Physics

Some of the content of this guide was modeled after a guide published by OpenStax and has been adapted for the NWP Learning Commons in March 2022. This work is licensed under a Creative Commons BY 4.0 International License.

Free Body Diagrams

Newton's three laws of motion contain all the basic principles we need to solve a wide variety of problems in mechanics. These laws are very simple in form, but the process of applying them to specific situations can pose real challenges.

Newton's first and second laws apply to a specific body. Once you have selected the body to analyze, you have to identify all the forces acting on that body.

Free-body diagrams are used to show all forces acting upon a body in a given situation. A free-body diagram shows the body itself without the surroundings, with vectors drawn to show the magnitudes and directions of all the forces applied to the body. These forces do not include the "reactionary" forces that the body puts onto its environment as described in Newton's Third Law.

Below is a base example of a free-body diagram:

• \(\vec{\textbf{F}}_{gravity}\) is the force that gravity exhibits on the body. This is also known as weight and is denoted as \({F}_{g}=mg=W\) where \(g=9.81m/s^2\) also known as the \((gravitational\,constant)\).
• \(\vec{\textbf{F}}_{normal}\) is the force that a surface exerts on a body to prevent solid objects from passing through each other.
• \(\vec{\textbf{F}}_{friction}\) is the force that resists the sliding or rolling of one solid object over another. Frictional force can be either static or kinetic and is calculated using a dimensionless coefficient of friction and the normal force.
  • \(\vec{\textbf{F}}_{fs}=\mu_s\vec{\textbf{F}}_{N}\), or
  • \(\vec{\textbf{F}}_{fk}=\mu_k\vec{\textbf{F}}_{N}\)
• \(\vec{\textbf{F}}_{applied}\) is the force that an external body is exerting on the subject body and is typically the reason for the free-body diagram in the first place.