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MechanicalMechanics

Free-Body Diagrams

The setup tool behind almost every statics and dynamics problem

Difficulty

Beginner

Read time

7 min

Review status

Needs review

Concept sketch

Isolate the body, then draw external actions

Typical block on an incline

WNfrictionapplied pull1. Select one body2. Replace contacts3. Write equations from arrows

Overview

A free-body diagram isolates one body or system and shows only the external forces and moments acting on it. It turns a physical situation into equations, making it the bridge between the problem statement and equilibrium or motion analysis.

How to read it

  • Identify the isolated body first; do not mix forces from different bodies.
  • Check that every arrow represents an external force or moment acting on that body.
  • Look for support reactions, applied loads, weight, friction, tension, and normal forces.
  • Match each arrow to an equation term before solving.

When to use it

  • Before writing equilibrium equations in statics.
  • Before applying Newton's second law in dynamics.
  • When solving support reactions, cable tensions, friction, or connected-body systems.
  • When a problem feels confusing because too many forces are shown in the original sketch.

What an FBD represents

A free-body diagram is not a picture of the whole scene. It is a simplified model of one selected body after it has been separated from its surroundings. Every contact, support, cable, weight, spring, or applied load that acts on that body becomes a force or moment on the diagram.

Choosing the body

The most important decision is what to isolate. For a single block, isolate the block. For a frame, truss member, beam segment, pulley, or connected system, choose the body that exposes the unknowns you need. A poor choice can make the algebra harder even if the physics is unchanged.

Replacing supports and contacts

Supports are replaced by reaction forces and moments. A pin usually gives two force components, a roller gives one normal reaction, a fixed support gives force components plus a moment, and a cable gives tension along its direction. Contact forces are drawn normal to the contact surface unless friction is included.

Turning the diagram into equations

After the diagram is complete, apply the correct model: static equilibrium for bodies at rest or constant velocity, or Newton's second law for accelerating bodies. The equations should come from the arrows on the diagram, not from memory alone.

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