The free body diagrams that you will create are math equations in picture form. By following some simple rules, you can typically create two equations for each free body diagram. These rules are not absolute. But they are designed to make the equations shorter and simpler.

Identify a coordinate system that has x and y being perpendicular to each other.

Choose a coordinate system that is parallel and perpendicular to the net force. If the net force equals zero , then make the coordinate system parallel to the surface.

To create an equation add up all the vectors that are pointing in the same line. With an x and y coordinate system, you will two lines perpendicular to each other.

All the vectors that point in one direction are positive. Vectors that point in the opposite direction are negative. You choose what is positive and negative.

The math is easier and the questions are generally shorter if the net acceleration's direction is made to be positive.

These two examples will show how these rules work.

Example 1: Creating a Pair of Equations from a Free Body Diagram

This YouTube video can be seen here, http://youtu.be/vMeL-WxQ9wg

Example 2: Creating a Pair of Equations from Another Free Body Diagram