# Free-body diagrams

A free-body diagram is a drawing of all external forces acting on a body. It is a useful tool to analyze many problems related to forces and motion. To construct a free-body diagram, follow these steps:

Step 1: Draw a simplified diagram of the object (it might be as simple as a square or circle) and draw a point where its center of mass would be. We will draw all forces from this point.

Step 2: Draw two perpendicular lines crossing at the point you drew in the first step. These will be the axes of a cartesian system of reference. You will usually draw one of these lines in the left-right direction and another in the up-down direction, but that is only one way to do it. Another possibility, in the case of having oblique forces, is drawing these axes to align with as many forces as possible. The choice of axes depends on the particularities of each problem, all of them are equivalent, but an ingenious choice can save much computation.

Step 3: Draw each external force that acts on the body as a vector, placing their tail on the point you drew at the center of mass. Pay attention to their direction: forces pushing down should be represented by a vector pointing down, forces pushing in an oblique direction should be represented by an oblique vector in a direction plausibly similar to that of the force. For clarity, stronger forces can be represented as longer arrows. The net force is not considered an external force and shouldn’t be drawn at this stage.

Step 4: If you have forces that don’t align with the axes you drew in the second step, decompose that forces along the axes.

Additional Step: If there are two or more objects or bodies in the problem, draw a separate free-body diagram for each object.

In most cases, it is not necessary to draw each force vector to its perfectly accurate magnitude and direction (especially because in some cases they are unknown). Instead, a free-body diagram is most useful as a qualitative technique to organize information that you will use to perform quantitative calculations later.

Figure 1: Steps to create free-body diagrams.