IB Physics HLTopic 1 — Motion, Forces & EnergyPaper 1 & 2Point particles & force arrows~9 min read
Drawing Free-Body Diagrams
Before you can work out what an object does, you need a clear picture of what’s pushing and pulling on it. A free-body diagram is that picture: you shrink the object down to a single dot and draw every force acting on it as an arrow. Get this one skill right and the rest of the forces topic — Newton’s laws, friction, momentum — becomes a matter of reading arrows off a diagram.
📘 What you need to know
A force is a push or a pull that comes from one object interacting with another
In a free-body diagram the object is drawn as a single point particle at its centre of mass
Forces are vectors, so each one is an arrow: its length shows the size, its direction shows which way the force acts
Only forces acting on the object are drawn — never the forces the object exerts on other things
Every arrow must be labelled (name or symbol) and drawn roughly to scale
Adding the arrows as vectors gives the resultant force, which tells you how the object will move
What a free-body diagram actually is
Real objects are complicated shapes, and forces act all over them — but for working out motion, all that detail just gets in the way. So we do two things to simplify. First, we treat the object as a point particle: a single dot placed at its centre of mass. Second, we draw each force as an arrow starting from that dot. Because force is a vector, the arrow carries two pieces of information at once: how long it is tells you the magnitude, and which way it points tells you the direction.
Here’s the key move. Take a box being pushed across a rough floor. In real life it’s a solid block with friction all along its base and its weight spread through it. On a free-body diagram, all of that collapses into one dot with four arrows.
The solid box on the left becomes a single point on the right, with each force drawn as a labelled arrow. Notice the friction arrow is shorter than the applied force — the box is being pushed to the right.
The dot isn’t the object shrinking away — it’s a promise that we only care about forces, not shape. Every arrow starts at that dot and points away from it, in the direction the force pushes or pulls. If you ever find yourself drawing an arrow into the dot, flip it: forces are drawn leaving the point.
Not every object has four forces on it. Hang a bag from a rope and there are only two: gravity pulling it down, and the rope’s tension pulling it up. Because the bag hangs still, those two arrows must be exactly equal in length — they cancel.
A bag hanging from a rope has just two forces. Because it doesn’t move, tension and weight are drawn the same length — balanced forces.
The forces you’ll actually draw
You’ll meet these force types again and again. For a free-body diagram, what matters is which way each one points, so here’s the quick version — each gets its own full page later in this topic.
The four forces you’ll draw most often, and the direction each one always points.
In short: weight (Fg) always points straight down toward the ground. Tension (FT) points away from the object, along whatever string or rope is pulling it. The normal reaction force (FN) points at 90° away from any surface the object rests on. And friction or drag (Ff, Fd) always points opposite to the object’s motion, trying to slow it down. Non-contact forces like gravity, plus magnetic and electrostatic forces, act at a distance — you’ll draw those too when they apply.
The rules for drawing one
A free-body diagram is only useful if it’s drawn properly. Follow these steps every time and you won’t lose marks on the easy part of a forces question.
🛠️ How to draw a free-body diagram
Shrink the object to a point. Draw a single dot for the object — ignore its shape entirely.
Add only the forces acting on it. Nothing the object pushes on other things; only what pushes on it.
Draw each force as an arrow from the dot, pointing in the correct direction, tip facing away.
Make the lengths roughly proportional. A bigger force gets a longer arrow, so the diagram shows the balance at a glance.
Label every arrow with a name (weight) or the correct symbol (Fg). Made-up notation loses marks.
💡 Top tips
Use the syllabus symbols — Fg for weight, FN for the normal force, Ff for friction. If the question gives you a symbol, use theirs instead.
Only forces on the object. The classic mistake is drawing the force the object exerts on something else — that belongs on a different diagram.
Length carries meaning. If two forces balance, draw the arrows the same length. If one wins, draw it longer — the examiner can see the resultant from the picture.
Every arrow leaves the dot. Forces are drawn starting at the point and pointing outward, never into it.
