A free body diagram is a simplified sketch that shows one chosen object as a dot or box, with every external force acting on it drawn as a labelled arrow. It strips away the surroundings, so the vector sum of those arrows gives the net force — which equals mass times acceleration.
You already do this without noticing. Push a stalled car and you feel exactly three things that matter: your push, the ground dragging back, and the car’s stubborn weight pressing down. Your brain quietly discards the paint, the passengers, the shopping in the boot.
A free body diagram is that instinct, made rigorous. Get it right and a page of confusing physics collapses into two short equations. Get it wrong — one stray arrow, one missing contact — and every number after it is wrong too.
What Is a Free Body Diagram?
A free body diagram is a drawing of a single object showing only the external forces acting on it, with each force drawn as an arrow starting at the object. Nothing else appears: no surfaces, no ropes, no neighbouring blocks.
The word free is doing real work here. You are freeing the body from its surroundings, then replacing every removed contact with the force it was exerting. The floor vanishes and becomes an upward arrow. The rope vanishes and becomes a pull along its old direction.
Why bother? Because forces obey vector arithmetic, and vector arithmetic needs a clean list. As soon as the picture contains a wall, a pulley and three blocks, you cannot tell which forces belong to which object.
One body, one diagram
This is the rule beginners break most often. If a problem has two blocks, it has two free body diagrams — never one crowded picture with arrows going everywhere.
The payoff is that each diagram gives you its own equation. Two diagrams, two equations, two unknowns: the system solves.
The Free Body Diagram Formula
Every free body diagram exists to feed one equation — Newton’s second law, applied separately to each axis.
In practice you never use it in that vector form. You split it the moment you have chosen axes:
- ΣF — the net force, the vector sum of every arrow on the diagram, in newtons (N)
- ΣFx, ΣFy — the net force along the x and y axes, in newtons (N)
- m — the mass of the body you isolated, in kilograms (kg)
- a — the acceleration of that body, in metres per second squared (m/s²)
- ax, ay — the components of that acceleration along each axis, in m/s²
Two details decide whether your answer is right. First, ΣF means sum: forces pointing along the negative axis enter with a minus sign. Second, m is the mass of the isolated body only — not the whole system, unless you deliberately drew the whole system as one body.
Once the diagram is done and the components are listed, the arithmetic is mechanical, and you can check any single-force result against our Newton’s Second Law Calculator before committing it to a full solution.
How to Draw a Free Body Diagram in 5 Steps
Draw a free body diagram by isolating one body, reducing it to a dot, adding one arrow for gravity and one for each physical contact, labelling every arrow, then choosing axes and resolving. These five steps work for every mechanics problem you will meet.
Step 1 — Pick one body and circle it
Decide what you are analysing before you draw anything. Literally draw a loop around it in the original picture — this single habit prevents most stray-arrow errors.
Step 2 — Redraw it as a dot
Shape and size rarely matter for force problems, so shrink the object to a point and put that point at the origin of your axes. All arrows will now start from this dot.
Step 3 — Add gravity, then walk the boundary
Weight always acts, so draw it first, straight down. Then trace around the object’s surface and ask at every point: is something touching me here? Each contact earns exactly one force — or two if the surface is rough, since a rough surface gives both a normal force and friction.
Step 4 — Draw and label every arrow
Each arrow starts at the dot and points the way the force actually acts. Length should roughly reflect size: if you know the object is not sinking through the floor, draw N about as long as W.
Label with symbols, not numbers — N, W, T, f. Numbers come later, and symbols keep the algebra honest.
Step 5 — Choose axes, then resolve
Pick axes that put as many arrows as possible directly on an axis. Any arrow left at an angle gets split into components, and only then do you write ΣFx and ΣFy.
The five steps in action: a real crate on a rough floor becomes four labelled arrows on a point.
The 4 Forces That Never Belong on a Free Body Diagram
Four forces show up on student diagrams again and again, and none of them is real in this context. Learning to spot them is faster than learning any formula.
1. The “force of motion”
A ball rolling across a floor has no forward arrow. It is moving because nothing has stopped it yet — motion needs no cause, only changes in motion do. Velocity is not a force and never earns an arrow.
The phantom “force of motion” is the most common wrong arrow in introductory mechanics.
2. Centrifugal force
Swing a conker on a string and the string pulls the conker inward, toward your hand. There is no outward arrow on the conker. The outward feeling belongs to your hand, which the conker really does pull.
3. The third-law partner
Newton’s third law pairs always act on different bodies, so they can never appear on the same diagram. The book pushes down on the table; the table pushes up on the book. Only the second one belongs on the book’s diagram.
4. The net force itself
ΣF and ma are results, not inputs. Drawing an extra arrow labelled “ma” double-counts forces you have already drawn, and the equation collapses.
