PHYSICS AT WORK IN THE GAME OF POOL

 

 

Newton's Laws:

 

To the untrained eye, Newton's laws seem fairly common sense; however, they are vital to a good understanding of the fundamentals of the game. All seasoned players, whether they know it or not, are intimately familiar with Newton.

 

1) Law of Inertia: "If the net force exerted on an object is zero, an object at rest remains at rest and an object in motion continue in motion with a constant velocity."

 

The billiard, when at rest, will not move unless an external force acts upon it. A player must know how to apply varying degrees of force with respect to both magnitude and direction (force is a vector) in order to successfully set the billiards in the pockets. He must also know that the billiards will remain in motion unless another force (usually friction) acts upon it. The billiard player must be able to know and apply this law in order to understand the dynamics of the billiards.

 

2) Σ F = ma : "The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass."

 

The greater the force applied on the cue ball, the greater its acceleration and the greater force (acceleration) it will impart to the other billiards. This knowledge is the key in the game. If there was a distance of one meter between the cue ball and the billiard you plan to hit, merely tapping the cue ball would not be a wise idea.  Knowing that a greater force would yield a greater acceleration and therefore make the cue ball travel further is crucial.

 

3) Equal, but opposite: "If two objects interact, the force F12 exerted by object 1 on object 2 is equal in magnitude and opposite in direction to the force F21 exerted by object 2 on object 1."

 

This law basically means that no single force can ever occur just by itself; forces always occur in pairs. The most basic example of this concept is the weight of the ball against the table and the table pushing back up on the ball to hold the ball in equilibrium.

 

Linear Momentum:

 

There are two types of collisions: elastic and inelastic. However, in either type of collision, momentum is always conserved. What is momentum? When there is a moving object, its momentum is the product of its mass and velocity. So, in a collision, the sum of the momentum of both objects before the collision should be equal to the sum of the momentum of both objects after the collision. Or m1v1i + m2v2i = m1v1f + m2vf.  This law holds true though only if no external force acts upon the system, and in this case there is. It's called friction.

 

 

                                  

 Friction:

 

Friction is the resistive force between two surfaces in contact. Knowing that there is a resistive force on the pool table is a must. In fact, without friction, there'd be no pool. When you hit the balls they would never stop moving unless they collide with another ball that has a force exactly equal and opposite to it. Actually, you wouldn't even be able to stand on the floor stably enough to hit the billiards in the first place. So, with the existence of friction, one must be able to estimate how much it resists the forces we place on the billiards.

 

There are also two different types of friction: static friction and kinetic friction. Static friction is the force that keeps stationary objects in place and kinetic friction is the friction of moving objects. The object of the game is to get the billiards in the pockets and to do so, one must know how to control the movement of the billiards. So, understanding how to overcome and manipulate the force of friction is the key. One way of doing so is understanding kinetic energy. Well, what is kinetic energy? Let's find out together!

 

 Kinetic Energy:

 

In complicated mumbo jumbo, the kinetic energy of a moving object is equal to the product of one-half of its mass and velocity squared (1/2mv2). Delicate control of the kinetic energy of the billiards is what a player needs to master. Not too much and not too little. Knowing that you can only control the velocity (masses of the billiards are fixed), that means you have to control the velocity to control the kinetic energy.

 

Torque:

 

Torque is basically rotational force. It is the product of the radius, force applied, and sin(θ). For any given radius and force, to yield the maximum torque, the ball must be hit 90º (perpendicular) between the radius and the force applied. This is because sin(90º) = 1 which is the maximum possible number for a sin value.  Values less than 90º would make the total torque smaller. Also, there is the obvious that a lesser force or a smaller radius would make the total torque less.