TL;DR:
A free-body diagram shows one object and every force on it, as arrows from the object, each labelled with what exerts it.
Draw directions clearly and keep the components off the diagram itself. Put them in a separate sketch if you need them.
Check the current course and exam description for how diagrams are used in scoring.
A block slides down a ramp that has friction. Before you write a single equation, draw the forces on it. The diagram is not decoration: it is where you decide what the problem contains, and if it is wrong, every equation after it is wrong too.
A free-body diagram is also something a reader can mark quickly. If your arrows, labels and directions are clear, they can see you understand the physics even when your arithmetic slips.
What counts as a good diagram
Only one object, drawn as a dot or a small box.
Only forces acting on that object, not forces it exerts on others.
One arrow per force, starting at the object, in the direction of the force.
Each arrow labelled with the force and what exerts it, such as "normal force by the incline".
No acceleration arrow, and no forces made up to explain motion, such as "force of motion".
Arrow lengths should roughly show relative size. If the block is at rest or moving at constant velocity, the arrows should balance.
Check the current course and exam description on the College Board site for what is expected in a diagram on the exam. Details of scoring change.
The method
Isolate the object: Decide what you are drawing the forces on. Draw it alone.
Ask what touches it, and what acts at a distance: Contact forces: normal, friction, tension, applied. At a distance: gravity.
Draw each arrow from the object: Point it where the force acts. Label it with the force and the source.
Mark a coordinate system separately: Choose axes, often along the incline and perpendicular to it. Do this beside the diagram.
Only then write equations: Resolve forces into components in your equations, not on the diagram.
Worked example: a block sliding down an incline with friction
A 2.0 kg block slides down a 30° incline. The coefficient of kinetic friction is 0.20. Use g = 9.8 m/s². Find its acceleration.
The diagram. Draw the block on a slope. There are exactly three forces:
Force | Exerted by | Direction |
|---|---|---|
Weight, | Earth | Straight down, toward the centre of the Earth |
Normal force, | Incline | Perpendicular to the surface, away from it |
Kinetic friction, | Incline | Along the surface, up the slope (opposing the sliding) |
Do not draw mg cos θ or mg sin θ on the diagram. They are not forces. They are the components of the weight, and drawing them as extra arrows double counts the weight. Put them in your equations.
The equations. Take the x-axis down the slope and the y-axis perpendicular to it.
Perpendicular direction, no acceleration:
N = mg cos θ = 2.0 × 9.8 × cos 30° = 19.6 × 0.866 = 17.0 N.Friction:
f = μN = 0.20 × 17.0 = 3.4 N.Along the slope:
mg sin θ − f = ma, so19.6 × 0.5 − 3.4 = 6.4 N.Acceleration:
a = 6.4 / 2.0 = 3.2 m/s²down the slope.
Check. The general result is a = g(sin θ − μ cos θ) = 9.8 × (0.5 − 0.20 × 0.866) = 9.8 × 0.327 = 3.2 m/s². Same answer. It is also less than the frictionless value g sin θ = 4.9 m/s², which makes sense, because friction opposes the motion.
When the object is at rest
A diagram for an object that is not accelerating must show balanced forces. Take a 2.0 kg book on a table: weight mg = 2.0 × 9.8 = 19.6 N down, and a normal force from the table of 19.6 N up. The arrows should be the same length. If you draw them unequal, you are claiming the book accelerates. This quick check catches many errors.
The same idea applies to a block on an incline at constant speed: the force down the slope must equal friction up the slope. If your arrows do not balance in a case where the object is not accelerating, something is missing or mislabelled.
Why sources matter
Labelling each force with what exerts it is not paperwork. It forces you to check that every force has a real source touching or acting on the object. If you cannot name the source, the force probably does not exist. "Force of motion" and "force of the push" after the push has ended are the usual culprits. The force you will meet most often that acts without touching is gravity.
Common diagram errors
Drawing a force of the block on the incline instead of the incline on the block.
Adding an arrow for the motion or acceleration.
Drawing weight perpendicular to the slope. Weight is always straight down.
Leaving out labels, so a reader cannot tell the normal force from a tension.
Pointing friction down the slope for a block sliding down. Friction opposes the sliding, so it points up the slope.
Your plan for this week
Draw diagrams for five situations: a book on a table, a hanging sign, a block pulled at an angle, a block on an incline, an elevator accelerating up.
For each, name the source of every arrow.
Check that arrows balance when the object is not accelerating.
Then solve one fully, using components in the equations.
Frequently asked questions
Should I draw components when I solve?
Put them in your equations or a separate sketch. Keep the free-body diagram itself to the actual forces.
What about air resistance?
Include it only if the problem says to. Otherwise ignore it and say so.
Get started
