# Where’s The Cue Ball Going? – Snookered by The Laws of Physics

BBC – World Snooker Championship 2016

With the World Snooker Championship having just wrapped up at the Crucible Theater in Sheffield, Ronnie O’Sullivan saw himself equaling Stephen Hendry’s record number of seven titles after two weeks of grueling matches. While the commentators praised the players for executing spectacular shots, a physics student may find themselves attempting to recall lessons on impacts and collisions, and perhaps wondering if professional snooker players and physicists are more alike than we are different.

## Newtonian Cue-Action

Snooker players often rely on striking the cue ball at an angle to the target ball in order to gain position for their next shot. Taking a shot straight on is undesirable as it makes it very difficult to change the direction in which the cue ball travels after it strikes the object ball. Mathematically speaking however, this type of shot is described very simply by Newton’s experimental law, which states that the ratio of the final and initial relative speeds of two bodies in collision is constant. This ratio is known as the coefficient of restitution and is denoted by the letter e. The value of reveals interesting properties of the collision. Namely,

• = 1 : Kinetic energy is conserved and the collision is classified as being “elastic”.
• 0 < e < 1 : Kinetic energy is not conserved and the collision is said to be “inelastic”.
• = 0 : The maximum amount of kinetic energy is lost in the collision.
• > 1 : Kinetic energy is gained in the collision.

## Introducing Spin

In the case of a snooker match, the player can manipulate the outcome of the collision by applying spin to the cue ball. This is achieved by striking the ball above or below the center of the ball. The diagram below gives a detailed visualization of the various ways spin can be applied to the cue ball.

http://news.bbc.co.uk/sportacademy/hi/sa/special_events/snooker/newsid_2952000/2952887.stm

Applying top spin is known as a stun shot and causes the cue ball to run forwards after striking the object ball. This is due to the cue ball having a greater forwards angular momentum which carries the cue ball forwards after the collision. Alternatively, a screw shot can be played, which places angular momentum in the direction opposite to the motion of the cue ball and causes the ball to retreat backwards in the direction of the collision. Each of these shots are useful for gaining position on the next shot of the match.

True professionals make use of side spin in conjunction with top or back spin to really take control of the cue ball and produce shots which may seem impossible to the uninitiated.

Ronnie O’ Sullivan demonstrating extreme accuracy and cue ball control using side spin.

It may come as a harsh realisation to some that there is low correlation between knowledge of collisions and snooker ability. While it appears there is a certain element of luck involved in snooker, one certainty is that the laws of physics are at play and unlikely to find themselves snookered.

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