Physics of Pool

Physics is the science that allows us to understand the fundamental behaviors of the universe. It can be

explored at the macroscopic and microscopic levels, giving insight into the way objects interact.

Here we will take a look at how physics can be applied to the game of pool. Almost all of the different

aspects of pool can be explained through physics, and a better understanding of these fundemental

principles can aid in performance playing pool.

In the game of pool there are sixteen balls, one cueball and fifteen physically identical numbered balls.

While there are many interactions between all the balls on the table, in order to simplify things we will

only look at the interactions between the cue ball and the first ball it strikes. These principles can be

expanded to evaluate the entire system of balls on the pool table.

In order to evaluate the physics of pool, first the measurable values of the system must be collected.

Parameter Symbol Value

Cue ball mass m1 1.6x10-1 kg

Cue ball radius r1 2.79x10-2m

Ball mass m2-m16 1.7x10-1 kg

Ball radii r2-r16 2.86x10-2 m

Coefficient of friction µk 0.027

Knowing these values the Motion, Work, and Energy can all be derived.

The motion of the balls can be catagorized into two general catagories which are collisions and spin or

rotation. Here the focus will be on collisions between the balls. The spin can have a

significant effect on the motion of the ball, but due to time constraints and complexity of the science of

it it will not be addressed to much detail.

"An elastic collision between two objects is one in which the total kinetic energy (as well as total momentum) of the system is the same before and after the collision." (Physics for Scientists and Engineers)

In a collision between the cue ball and another ball, since the masses are so similar the resulting angle

between the vectors of the balls is approximately ninety degrees.