Common Forces and Which Way They Point
Most diagrams are built from the same short list of forces. This table is the one to memorise — direction first, magnitude second.
| Force | Symbol | Direction of the arrow | Magnitude |
|---|---|---|---|
| Weight | W | Always vertically down, whatever the surface is doing | mg, with g ≈ 9.81 m/s² |
| Normal force | N | Perpendicular to the contact surface, pushing away from it | Whatever balances the perpendicular direction — not automatically mg |
| Friction | f | Along the surface, opposing sliding or the tendency to slide | Kinetic: μkN. Static: anything up to μsN |
| Tension | T | Along the rope, away from the body — ropes pull, never push | Usually an unknown you solve for |
| Applied force | F | Whichever way the push or pull acts | Given in the problem |
| Drag | Fd | Directly opposite the velocity through the fluid | Grows with speed |
| Spring force | Fs | Opposite the stretch or compression, back toward natural length | kx |
Notice how many entries describe direction by a rule rather than a picture. That is deliberate — the rules survive when the geometry gets strange, and a good grasp of the different types of forces in physics is what lets you populate a diagram quickly.
Free Body Diagrams on an Inclined Plane
On an inclined plane, tilt your axes so x runs along the slope and y runs perpendicular to it, then resolve the weight into mg sin θ down the slope and mg cos θ into the surface. This one choice removes almost all the algebra.
Why does it help so much? Because on a slope, N and f already lie along the tilted axes. Leave the axes horizontal and you must split three forces instead of one.
Tilting the axes on an incline turns a three-force resolution into a one-force resolution.
The perpendicular equation is where the insight hides. Since the block does not accelerate into the ramp, N = mg cos θ — smaller than the weight, and smaller still as the slope steepens.
That is why friction fades on a steep ramp: friction depends on N, and N is shrinking exactly when gravity’s pull along the slope is growing. Our full guide to inclined plane physics works through the sliding condition in detail.
Real-World Examples of Free Body Diagrams
These diagrams are not a classroom ritual. Every one of the situations below is solved this way in professional practice.
A lift accelerating upward
Standing in a lift, you feel heavier as it starts to rise. Your diagram has just two arrows: N up from the floor, W down. Because you accelerate upward, N must exceed W — and N is exactly what a bathroom scale reads.
A climber on a rope
A hanging climber has weight down and tension up, and while they hang still the two are equal. The moment they are lowered with acceleration, tension drops below weight — which is why a controlled lower feels gentler than a sudden stop.
A plane in level flight
Four arrows: lift up, weight down, thrust forward, drag back. Cruising at constant speed and height means both pairs cancel exactly, and the whole of aerodynamics starts from that balance.
A crate on a lorry that brakes
Here friction is the only horizontal force on the crate, and it must point backward to slow the crate with the lorry. If the required friction exceeds μsN, the crate slides forward — the calculation that sets load-securing rules.
A parked car on a hill
Weight down, normal force out of the slope, friction up the slope, and nothing accelerating. Engineers size handbrakes by asking whether friction alone can supply mg sin θ.
Common Misconceptions About Free Body Diagrams
“The normal force always equals the weight”
It equals the weight only in the narrow case of a flat surface with nothing else acting vertically. Tilt the surface, add a rope pulled at an angle, or accelerate vertically, and N changes immediately.
This is the single most expensive mistake in force problems, because friction depends on N. Get N wrong and every friction value downstream is wrong.
“Static friction equals μsN”
That product is the maximum static friction, not its actual value. Static friction is whatever it needs to be to prevent sliding, right up until it cannot manage any more.
A book resting on a gentle slope needs only a few newtons of friction, even if the surface could supply thirty. Read more in our guide to what friction is and how it works.
“If it’s moving, something must be pushing it”
Constant velocity means zero acceleration, which means the forces balance exactly. A car at a steady 70 mph has thrust and drag in perfect opposition — it is a case of equilibrium, not of a winning force.
“Two cables each carry half the weight”
Only if both cables hang vertically. Angle them and each carries more than half, because only the vertical component of each tension does the lifting — a point Worked Problem 4 below makes concrete.
How Free Body Diagrams Fit With Newton’s Laws
Each of Newton’s three laws of motion maps onto a different part of the diagram, which is why the technique feels natural once it clicks.
- First law — tells you what a balanced diagram means: at rest or at constant velocity, every arrow cancels.
- Second law — turns an unbalanced diagram into numbers through ΣF = ma.
- Third law — tells you which arrows are forbidden, since a reaction force lives on the other body’s diagram.
The diagram is also where vector skills earn their keep. Forces are vectors, so direction carries as much information as size, and confidence with vector and scalar quantities is what makes resolving components feel routine.
One more connection worth holding on to: ropes and pulleys are just tension arrows with a geometric constraint attached. Our guide to tension force covers the ideal-rope assumptions that let you carry one symbol T across two diagrams.
Worked Problems
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Frequently Asked Questions
What is a free body diagram in simple terms?
What forces should be included in a free body diagram?
Do you include acceleration in a free body diagram?
Why is the normal force not always equal to the weight?
How do you draw a free body diagram for two connected objects?
What is the difference between a free body diagram and a force diagram?
Free body diagrams reward practice more than memorisation. Draw one for the next five problems you meet — even the easy ones — and the harder ones stop looking hard. For a rigorous parallel treatment, the OpenStax University Physics section on drawing free-body diagrams works through coupled blocks in detail, and MIT OpenCourseWare’s 8.01 Week 2 materials include filmed worked examples on stacked blocks and pulley systems.
