size.

Further, even this calculation neglects friction (and that’s all friction, meaning you can’t consider spin either) and assumes a perfectly elastic collision. It’d take someone more experienced than I am with this sort of calculation to get a rough estimate of the deviation from the ideal introduced by the slight inelasticity of the collision and the friction of the balls against each other and the table, the deviation introduced by differing masses, and the deviation introduced by magnets (oh, and we’ll need some stats on the magnets used). I see no reason to assume a priori that quirky shots are more due to magnets than to differing masses or the effects of friction and such.

If magnetic balls behave noticably differently than do unmagnetised balls in play, my first guess would be that, due to the different materials used in the construction of the balls, the magnetised ones have different elastic properties.

And the assumption that friction (of all sorts) is negligible is valid for at least a short time following each collision (since the timescale of the collision itself is much shorter than any timescale associated with friction). Identical masses is a valid assumption for any well-made magnetised cue ball, since the purpose of magnetisation is to avoid the need for a differing radius, mass, or moment of inertia. This leaves only the assumption of perfectly elastic collisions, but I suspect that this is a sufficiently good approximation in most cases that the resulting deviation from a right angle is undetectable. If a collision does significantly deviate from a right angle, this could even be considered evidence that magnetised cue balls are not adequately elastic.

Okay, so we’ve got two competing theories. Can anyone who knows more about these things do a BotE and figure whether the inelasticity or the magnetism has a larger effect on the collision?

I was just explaining what BristolBoy meant about the 90-degree comment, not defending his general point about the balls. The 90-degree rule works in practice closely enough to the ideal case that I can’t tell any difference. I use it often, for example to ensure that the cue ball won’t scratch in a side pocket after contacting an object ball. My first-pass approximation is to use the 90 degree rule, then if that goes towards the side pocket, I use top or back spin to adjust it from there. I can confidently get quite close to the side pocket in these cases without worry of scratching.

You’re right that the equal-mass assumption is critical, but I play only on non-coin-op tables with very few exceptions. I have no idea why the magnetic cue balls would cause strange behavior if they’re equal mass and size (it doesn’t seem like a small difference in moment of inertia would cause that).

For the magnetism to have any effect at all, you’d need a magnetic field for it to interact with, and the only field available is the Earth’s, so far as I know (which is pretty small). Even at that, the magnetic balls probably just have an iron core, not a permanent magnet, so they’ll only react to a magnetic field gradient, which is smaller yet. Now add in the fact that the magnetic force, such as it is, acts continuously over time, like friction, so it would have no effect on the initial direction of motion. The only way that magnetism could have an effect on the initial direction would be if the collision timescale were very large, but a long collision timescale would probably also tend to make the collision inelastic. In other words, the only way to make the magnetism significant would be to make the inelasticity even more so. Finally, we consider the fact that trick bounces and other sorts of “stun” are possible even in standard free pool balls (i.e., ones where all of the balls are indistinguishable, and none have magnets), and I think it’s pretty safe to say that inelasticity dominates over magnetism.

Pretty soon now, somebody will assert that playing pool with a magnetic cue ball has wondrously cured his arthritis. :rolleyes:

No, that’s playing with brass balls.


Sorry, I replied directly off my email and didn’t notice that you weren’t he. My bad.

The presense of the magnet will have some effect on the moment of inertia of the cue ball. Remember, these are rolling balls, not CO[sub]2[/sub] pucks.

Don’t get me wrong, I’m no physicist - but maths and pool I can handle :smiley:

Of course, this is all just anecdotal evidence and I’m making a large number of assumptions, but in my experience (which is a lot, I’ve been playing pool regularly for 15 years, and irregularly a lot longer still), what I already stated is true.

Professionals will tell you of the 90 degree theory, because as you can imagine, as with most sports that involve moving a ball along a surface (bowling, for example), the ball doesn’t start rolling until friction catches up with it (OK, so that’s not the most technical way of describing it, but you know what I mean). As for straight shots, yes, there is a difference, but only insofar if the cueball is already rolling as opposed to sliding when it contacts the object ball - this is how spin (English, for you guys) is applied and how it affects the movement of the cueball after contact. Massé shots are something different altogether, and are dependant on the player’s ability to start the ball spinning along 2 axes at once before rolling, and still have enough rotational speed on the ball when the friction of the cloth grabs the ball.

One could arrange other materials of appropriate density through the ball in such a way as to cancel this, and I presume that this is actually done with magnetised balls. After all, a differing moment of inertia would itself be enough, in principle, to sort the balls, so if you’re going to have a different moment, why bother with the magnet at all? But all of these compensations would have a further effect on the elasticity, and elasticity is not nearly as simple as moment of inertia, so one can’t necessarily cancel out the effects on elasticity.

I doubt making the moment of inertia match a homogeneous sphere is done with magnetized balls. Why would they bother? The BCA EQUIPMENT SPECIFICATIONS don’t give any specifications for moment of inertia, and the difference probably wouldn’t be especially noticeable. A quick Google search for magnetic “cue ball” gives a lot of sites with magnetic cue balls for sale (here for example), but they don’t mention moment of intertia, just size and weight. Adding moment and inertia to the search just gets me a bunch of physics experiment sites.

That particular site lists a novelty cue ball whose center of mass is off-center. BristolBoy, could someone have been playing a joke on you?

I was looking around to see if any sites showed a cross-section of a magnetic core cue ball, and I found this site. It’s a patent application for a magnetic cue ball that uses a ring of metal, rather than a ball. This one wouldn’t even have the same moment of inertia around all three axes.

Of particular interest is the justification for using this design instead of the usual metal spheres:

Based on this, I’m willing to believe (some) magnetic cue balls really do roll differently, not because of the magnetism or difference in elasticity, but due to a center of mass which doesn’t match the geometric center.