Game Pigeon - Physics right in our Phones!

I apologize for the Android users in this class, as the Game Pigeon app (an app where you play games over text message) which my discussion is based upon is only available on iPhones. BUT the physics concepts we can learn from it are accessible to everyone!

One of my favorite Game Pigeon games is Pool. It is essentially a mobile version of a pool game. In one of the modes, there are vectors for the cue ball and target ball. As we know, vectors depict magnitude and direction. The concept of vectors to dictate velocity or magnitude plus direction is something we constantly use in physics class, especially when dealing with kinematics or showing forces in free body diagrams. Here is a picture from the vector mode:

The image above shows two vectors coming from the point of collision of the cue ball with the solid orange ball. The vector that points to the left is much smaller than the vector pointing nearly straight up. This is due to the adding up of vectors drawn using the tail-to-tip method. The angle 𝛳 made by the vectors will always be 90º, even as the angle at which the cue ball collides with the target ball changes. Using this knowledge of angles and vectors, one can aim and score a shot!

A second physics concept of pool is the idea of elastic collisions. The collision between billiard balls is perfectly elastic in Game Pigeon. This means there is a transfer of energy between the balls as they collide and bounce apart. The equation relating velocities of objects with elastic collisions is:

1/2m1(v1, initial)^2 = 1/2m1(v1, final)^2 + 1/2m2(v2, final)^2

And because the masses are equal, they cancel to give the equation:

(v1, initial)^2 = (v1, final)^2 + (v2)^2

These are just a couple of physics concepts that are present in a pool game, but there are tons more including rotational dynamics, frictional forces, or moments of inertia of a spinning ball.