Free-Body Diagrams

A free-body diagram shows all the forces acting on a single object. Each force is drawn as an arrow starting from the object, pointing in the direction the force acts. The length of each arrow represents the relative size of the force.

Rules for drawing

1. Identify the single object you are analysing.
2. Draw the object as a simple shape (a dot or box).
3. Draw one arrow for each force acting on the object (not forces the object exerts on other things).
4. Label each arrow with the force name and, where known, its value in newtons.
5. Make arrow lengths proportional to force size.

Example: a book on a table

Forces on the book:

• Weight (W) acting downward.
• Normal contact force (N) acting upward.

If the book is stationary, the arrows should be the same length because the forces are balanced.

Example: a car accelerating

Forces on the car:

• Engine force (driving force) acting forward.
• Friction and air resistance acting backward.
• Weight acting downward.
• Normal contact force acting upward.

The forward arrow is longer than the backward arrow because there is a net forward force causing acceleration.

Common errors and how to correct them

Including forces the object exerts on other objects. A free-body diagram shows only forces on the chosen object. The book pushes down on the table, but that force belongs on the table’s diagram, not the book’s.

Drawing weight from the bottom of the object. Weight acts through the centre of gravity. Start the weight arrow from the centre of the object.

Making all arrows the same length when forces are unbalanced. If the object is accelerating, the resultant force is non-zero, so the arrows must differ in length.

How to apply this in an exam

Examiners check that every relevant force is shown, labelled, in the correct direction, and with a proportional length. Missing a force or drawing it in the wrong direction loses marks. Start by listing every force before drawing.