# What is a free body diagram

1. Jul 24, 2014

### Greg Bernhardt

Definition/Summary

A free-body diagram is a diagram of all the contact and non-contact forces acting directly on a body (in a non-inertial frame, that includes "fictitious" forces).

Indirect forces (such as the weight of a different body), and internal forces, should not be shown.

Centripetal force should not be shown (see below).

When a body is made of smaller bodies, many free body diagrams may be drawn.

A free-body diagram is used as a visual tool to help solve static and dynamic problems. Rules for drawing and using one are outlined below.

Equations

Newton's Second Law:

$$\sum\vec{F}=m\vec{a}$$

Newton's Second Law for Torque:

$$\sum\vec{\tau}=\sum\vec{r}\times\vec{F}=I\vec{\alpha}$$

Extended explanation

Procedure For Making and Using a Free-Body Diagram:

1) Set up a coordinate system.

2) Draw the body at the origin leaving out all things connected to the body (ropes, pulleys, etc.).

3) Draw all forces acting on the body (contact and non-contact forces) as vectors in the coordinate system.

4) Do not include forces which are not acting on the body.

5) Use the diagram, along with Newton's Second Law and the kinematic equations, to solve for the unknown.

Weight and reaction forces:

The weight of a body acts only on that body, not on any body underneath it.

The reaction force from an upper body on a lower body should be shown. It may be equal to the weight, but often it is not!

When one body rests on top of another, three free body diagrams may be drawn: one for the upper body, one for the lower body, and one for both bodies as a single unit.

The diagram for the lower body must not contain forces on the upper body (such as its weight, mg), but must contain forces on it from the upper body (such as the normal force, or friction).

Centripetal force and acceleration:

In a free body diagram, centripetal force should never be mentioned by name (it should be called "tension" "friction" etc), and should not be shown at all if it is only the component of a force or forces.

In a free body diagram in an inertial frame, centripetal acceleration should be shown by a different sort of arrow (doubled or squiggly), completely separate from the body it relates to.

For example, the inertial frame free body diagram for a mass suspended by string and rotating in a horizontal circle should show the mass itself with two ordinary arrows leaving it, one down and one along the string. Underneath or to the side, a squiggly arrow may be drawn indicating the centripetal acceleration.

"Fictitious" forces (including centrifugal force):

In a free body diagram in a non-inertial frame, "fictitious" forces (such as centrifugal and Coriolis force) should be shown exactly like "real" forces.

For example, the rotating frame free body diagram for a mass suspended by string and rotating in a horizontal circle should show the mass itself with three ordinary arrows leaving it, one down, one along the string, and one horizontally outward labelled "centrifugal force". Centripetal acceleration is not relevant in this case, and should not be shown.

For example, the car frame free body diagram for a body in a uniformly accelerating car should show an arrow leaving the body "backward" depicting a "fictitious" force equal to the mass of the body times the acceleration of the car.

"Straightening" a bent one-dimensional system:

A number of bodies joined together linearly (by inextensible string or by contact), with constant relative distances, may be treated as a single body, with all internal forces (such as tension or reaction forces) ignored.

Even if the string is bent, a free body diagram may sometimes still be used, drawn as if the bend was straightened out … for example, a string horizontally joining bodies on a table, then going over a pulley and joining bodies hanging vertically may be treated as entirely horizontal, provided the weight of the hanging bodies is shown horizontally (instead of vertically).

* This entry is from our old Library feature. If you know who wrote it, please let us know so we can attribute a writer. Thanks!

2. Oct 7, 2015

### EternusVia

Hello, thank you for your post. Where do moments fit into this? Is a moment the same as a torque? Should they be shown in a free body diagram?

3. Oct 7, 2015

### Maylis

Moment and torque are synonymous. Although there are a few types of "moments", in the context you are using it, they are equivalent.

4. Oct 7, 2015

### EternusVia

Do people normally draw torque in a free body diagram as a curved arrow?

5. Oct 7, 2015

### Maylis

Yes, that is the normal convention.

6. Oct 8, 2015

### EternusVia

Perfect, thank you!