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The Physics of Cue SportsTeo Jim Yang3O3 26

ContentsIntroduction to Cue SportsPhysics Concepts Involved in Cue SportsBefore Collision: Hitting the Cue BallDuring Collision: When the Cue Ball hits the Object BallAfter Collision: The Motion Path of the Cue BallKicks and Banks: How to pot the Object Balls efficiently

Introduction to Cue SportsUsing a cue stick, the objective is to strike the cue ball to hit other billiard balls into one of six pockets or pots on a billiard tableGenerally known as billiards, but has many sub-categories including:SnookerPool (pocket billiards)Carom Billiards

Physics Concepts InvolvedKinematics and DynamicsVelocityAccelerationMomentumImpulseFrictionAngular Momentum (or Spin)

The physics of billiards is a lot similar to the way light rays behave!Kinematics and Dynamics of BilliardsVelocity (displacement/time)The speed at which the balls move across the tableDependent on the force exerted by the cue stickAcceleration (displacement/velocity)The rate of change in speedSpeeds up and slows down due to human force (via the cue stick) and frictional force respectively

Kinematics and Dynamics of BilliardsMomentum (mass x velocity)When one ball hits another, the first will impart velocity to the second through momentumWhen the cue ball hits another ball, the other ball will move with similar velocity, but the cue ball will slow, if not halt altogetherThe total momentum of the system, before, during, and after the hit remains the same

Impulse (mass x change in velocity)Change in momentum of an object over timeDescribes the collision and transference of velocity from ball to ball

Friction in BilliardsA billiard table is made to be as flat as possible, with few surface imperfectionsInsures that game play is predictable and consistent between tablesTable material: FeltSlows down the movement of the balls considerablyAs the ball rolls across the table, the fibres in the felt gently push on the surface of the ball, producing spin

Before CollisionAngular Momentum: SpinMass x Directional VelocityOccurs when the cue ball is hit off-centerJust like when a light ray enters a medium, it will refract unless it enters perpendicular to the medium3 types of billiards spinFollowDrawEnglishIt is a form of momentum, thus:Can be imparted from one ball to another

Angular Momentum: SpinFollowCaused by hitting the ball above the horizontal planeDrawCaused by hitting below the horizontal planeEnglishCaused by hitting the ball somewhere on either side of the vertical plane

When the cue ball is hitCenter ball (hitting it dead center)It slides for a short distance before rollingThe harder the ball is hit, the farther it slides before the ball is rolling

When the cue ball is hitDraw (below center)First the ball rotates backwardThis rotation slows as the ball slides, and then the ball rolls forward as it does on other shotsThe harder the ball is hit, the farther the ball will travel with this backward spinIf the cue ball hits another ball solidly when it still is spinning backwards, this backward spin will make it come back toward you after the collision

When the cue ball is hitFollow (above center)Cue ball rotates forwardIf the cue ball then hits another ball, it will roll forward after the collisionOther ShotsStop Shot (cue ball stops after collision)The cue ball slides to the object ball and stops dead as the object ball shoots ahead because of the collisionCan be accomplished using center ball or drawJump Shot (cue ball jumps over one billiard ball to hit another)Impart extreme spin on the cue ball or elevate greatly the cue stickJump Shot ExampleA shorter jump cue makes the jump higher and more dramaticThe type and thickness of the cloth may also be a factor in how high the cue ball jumpsSweet SpotThe area of the cue ball where it is struck so that no friction force develops between the ball and the tablePure rolling of the ball will always result after impact

During CollisionBall-Ball CollisionsWhen two billiard balls collide the collision is nearly elasticAn elastic collision is one in which the kinetic energy of the system is conserved before and after impactConservation of EnergyEnergy cannot be created nor destroyed; only transferred from one object to anotherKE is thus transferred from ball-to-ball during collisionsBall-Ball CollisionsIn the simplest case, when a cue ball hits an object ball in a straight line, the resulting path of the object ball will be along the line that connects the center of the two balls at contact90 Degree Rule: The resulting path of the cue ball will be perpendicular (90 degrees) to that line

Ball-Ball CollisionsWhen the cue ball hits the object ball at an angle, the 90 Degree Rule still appliesThe line L1is drawn at a tangent to both balls at the point of contactL1is perpendicular to the line passing through the centre of the two balls and the contact point CPL1also makes an angle with the vertical, and the line passing through the centre of the balls makes an angle with the horizontal.

Ball-Ball CollisionsAfter impact at CP, ball B moves in the direction of the line joining the centre of the two balls (blue line)Force delivered by ball A to ball B acts normal to the surface of ball B, Thus, ball B moves in the direction of this forceAfter impact, ball A moves in a direction perpendicular to the direction of ball B

Ball-Ball CollisionsUsing a vector diagram of the blue, green and red lines (the displacement of the balls before and after collision), the relationship between the forces can be easily seen:

ThrowHowever, the resultant direction of the object ball after collision usually deviates slightly due to frictional force with the tableThis deviation is known as throwThis is common when the cue ball is struck English or when the cue ball strikes the object ball at an angle

ThrowWhen the cue ball is given side English, as in the diagram, it spins anti-clockwiseSimilar to the movement of gears, the red and yellow balls spin in the opposite direction to the adjacent ballThis causes the yellow ball to be thrown to the right

After CollisionAfter collidingIf the cue ball had center ball during collision, it should moveat a right angle to the path of the object ball (perpendicular)With follow, the cue ball will curve forwardWith draw, the cue ball will curve backward

Kicks and BanksVideoDonald Duck and Billiards

The video shows how the paths of the balls can be perfected by using concepts of physics and mathematicsKicks and BanksA bank shot is when you drive an object ball into the rail (side of the table) and then into a pocket, somewhere on the other side of the tableA kick shot is when you drive the cue ball into the rail, and then into the object ballThis is a lot like the reflection of a light ray off a mirrorKicks and BanksThere are many ways to accomplish kick and bank shotsBank ShotKick Shot

ConclusionBy using physics concepts, cue sports can be more easily understood and picked upOn the other hand, using cue sports is also a fun way to understand physics concepts betterReferenceshttp://www.klsgametables.com/english.htmlhttp://www.pool-billiards-game.com/billiard-drills.htmlhttp://www.trickshottim.com/learn/pool-physics.htmlhttp://www.real-world-physics-problems.com/physics-of-billiards.htmlhttp://www.jimloy.com/billiard/phys.htmhttp://www.suite101.com/content/billiards-and-angular-momentum-a24691http://www.billiardworld.com/index.html