Free-body diagrams
Key idea: A free-body diagram shows every force acting on one body, with labelled arrows for direction and size. Find each force's source; motion itself is not a force.
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Guided lessons · coming soon
Guided lesson
Guided steps
- Draw only interaction forces acting on the chosen body.
- Name the Earth and table forces on the book.
- Choose the picture and build its forces, sources and directions.
- Remove the resultant arrow and explain the double counting.
- Name the forces on the rising ball after release.
- Draw the two vertical interactions; upward motion alone does not establish which arrow is larger.
- Build the skydiver’s forces on one vertical line, or draw on paper. Check the interaction and direction for each arrow.
- Draw only the forces on the boy, then identify the separate force received by the scale.
- Draw the jumper’s forces on paper and compare their sources.
- Remove the motion arrow and name the actual forces.
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ContinueBefore you can say how an object will move, you need to know every force acting on it, and only those. A free-body diagram picks out one body and draws each force on it as a labelled arrow. It is the first step in every dynamics problem, because a missing force, or a force that acts on something else, makes every later answer wrong. The forces themselves, weight, normal force, tension, friction and air resistance, come from force and pressure.
Draw the forces on one body
A free-body diagram shows one body on its own, drawn as a box or a dot, with every force that acts on it. Each force is an arrow that:
- starts on the body;
- points in the direction of the force;
- is labelled with the name of the force, and its size if you know it.
If you know the sizes, draw a larger force with a longer arrow.
The diagram shows only the forces acting on that body. It leaves out the forces the body exerts on other things. Later you add these forces to find their resultant, so a missing force or an extra one gives a wrong answer.
Every force comes from an interaction
Each force on the body is exerted by something else. To find the forces, list what acts on the body: Earth, and each thing that touches it.
| What acts on the body | Force on the body | Direction |
|---|---|---|
| Earth | weight, W | vertically downward |
| a surface it rests or presses on | normal force, N | at right angles to the surface, pushing away from it |
| a string, rope or cable | tension, T | along the string, pulling away from the body |
| a rough surface it slides or tends to slide on | friction | along the surface, opposing the sliding or the tendency to slide |
| air or water it moves through | air or water resistance | opposite to its motion through the air or water |
| a hand, the road on driven tyres, or expelled rocket gas | push, pull, driving force or thrust | the direction of the push or pull |
Weight is the only force here that acts without contact. Every other force needs something touching the body.
Four steps for any free-body diagram
- Name the body. Draw it as a box or a dot.
- List the interactions. Start with Earth (weight). Then go round the body and name everything that touches it.
- Draw one arrow for each force. Start each arrow on the body, point it in the direction of the force and label it.
- Check the diagram. Remove any force the body exerts on something else, any arrow that shows motion, and any extra arrow for the resultant force.
Worked example 1
A book at rest on a table
Problem
Draw the free-body diagram of a book at rest on a table.
Show full solution
Choose the body
Method
Draw forces on the book only.Reason
A free-body diagram shows forces acting on one body.Working
Answer
Body: the book
Name each force on it
Method
List what pulls or touches the book.Reason
Each force comes from an interaction: Earth pulls it, and the table touches it.Working
Answer
Weight W, downward; normal force N, upward at right angles to the table top
Draw the arrows
Method
Draw W down and N up from the book.Reason
The book is at rest, so the forces balance and the arrows have the same length.Working
Answer
Two equal arrows: W down, N up
Leave out forces on other bodies
Working
Answer
The book’s push on the table acts on the table, so it is not on the book’s diagram.
Check your understanding 1 A hanging picture
A picture hangs at rest from a single vertical string. Name each force on the picture, the object that exerts it and its direction.
Build the diagram here or draw on paper and compare with the answer below. This builder checks the body, force names, sources and directions; arrow lengths are schematic.
Show answer
Weight, exerted by Earth, vertically downward. Tension, exerted by the string, upward along the string.
Check your understanding 2 One arrow too many
A crate is lowered on a rope at a steady speed. A student draws its free-body diagram with three arrows: weight downward, tension upward, and “resultant force” downward. Which arrow is wrong? Explain.
