A free-body diagram strips a problem down to one object and the forces acting on it. Shrink the object to a dot, draw each force as an arrow, and get the directions and rough lengths right — do that and almost every force question becomes easier to set up and solve.
📘 What you need to know
A free-body diagram shows a single object as a point (a dot) with every force acting on it drawn as an arrow.
The direction of each arrow is the direction of the force; the length is proportional to its size.
Only draw forces acting on the object — never the forces the object exerts on other things.
The common forces: weight (Fg, always down), normal (FN, perpendicular to the surface), tension (FT, along a rope away from the object), and friction / drag (Ff or Fd, opposing motion).
If the arrows cancel, the resultant force is zero (object at rest or moving at constant velocity). If they don’t, there is a resultant force.
What a free-body diagram is
When several forces act on an object, it helps to simplify the picture without losing any information. We do this by treating the object as a point particle placed at its centre of mass, then drawing each force as a vector arrow starting at that point and pointing outwards.
The length of an arrow represents the magnitude of the force.
The way it points shows the direction the force acts.
Each arrow is labelled — either with the type of force, its name, or its symbol (e.g. Fg for weight).
The object becomes a dot; each force is an arrow from that dot. The push is longer than friction, so there is a resultant force to the right.
The forces you’ll meet
Most diagrams are built from a small set of forces. Learn the symbol and the rule for the direction of each:
Weight, Fg — the gravitational pull of the planet, always pointing straight down (towards the centre of the Earth).
Normal (reaction) force, FN — the support from a surface, always perpendicular to that surface.
Tension, FT — the pull in a rope or string, acting along the rope, away from the object.
Friction, Ff — resists sliding between surfaces, acting parallel to the surface, opposite to the motion.
Drag / fluid resistance, Fd — opposes motion through a liquid or gas (air resistance is a type of drag).
Buoyancy / upthrust, Fb — the upward push from a fluid on a body in it.
Weight from massFg = mg • g ≈ 9.81 m s⁻² (downwards, on Earth)
🛠 How to draw one
Shrink the object to a single dot at its centre of mass.
Add weight first — straight down, every time.
Add any surface forces: normal perpendicular to the surface, friction along it opposing motion.
Add any ropes or strings: tension along the rope, pointing away from the object.
Add any pushes, pulls or drag, then make each arrow length roughly proportional to the size of the force.
Label every arrow with the correct symbol (Fg, FN, FT, Ff …).
Worked examples
WE 1
A box sliding down a slope
A box slides down a rough ramp. Identify the three forces acting on the box and state the direction of each.
On a slope the normal force is perpendicular to the ramp (not vertical), and friction points up the slope, against the motion.
Weight, Fgacts straight down, towards the EarthNormal force, FNacts perpendicular to the slope surfaceFriction, Ffacts up the slope, opposite to the direction of motion
WE 2
A picture frame hanging from a nail
A frame hangs from a single nail by two cords. Draw the free-body diagram and explain what its arrows tell you.
Two tension forces share the load; together they balance the weight, so the frame stays still.
Two tensions (FT) act up along each cordWeight (Fg) acts straight downthe frame is at rest, so the forces are balancedarrows form a closed triangle
WE 3
Reading a resultant off the diagram
A toy sailboat (weight 30 N) floats while being pulled to the right with a force of 35 N. The water provides 30 N of buoyancy upward and 5 N of drag to the left. Draw the diagram and find the resultant force.
Make arrow lengths roughly to scale: the 35 N pull is clearly longer than the 5 N drag, showing a resultant to the right.
Vertical: buoyancy up = weight down30 − 30 = 0 Nvertical forces are balancedHorizontal: take right as positive35 + (−5) = 30 Nresultant = 30 N to the right
Quick reference: weight Fg → down • normal FN → perpendicular to surface • tension FT → along rope, away from object • friction Ff → opposes motion • drag Fd → opposes motion through a fluid • buoyancy Fb → up.
💡 Top tips
Weight is always vertical — even on a slope, it still points straight down, never along the ramp.
Tilt your axes on a slope so they line up along and perpendicular to the surface, not horizontal and vertical.
Make lengths mean something. A bigger force should have a longer arrow; a clear resultant should look like one.
Use the standard symbols (Fg, FN, FT, Ff). Invented notation can cost you marks.
Start every arrow at the dot and point it outwards.
⚠ Common mistakes
Drawing forces the object exerts on other things. Only forces acting on the chosen object belong on its diagram.
Treating the normal force as vertical on a slope. It is perpendicular to the surface, so it tilts with the ramp.
Making every arrow the same length when the forces are clearly unequal.
Inventing a “force of motion” in the direction of travel — there is no such force on a free-body diagram.
Confusing balanced forces with a Newton’s third-law pair — equal and opposite forces on the same object are not a third-law pair.
Up next: Newton’s First Law — what a zero resultant force really means for an object, and why something can move at a steady speed with no net force on it at all.
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