WE 1
A toy sailboat weighing 30 N floats on water while being pulled to the right by a rope with a force of 35 N. The water pushes up on the hull with a buoyancy force of 30 N, and the total drag on the boat is 5 N. Sketch the free-body diagram and state the resultant force.
The rope force (35 N) is drawn much longer than the drag (5 N), so you can see the horizontal forces don’t balance — while buoyancy and weight, both 30 N, do.
Step 1 — list every force and its direction
weight = 30 N down | buoyancy = 30 N up
applied (rope) = 35 N right | drag = 5 N left
Step 2 — balance the vertical forces
up 30 N vs down 30 N → they cancelStep 3 — balance the horizontal forces
right 35 N minus left 5 N = 35 − 5 = 30 N rightresultant = 30 N to the rightThe boat speeds up to the right; the up/down forces are balanced so there’s no vertical motion.
From diagram to resultant force
Once the arrows are drawn, the payoff is the resultant force — the single force that has the same overall effect as all of them combined. It’s just the vector sum of every arrow, and it’s what actually decides how the object moves. If it comes out to zero, the forces are balanced and the object stays still or keeps a constant velocity. If it’s not zero, the object accelerates in the direction of the resultant.
Resultant force
resultant = vector sum of all forces → if resultant = 0, forces are balanced
When the arrows cancel, the resultant is zero and the object’s motion doesn’t change. When they don’t, the leftover resultant force makes it accelerate.
Forces along one line
When every force lies along the same straight line, adding them is simple arithmetic — you just pick a positive direction and add, treating anything the other way as negative.
WE 2
Three horizontal forces act on a crate: 12 N to the left, 5 N to the right, and 9 N to the right. Taking right as positive, find the resultant force.
Step 1 — choose a positive direction
right = positive, so left = negative
Step 2 — add the forces with signsF = (−12) + 5 + 9 = +2 NStep 3 — read off the sign
positive → the resultant points right
resultant = 2 N to the rightThe crate accelerates gently to the right — the two rightward pushes just outweigh the single leftward one.
Forces at right angles
When the leftover forces point in two directions at 90° to each other — one horizontal, one vertical — you can’t just add them. Instead you combine them with Pythagoras for the size and trigonometry for the direction, exactly like finding the hypotenuse of a right-angled triangle.
Two perpendicular forces of 24 N and 7 N combine into a single 25 N resultant, tilted about 16° above the horizontal — a neat 7-24-25 right triangle.
WE 3
After adding up its forces, an object is left with a net horizontal force of 24 N to the right and a net vertical force of 7 N upward. Calculate the magnitude and direction of the resultant force.
Step 1 — use Pythagoras for the magnitudeR = √(24² + 7²) = √(576 + 49) = √625
R = 25 N
Step 2 — use trig for the directiontan θ = 7 ÷ 24
θ = 16° above the horizontal
resultant = 25 N at 16° above horizontalAlways give both parts — a resultant force isn’t fully described until you’ve stated its direction as well as its size.
Quick recap: shrink the object to a point, draw every force acting on it as a labelled arrow (correct direction, length to scale), then add the arrows as vectors. Along one line, add with signs; at right angles, use Pythagoras and trig. A zero resultant means balanced forces; a non-zero resultant means acceleration.
⚠ Common mistakes
Drawing a force the object exerts on something else — only forces acting on the object belong on its diagram
Forgetting an implied force like weight or buoyancy just because the question didn’t spell it out
Making all arrows the same length when the forces aren’t equal — the lengths should show the balance
Adding perpendicular forces directly (e.g. 24 + 7 = 31) instead of using Pythagoras
Giving only the size of a resultant force and forgetting to state its direction
You now have the one tool the whole forces topic leans on. Every question from here — Newton’s laws, contact and non-contact forces, friction, momentum — starts by asking “what are the forces on this object?” and answering it with a free-body diagram. Next up: Newton’s First Law, where we find out what a zero resultant force really means for a moving object.
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