Free body diagram

Free body diagram

A free body diagram is a pictorial representation often used by physicists and engineers to analyze the forces acting on a free body. A free body diagram shows all contact and non-contact forces acting on the body. Drawing such a diagram can aid in solving for the unknown forces or the equations of motion of the body. Creating a free body diagram can make it easier to understand the forces, and moments, in relation to one another and suggest the proper concepts to apply in order to find the solution to a problem. The diagrams are also used as a conceptual device to help identify the internal forces—for example, shear forces and bending moments in beams—which are developed within structures.


A free body diagram consists primarily of a sketch of the body in question and arrows representing the forces applied to it. The selection of the body to sketch may be the first important decision in the problem solving process. For example, to find the forces on the pivot joint of a simple pair of pliers, it is helpful to draw a free body diagram of just one of the two pieces, not the entire system, replacing the second half with the forces it would apply to the first half.

What is included

The sketch of the free body need include only as much detail as necessary. Often a simple outline is sufficient. Depending on the analysis to be performed and the model being employed, just a single point may be the most appropriate.

All external contacts, constraints, and body forces are indicated by vector arrows labeled with appropriate descriptions. The arrows show the direction and magnitude of the various forces. To the extent possible or practical, the arrows should indicate the point of application of the force they represent.

Only the forces acting on the object are included. These may include forces such as friction, gravity, normal force, drag, or simply contact force due to pushing. When in a non-inertial reference frame, fictitious forces, such as centrifugal force may be appropriate.

A coordinate system is usually included, according to convenience. This may make defining the vectors simpler when writing the equations of motion. The x direction might be chosen to point down the ramp in an inclined plane problem, for example. In that case the friction force only has an x component, and the normal force only has a y component. The force of gravity will still have components in both the x and y direction: mgsin(theta) in the x and mgcos(theta) in the y, where theta is the angle between the ramp and the horizontal.

What is excluded

All external contacts and constraints are left out and replaced with force arrows as described above.

Forces which the free body applies to other objects are not included. For example, if a ball rests on a table, the ball applies a force to the table, and the table applies an equal and opposite force to the ball. The FBD of the ball only includes the force that the table causes on the ball.

Internal forces, forces between varies parts that make up the system that is being treated as a single body, are omitted. For example, if an entire truss is being analyzed to find the reaction forces at the supports, the forces between the individual truss members are not included.

Any velocity or acceleration is left out. These may be indicated instead on a companion diagram, called "Kinetic diagrams", "Inertial response diagrams", or the equivalent, depending on the author.


The free body diagram reflects the assumption and simplifications made in order to analyze the system. If the body in question is a satellite in orbit for example, and all that is required is to find its velocity, then a single point may be the best representation. On the other hand, the brake dive of a motorcycle cannot be found from a single point, and a sketch with finite dimensions is required.

Force vectors must be carefully located and labeled to avoid assumptions that presuppose a result. For example, in the accompanying diagram of a block on a ramp, the exact location of the resulting normal force of the ramp on the block can only be found after analyzing the motion or by assuming equilibrium.

Other simplifying assumptions that may be considered include two-force members and three-force members.

Engineers (and now you) often make simple, though still perfectly good, sketches called Free Body Diagrams to show the position of all the forces acting on an object. They get their name from the fact that they have been cut free from their surroundings, allowing a close examination of the forces acting on them. In our example at right, we've broken down the forces on a hanging obelisk (don't ask for an explanation, for the idea or the picture) to three simple ones: gravity pulling it down and the two ropes keeping it up. However, all forces are represented the same in the free body diagram. By simplifying the forces like this, it becomes possible to solve a system using math, which we'll explore later in Calculating Equilibrium.

A free-body diagram is a sketch of an object of interest with all the surrounding objects stripped away and all of the forces acting on the body shown. The drawing of a free-body diagram is an important step in the solving of mechanics problems since it helps to visualize all the forces acting on a single object. The net external force acting on the object must be obtained in order to apply Newton's Second Law to the motion of the object.
A free-body diagram or isolated-body diagram is useful in problems involving equilibrium of forces.

Free-body diagrams are useful for setting up standard mechanics problems.