Show answer
The “resultant force” arrow is wrong. The resultant is what the weight and the tension add up to, not another force: nothing else pulls or touches the crate to exert it. The crate’s diagram has only weight downward and tension from the rope upward.
Motion is not a force. A ball that is still rising after it leaves your hand has no upward force on it: the hand no longer touches it, so it no longer pushes. The ball keeps moving up only because it was already moving.
Check your understanding 3
A ball has left a player’s hand and is still rising. Air resistance is not negligible. Name each force on the ball and its direction.
Show answer
Two forces act on the ball, both downward: its weight (Earth pulls it down) and air resistance (the ball moves up through the air, so the air resistance acts down). There is no upward force.
In G2, all the forces act along one line
In this course every free-body diagram has all its forces along one line. Most are vertical: something hanging, lifted, resting or falling.
Worked example 2
A lift moving upward
Problem
A lift hangs from its cable and moves upward. Air resistance is negligible. Draw the lift’s free-body diagram.
Show full solution
Choose the body
Method
Draw forces on the lift only.Reason
The diagram shows the forces acting on one body.Working
Answer
Body: the lift
Name each force on it
Method
List what pulls or touches the lift.Reason
Earth pulls it, and the only thing touching it is the cable.Working
Answer
Weight W, downward; tension T, upward along the cable
Draw the arrows
Method
Draw T up and W down on one vertical line.Reason
Both forces act along the vertical line of the cable.Working
Answer
T up, W down
Check for a motion arrow
Working
Answer
There is no extra arrow for “moving up”: motion does not add a force. How T compares with W depends on whether the lift speeds up, slows down or moves steadily, which you work out in the next two lessons.
Check your understanding 4
A skydiver falls before opening the parachute. Air resistance is not negligible. Build the skydiver’s free-body diagram below, labelling the forces and their sources, or draw on paper and compare with the answer. Hint: what touches the skydiver while falling?
Build the diagram here or draw on paper and compare with the answer below. This builder checks the body, force names, sources and directions; arrow lengths are schematic.
Show answer
Only the air touches the skydiver, and Earth pulls on the skydiver. So there are two arrows on one vertical line: weight downward and air resistance upward, opposite to the downward motion. There is no separate “falling force”: the weight is the downward force.
Check your understanding 5
A boy stands still on a bathroom scale. Draw the boy’s free-body diagram on paper. Then say which force the scale’s reading is about, and why it is not on the boy’s diagram. Compare your drawing directly with the answer; use the box for the explanation or a note about a difference.
Show answer
Two arrows on one vertical line from the boy: weight downward (Earth) and the normal force upward (the scale pushes him up). The scale reads how hard the boy pushes down on it. That push acts on the scale, so it is not on the boy’s diagram.
Check your understanding 6 A bungee jumper
A bungee jumper is still moving downward after the cord has started to stretch. Air resistance is not negligible. Draw the jumper’s free-body diagram on paper and label each force and its source. Compare the drawing directly with the answer; you do not need to copy it into prose. The box is available for a short note about a difference.
Show answer
Self-review the drawing: label the jumper as the selected body, with three force arrows on one vertical line. Weight downward (from Earth), tension upward along the stretched cord (from the cord) and air resistance upward (from the air, opposing the downward motion).
Check your understanding 7 An arrow for the motion
A ball rolls to the left across a smooth, level floor, and air resistance is negligible. A student adds an arrow labelled “motion” pointing left. What should the diagram show instead?
Show answer
Only forces: weight downward and the normal force from the floor upward. Motion is not a force, so leave that arrow out: nothing pushes the ball to the left, and it keeps rolling because it was already moving.
Common mistakes
- Drawing “the book pushes the table” on the book’s diagram. That force acts on the table.
- Adding an upward “force of the throw” to a rising ball. Once the ball leaves the hand, nothing is pushing it upwards.
- Adding an arrow for the resultant force. The resultant is what the forces add up to, not another force.
- Drawing an arrow for the direction of motion. Velocity is not a force.
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Syllabus and review details
- SEC G2 Science Physics component 2027 · 2027
Physics section, PDF pages 8–23
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