What is a free body diagram and how do you draw it correctly for equilibrium problems?

In one line

A free body diagram (FBD) is a sketch of the body cut free from its surroundings, showing every external force and reaction acting on it.

Explained simply

Imagine you could lift a book off the table and replace the table with arrows showing how hard it pushed. That sketch, with the book's weight arrow and the table's push arrow, is a free body diagram. It turns a messy picture into a clean list of forces.

Technically, an FBD isolates a body (or a joint, or a part of a system) and replaces every support, contact, string and connection by the force or moment it exerts.

How it works

1. Decide which body to isolate (one block, one sphere, the whole beam).
2. Draw its outline alone, without the supports or other bodies.
3. Add known loads: weight W at the centre of gravity, applied forces and couples with their actual directions.
4. Replace each support with its reactions: smooth surface: normal force perpendicular to the surface; string: tension away from the body along the string; roller: one reaction perpendicular to the surface; hinge: \( H \) and \( V \); fixed: \( H \), \( V \) and a moment.
5. For rough surfaces add friction along the surface, opposing impending motion.
6. Mark dimensions and angles needed for moments.
7. For connected bodies, draw a separate FBD for each, with equal and opposite contact forces (Newton's third law).

Quick example

A sphere of weight W resting in a V-shaped smooth groove: its FBD is a circle with W downward through the centre and two normal reactions, each perpendicular to the groove face and passing through the centre. Three concurrent forces, so Lami's theorem applies.

Common mistakes

• Including internal forces between parts of the same body.
• Drawing the normal reaction vertical on an inclined surface; it must be perpendicular to the contact surface.
• Showing a string pushing the body; strings can only pull.

How MU asks it

A 3-mark part: 'What is a free body diagram? Draw the FBD of ...'. It also carries method marks in every equilibrium and friction numerical. Always draw a separate, labelled FBD before writing any equation; examiners deduct marks when it is missing.