Physics of Pool :: Sport Sports Billiard Billiards

When most of us go out to play pool we do not realize how much physics effects our game. If we took the time to understand at least the basic physics of pool it might be amazing to what degree we could improve our skills. Most of us already know at least somewhat the general idea of how to play pool well. Below I will give a brief description of how physics plays a part in improving you game of pool. So read on if you care to impress your fellow pool players! -Basic Momentum & Kinetic Energy For the purpose of billiards we will not go into great detail as to what momentum is. Basically though it can be thought of using the following equation; p = mv where p = momentum m = mass of object v = velocity of object Kinetic energy is energy associated with the motion of an object. For basic purposes we can just look at the following equation which relates kinetic energy with mass and velocity of an object. K =  ½mv2 where K = kinetic energy When you strike another ball with the cue ball it is almost a perfect elastic collision. An elastic collision is one in which total kinetic energy as well as total momentum are conserved within the system. This can be shown by the two basic equations; Conservation of Kinetic Energy:  ½m1v1i2 +  ½m2v2i2 =  ½m1v1f2 +  ½m2v2f2 Conservation of Momentum: m1v1i + m2v2i = m1v1f + m2v2f where m = mass of object v = velocity Since the cue ball has virtually the same mass as the other balls and the velocity of our second ball will always be zero, since we are striking a static ball with the cue ball. In addition this is considered a two- dimensional collision. From this we know that momentum is saved within the y component and within the x component. Therefore in the case of pool we can rewrite these two equations as: Conservation of Kinetic Energy:  ½m1v1i2 =  ½m1v1f2 +  ½m2v2f2 Conservation of Momentum: m1v1i = m1v1f cosà ¸+ m2v2f cosØ 0 = m1v1f sinà ¸ - m2v2f sinØ In this last equation the minus sign comes from the fact after the collision ball two has a y component of velocity in the downward direction from the x-axis. This can be seen in the following diagram. The above diagrams show the initial velocity (both x and y directions) of both balls (Vxi &Vyi) as well as the final velocities (Vxf & Vyf). As we can see Vxi = Vxf (total of red and blue balls) as well as Vyi = Vyf.