Free body diagram

In the fields of physics and engineering, a free body diagram (FBD) is a vital graphical tool. It is used to visualize all the applied forces, moments, and resulting reactions acting on a specific object. By creating these diagrams, scientists can analyze how an object will behave under different conditions. The term "free body" refers to the object being singled out for analysis. This does not mean the object is unconstrained or moving freely. Instead, it means the object is treated as an isolated entity to study its response to forces and torques.

To create an effective diagram, a researcher must first choose how to model the body. There are three common ways to do this. First, the body can be modeled as a particle. This is a small symbolic blob used when rotational effects are zero or unimportant. Second, it can be modeled as a rigid extended body. In this case, the object has a shape, and rotational effects like torque are important. Third, it can be modeled as a non-rigid extended body. For these, the exact point where a force is applied becomes crucial.

Once the body is modeled, the diagram is populated with specific elements. An FBD is not a scaled drawing, but a schematic representation. It consists of a simplified version of the body, such as a dot or a box. Forces are represented by straight arrows pointing in the direction they act. Moments, which represent rotational force, are shown as curves with an arrowhead or as vectors with two arrowheads.

To make the math manageable, a reference coordinate system is always included. This allows the user to define directions, such as the x and y axes. By convention, if a force is a reaction to another force, it is shown with hash marks through the stem of the vector.

Analyzing these diagrams often involves breaking down complex forces. If a force acts at an angle to the coordinate axes, it can be rewritten as components. These components, often labeled Fx and Fy, are vectors directed along the axes.

This process helps in calculating the sum of all forces and moments. In statics, the sum of all forces and moments must equal zero for the body to be in equilibrium. If the sum is not zero, the body is in a state of dynamics. In dynamics, the resultant forces and moments cause the body to accelerate.

One powerful technique is to use the diagram to analyze internal forces. A large, complex structure can be broken into smaller parts. For example, consider a gymnast performing the iron cross on ropes. An engineer might first model the entire system of ropes and the person. They might neglect small forces like breezes or the weight of the ropes to simplify the problem. Then, they can remove the person and look only at one rope to find the force direction. They can then look only at the person's arm to find the forces at the shoulder. This allows for the calculation of internal stresses at different locations within a single physical body.

There are specific rules about what should and should not be included in an FBD. The diagram should only show the body of interest and the external forces acting upon it. It should not show the forces that the free body exerts on other objects. According to Newton's third law, these forces are equal and opposite, so including them would be confusing. Additionally, internal forces within the body itself are excluded. Constraints are also not drawn directly; instead, they are replaced by the specific forces they exert on the body. Finally, velocity and acceleration vectors are excluded from a standard FBD.

Free body diagrams are used across almost all engineering disciplines. They are essential in biomechanics, where they help study the human body, and in structural engineering, where they help design buildings. They are also fundamental in educational settings to teach classical mechanics. By using tools like the polygon of forces, researchers can even find the resultant of multiple forces graphically.

This method involves arranging force vectors as the edges of a polygon. The missing edge that completes the shape represents the resultant force. Whether used for a simple block on a ramp or a massive bridge, these diagrams turn complex physical interactions into clear, solvable mathematical problems.