# Billiards and Collisions

The game of billiards shows the principles of collisions, momentum & impulse, and kinetics at work!

Have you ever thought that you were going to sink a billiard ball, only to have it fly off in the other direction? Some people have mastered the art of playing billiards, or cue sports, while also making it pretty entertaining to watch.

Billiards is a game that involves a cue stick and several balls on a felt-covered table. One of the most popular versions of billiards is a game called pool. In pool, players use the cue stick to strike a white ball called the cue ball to hit other similar balls into semicircular holes called pockets along the inner edge of the table.

Did you know?

Florian “Venom” Kohler holds the Guinness World Record in many pool trick shots. In 2017, he sank 70 billiard balls in one minute! He also holds the record for highest billiard ball jump. He made a ball jump 34 centimetres high!

Officially, there are three billiards sports: pool, carom, and snooker. You may be most familiar with pool. Pool involves 15 coloured balls, a cue ball, and a pocketed table. Snooker is a variation of pool that involves 21 coloured balls, a cue ball, and a larger table. Carom, or French billiards, involves 3 balls and a table with no pockets.

Billiards shots might seem complicated. But physics concepts such as momentum, impulse, and kinetic energy can help us understand these complicated billiards shots.

### What is momentum?

In mathematics, the momentum of an object is equal to its mass times its velocity (speed with direction). This is really just a measure of how likely it is that a moving object will stay in motion. If a billiards ball is rolling around on the table, it has momentum.

When the balls strike each other or the table walls, their velocity will change. A change in velocity can be from a change in speed, a change in direction, or both. If the ball’s velocity changes, so does its momentum. The word for this change in momentum over time is impulse.

Did you know?

Billiard balls used to be made of strange materials -- wood, clay, and even elephant ivory. Today most balls are made of resin.

### What happens during collisions between balls?

A collision is a concept that describes what happens when two objects strike each other. There are two types of collisions -- inelastic and elastic. No matter what type of collision you have, momentum will be conserved. This means that the total momentum of all of the colliding objects before the collision will be the same as the total momentum afterwards.

If momentum is conserved in all types of collisions, then how can you tell the difference between the two types? You can tell the difference by how the objects move after they hit each other. This movement depends on their kinetic energy, which is the energy that an object possesses whenever it is in motion.

### What happens during inelastic collisions?

In inelastic collisions, colliding objects don’t bounce off of each other. The kinetic energy of the objects before the collision is not the same after the collision. Some of the kinetic energy is changed to different kinds of energy such as heat, light, or sound energy. One example of an inelastic collision in billiards is when the player hits the cue ball with the pool stick.

Before the collision, the stick is moving towards the ball at a high speed. After the collision, the stick stops moving. It transfers some of its kinetic energy to the cue ball, which rolls forward. But some of the kinetic energy is also lost to friction between the ball and the table, causing it to roll.

### What happens during elastic collisions?

In elastic collisions, the kinetic energy in the two objects stays the same. This means that the total velocity of the two objects after impact is the same as their total velocity before impact. None of the energy is converted to other types of energy, such as heat or light. So where do we see elastic collisions in real life? They are hard to find, but when one billiard ball hits another, it comes pretty close. When one ball hits another, it typically makes a sound. But the energy lost as sound is very small compared to the total energy. Since this energy loss is so small, it is usually ignored.

If the cue ball strikes a stationary billiard ball straight on, then the cue ball will stop moving after the collision. It will have transferred all of its kinetic energy to the other ball, which will move forward with the same velocity that the cue ball had before the collision.

Collisions can only be elastic if the masses are equal. The masses of billiard balls are the same, which can make some collisions close to elastic.

### What happens when you hit the ball on an angle?

Most collisions between billiard balls don’t happen in a straight line. Oftentimes, you need to hit the ball on an angle to get it to go where you want. This is where an understanding of the physics of collisions really becomes key. When the cue ball hits another ball on an angle, the cue ball will keep some of its original velocity. Both balls will roll. The further off-centre that you strike the ball, the more velocity the cue ball will keep.

### Summing up...

The next time you play billiards, try using your new knowledge of physics and collisions. It can make you a better billiards player. With practice, you’ll be shooting trick shots like Florian “Venom” Kohler before you know it!

• Have you played billiards before? What challenges did you encounter? What things are you thinking about as you set up for a shot?
• Would you like to be able to do billiards tricks like Florian “Venom” Kohler? What do you think contributes to the skill and success of a master billiards player?
• Can you think of any other games where a knowledge of how collisions work can help you to win? (e.g., croquet, bowling, marbles)
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• How does an understanding of collisions help with investigating accidents?
• When are materials chosen to build an object because of their elastic properties in a collision? (e.g., foam ball, baseball bat, bike helmet)
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• What is an inelastic collision? What are some examples of inelastic collisions?
• What is an elastic collision? What are some examples of elastic collisions?
• How does the  mass of an object affect its momentum?
• Explain the energy transfer that takes place when a cue ball hits a billiard ball straight on?  What happens to the energy transfer when the cue ball hits a ball at an angle?
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• This article and embedded video can be used to support teaching and learning in Math and Physics related to kinetic & potential energy, collisions, momentum & impulse and kinematics. Concepts introduced include pool stick, cue ball, pockets, velocity, speed, direction, impulse, collision, kinetic energy, inelastic collisions, elastic collisions and inelastic collisions.
• After reading this article and viewing the embedded videos, teachers could have students complete a Concept Definition Web for the concept of collisions. Ready-to-use Concept Definition Web are available in [Google doc] and [PDF] formats.
• After reading the article and viewing the embedded video, Collisions: Crash Course Physics #10, teachers could have students collect and compare information provided in the article and the video using a Print-Video Venn Diagram learning strategy. Ready-to-use Print Video Venn Diagram reproducibles are available in [Google doc] and [PDF] formats.

Insane Trick Shots (2016)

A video (2:54 min.) compilation from StuntsAmazing of some of Florian “Venom” Kohler’s most impressive trickshots.

In this video (8:32 min.), Florian “Venom” Kohler gives the inside scoop on how to perform some simple billiards trickshots .

## References

Crash Course. (2015, June 2). Collisions: Crash course physics #10.

Encyclopaedia Britannica. (2018). Billiards: game group.

Isaac Physics. (n.d.). Collisions. University of Cambridge.

Jain, M. C. (2009). Textbook of engineering physics: Pt. i. Phi Learning.

MIT Blossoms. (2015, September 28). The physics of pool.

Science Clarified. (n.d.). Momentum - Real-life applications.

Shamos, M. I. (2003). The new illustrated encyclopedia of billiards. Lyons Press.