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.