Converting Momentum to Kinetic Energy

When converting one mathematical concept to another it is important to keep two things in mind.

1. Are all of the variables represented in both of the concepts. If all the variables aren't represented is there away to substitute one variable for another.

2. Are there vectors involved? how do you keep track of direction in the other mathematical concept?

Example: Converting momentum to kinetic energy

1. In the case of kinetic energy and momentum mass and velocity is in both concepts, with no additional variables floating around.

2. Here is the really problem, momentum is a vector while energy is a scalar so how do you deal with direction? In the case of momentum, positive and negative values refer to positive and negative directions. Destroy that information and you have a scalar, so the first step is to square momentum (turning all negative values positive)