by Ron Shepard
In this case, the CB stops. Figure 9 illustrates the physics involved with a stop shot. As the CB slides along the cloth,. The spin rate decelerates as indicated. In this case, the CB actually accelerates because the sliding friction force is in the same. If the CB is struck with the cue tip at the. To get over-spin e. Figure 9c , the CB must be struck above this height, which is risky due to likelihood for miscue. In TP 3. The center of the range is the half-ball hit, but the CB deflection is.
The exact CB deflection. For a small ball-hit fraction i. For a large ball-hit fraction i. In the center of the range, both the post-. As determined by Coriolis see also:. Figure 14 illustrates the ball-hit-fraction range, and corresponding cut angles, to illustrate the. Examples of all of these types of shots. This is actually quite typical for most pool shots In still. Notice how much the cue tip deflects away down in the diagram from its original line. Also notice how much the cue tip deforms e.
Those leather tips, which. While the tip is in contact with the ball, the ball starts rotating. Because the end of the shaft has mass, it takes force to move the end of the shaft down as the ball. The endmass relates to how far the transverse elastic wave travels down the. It would.
In the squirt analysis, the tip is assumed to remain in contact with the ball as the ball rotates. While the tip and ball are in contact, the velocity of the tip and ball are equal at the point of. The squirt angle is very close to a linear function of tip offset, provided miscues. Cross  has verified this theoretical result with a series. Cross  also investigated how squirt angle changes with tip offset under conditions of cue. The machine consists of a spring-loaded carriage on.
With more mass added to the end of the cue, and the closer the mass is to the tip, the more.
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Also, if mass is added beyond a certain distance from the tip, it has no. Figure 18 Squirt vs. If that were the case, we might have. In the. Throw can also be caused by cut angle alone, in which case it is called cut-. In Figure 19, the right counterclockwise sidespin creates a sliding friction. This force is what creates the throw angle. The spin imparted. In this case, the throwing force to the left creates clockwise. Spin transfer is an important effect with bank shots e. Previous treatments of pool-ball throw in the literature e.
The exponential model of friction in Equation 3 fits experimental data quite well see TP A. Possible reasons for why the friction coefficient decreases with higher relative surface.
At small cut angles, sliding between the balls ceases during impact, and the coefficient of. If friction did not vary with speed e. However, the point of the figures is to show that the experimental data do exhibit the. Other experiments e. Figure 20 Stun shot collision-induced throw. This article has presented a collection of pool and billiards principles that make for excellent.
I have used pool examples in. Instead, I have referenced online resources where the details can be found. I wanted this. In future articles, I plan to present more details concerning derivations and experimental. IV," Dr. Dave's Illustrated. Dave's Illustrated Principles, Billiards. Dave's Illustrated Principles.
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Illustrated Principles, Billiards Digest, Vol. All of the Billiards Digest articles referenced above are also available at:. Read Free For 30 Days.
2d pool physics?
Description: The purpose of this paper is to provide illustrations and explanations of many important pool and billiards physics principles. The goal is to provide a single and complete resource to help physics instructors infuse billiards examples into their lectures. The main contributions of Coriolis in his billiards physics book are presented along with other more recent developments and experimental results. Also provided are numerous links to pool physics references, instructional resources, and online video demonstrations. Technical derivations and extensive experimental results are not included in the article, but they are all available and easy to find online with the references and links provided.
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By David G. Flag for inappropriate content. For Later. Related titles. Carousel Previous Carousel Next. Advanced Technique in Pool and Billiards Edition. Jump to Page. Search inside document. It involves many physical principles including conservation of momentum and energy, friction, elastic and inelastic collisions, translational and rotational equations of motion, solid mechanics, vibrations, etc. Furthermore, because the playing surface of a pool table is ideally flat and the balls are ideally perfectly round and homogeneous spheres of equal mass, and ball collisions are nearly elastic and nearly friction-free, equations written for ball trajectories can actually be solved analytically, with only a few idealized assumptions.
In , Gaspard-Gustave Coriolis wrote a comprehensive book presenting the physics of pool and billiards. Coriolis was not only a great mathematician and physicist There has also been many technical papers and online material published over the years expanding on pool physics knowledge . In this article, I want to give an overview of many of the important and useful principles that can be used as examples in physics classes. To keep this paper of reasonable length, many of the technical derivations are provided online. I also plan to write more papers in the future that will delve more into some of the technical details and experimental results related to some of the principles.
And I have a very, very rough sense that a hard, sharp, and even strike of the cue ball tends to make it bounce back more while a slower or more angled strike will make it roll forward after collision. Can anyone give a more rigorous analysis of the phenomena, or point me to a resource for this? I've tried googling but haven't see anything that really seems to address this as far as I can tell.
So in cars colliding, or pool balls, or a skater on ice throwing a baseball--what features of the system determine the amount of momentum imparted to each component? Those shots in which the cue ball "draws" backwards after hitting the target ball involve backspin. Without backspin, the cue ball cannot reverse direction. Consider what happens when the cue ball is not spinning at all when it hits the target ball. The cue ball will come to a dead stop if it hits the target ball straight on.
Think of Newton's cradle.
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The cue ball will continue moving forward but at an angle if a non-spinning cue ball hits the target ball obliquely. The cue ball always moves forward after striking the target ball if the cue ball is rolling without slipping whilst hitting the target ball. A rolling cue ball will initially stop if it hits the target ball straight on. The cue ball will still be spinning, however, and this spin will soon make the cue ball start moving forward again.
When a rolling cue ball hits the target ball obliquely, the collision will change the cue ball's direction and the spin will accentuate the forward motion. The only way to combat these effects is to have the cue ball spinning backwards when it strikes the target ball. A backspinning cue ball that hits a target ball straight on will initially stop, but now the backspin will make the cue ball reverse direction.
So how can one make the cue ball have backspin? The answer is simple: Strike the ball below center. How much below depends on the distance to the target ball. This is easy if the target ball is close to the cue ball: Strike the cue ball a bit below center. You'll need to strike the cue ball a bit further below center if the target ball is further away.
When the target ball is very far away across the length of the table , it's very hard to have the cue ball spinning backwards at the point of collision. You need to take care in your shot and how far from off-center you hit the cue ball. Hit the cue ball too far off-center and you'll hear a nasty "clink" sound. You've just miscued; the cue ball won't move anything like you planned. And maybe you've even ripped the table, bad move!