The ultimate purpose of a free body diagram is to develop a math model to answer a question. This math model will look like a set a equations. In order to be successful at this, the you must know when each force in the previous section applies to a problem and in which direction is points. Below is summary.
To develop the math model a set of equations will be created. The set of equations varies from problem to problem.
To create a equation the force will be added in one or more directions. This is called summing and the math symbol that is used to indicate this is the capital Greek letter sigma, "Σ." If the forces are going to be summed in the x-direction, then the summation looks like the one shown below.
To indicate that the forces are added up in the y-direction the symbol below is used.
The next step is to show what these summed forces will equal. They will either equal zero or a net force. If the body is moving at a constant velocity then the summation will equal zero. (Recall that a body at rest is moving at a constant velocity of zero.) If the body is accelerating, then the summation will equal Fnet or as it is sometimes written, manet.
These summations do not need to be the same. One may be equal to zero and the other may be equal to manet.
by Tony Wayne ...(If you are a teacher, please feel free to use these resources in your teaching.)