The Laws of Motion
Why does a jeepney passenger fall forward when the driver brakes? Why is an empty cart easier to push than a full one? Why can a rocket fly in space, where there is nothing to push against?
Three laws answer all of it. Isaac Newton wrote them down more than three hundred years ago, and they still explain every push, pull, slip and crash you will meet today.
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What is a force?
Before the three laws, one idea. Everything that follows is built on it, and it is short enough to fit in four words.
Measured in newtons (N). One newton is about the weight of a small apple resting in your hand — which is a happy accident, given who the unit is named after.
A force has a direction
Ten newtons east is not the same as ten newtons west. A quantity that needs both a size and a direction is called a vector, and force is one. Always draw it as an arrow.
Forces come from something
Every force has a source you can name — a hand, the floor, a rope, the Earth. If you cannot say what is producing it, it is probably not a force.
Forces add up
Objects almost never feel just one force. What matters is the total, which we call the net force — the whole of the next section.
Nine forces, two families
Some forces need the two objects to be touching. Others reach across empty space. Tap any one to see what it is and where you have met it.
Free-body diagrams: the one drawing that solves everything
A free-body diagram shows one object and every force acting on it, drawn as arrows pointing away from it. A longer arrow means a bigger force.
There is one rule students break constantly: draw only the forces acting ON the object. The forces the object exerts on other things belong on their diagrams, not on this one. Get that right and half of physics becomes bookkeeping.
Net force: adding the arrows up
An object does not respond to each force separately. It responds to the total — and that total decides whether anything changes at all.
Same way, add. Opposite ways, subtract.
Two people pushing a cart the same way with 30 N each give a net force of 60 N. If one pushes 30 N forward and friction pushes 12 N back, the net force is 18 N forward — the direction of the bigger one.
We write the net force as ΣF. The Greek letter sigma just means "the sum of".
Balanced or unbalanced
Balanced (ΣF = 0) — nothing about the motion changes. If it was still, it stays still. If it was moving, it keeps the same speed in the same direction.
Unbalanced (ΣF ≠ 0) — the object accelerates in the direction of the net force. It speeds up, slows down, or turns.
Build the diagram yourself
Four forces act on this crate. Move the sliders and watch the arrows, the net force and the verdict change together. Start with the presets at the bottom.
The sentence to take away
Zero net force does not mean zero motion. Try the preset "pushing a crate at constant speed": the crate is moving, and the net force is nothing at all. A net force is what it takes to change motion — never to keep it going. That idea is so important it became the First Law, which is next.
First Law: the Law of Inertia
The law that says objects are lazy — not because they refuse to move, but because they refuse to change.
An object at rest stays at rest, and an object in motion keeps moving at the same speed in the same direction — unless an unbalanced force acts on it.
Inertia
Inertia is an object's resistance to a change in its motion. It is not a force and you never draw it on a diagram — it is a property, like colour or temperature.
Mass is the measure of inertia. A bus has more inertia than a bicycle, so it is harder to start, harder to stop and harder to turn.
The misconception this law exists to kill
Almost everyone starts out believing that a moving object needs a constant force to keep moving. It feels obviously true — stop pedalling and the bicycle stops.
But the bicycle does not stop because the motion ran out. It stops because friction and air resistance are real unbalanced forces pushing backward on it. Take those away and it would coast forever. That is exactly what a spacecraft does.
Watch it happen
A passenger stands in a jeepney. Make the driver start or brake suddenly, then run it again with the other view selected — the same event tells two very different stories depending on where you are standing.
Nothing throws you forward in a crash
This is worth saying slowly, because the wrong version is everywhere. When a vehicle stops suddenly, no force throws you at the windshield. You were already travelling at 60 km/h, and nothing has acted on you, so you simply continue at 60 km/h while the vehicle stops. The seat belt is not there to hold you against some mysterious forward force — it is there to be the force that finally stops you, over half a metre instead of half a centimetre.
Second Law: F = ma
The First Law says an unbalanced force changes motion. The Second Law says by how much — and it is the most useful equation in this course.
net force (N) = mass (kg) × acceleration (m/s²) · rearranged: a = ΣF ÷ m and m = ΣF ÷ a
More force → more acceleration
Keep the mass the same and double the net force: the acceleration doubles. Triple it and the acceleration triples. Push a swing harder and it picks up speed faster — that is all this half of the law says.
More mass → less acceleration
Keep the force the same and double the mass: the acceleration halves. This is why an empty cart darts forward and a loaded one crawls, even though you are pushing exactly as hard.
Both halves, side by side
The two graphs show the same law from two directions. Move either slider and both dots move. The shapes are what you are meant to remember: a straight line for force, a falling curve for mass.
Three quantities, three questions
Cover the one you want with your finger and read off the rest. Want a? It is ΣF over m. Want ΣF? It is m times a. Want m? It is ΣF over a. Then check your units: newtons divided by kilograms must come out as m/s², or you have divided the wrong way round.
Solve it: F = ma problems
Pick what you are looking for, type what you were given, and either follow every line of the working — or hide it and let the solver mark you.
Step zero, every single time: find the NET force
In ΣF = ma, that Σ is not decoration. If a problem mentions friction, air resistance, or a second person pushing, you must combine the forces before you divide by anything. Using the applied force where the net force belongs is the most common mistake in this whole topic — and the solver below will say so by name if you make it.
Answer on paper first
Load a problem, work it out in your notebook, then switch to Check my answer. Recognising a right answer is not the same as producing one, and only one of those earns marks.
It names your mistake
Multiply instead of divide, forget the friction, use weight where mass belongs — the marker recognises each of those and tells you which one you did.
Always check the units
N ÷ kg = m/s². kg × m/s² = N. If your units do not come out right, the arithmetic cannot be right either — no matter how neat the number looks.
Third Law: forces come in pairs
The most quoted law in physics, and the most misunderstood. Almost everyone can recite it. Far fewer can use it.
Equal in size, opposite in direction, at the very same instant. The old wording is "for every action there is an equal and opposite reaction" — but the version above is harder to get wrong.
The four tests for a pair
Equal in size
Always. It does not matter if one object is a truck and the other a mosquito.
Opposite in direction
Exactly opposite — one points forward, the other backward, along the same line.
The same type of force
Gravity pairs with gravity. A push pairs with a push. Never one of each.
On DIFFERENT objects
This is the one that matters most. Each half of the pair acts on a different thing.
"If the forces are equal and opposite, why does anything ever move?"
This is the question that separates knowing the law from understanding it, and the answer is one line: the two forces act on different objects.
Forces can only cancel when they act on the same object. When you push a cart, your push acts on the cart and the cart's push acts on you. The cart never feels its own reaction. So when you work out whether the cart moves, you add up only the forces on the cart — and your push is the only one there.
Name the reaction
Eight situations. Each one gives you the action force and four candidates for its partner. Only one passes all four tests.
Friction, weight and the normal force
Three forces you will meet in nearly every problem from here on — and the reason the real world does not behave like the frictionless one in the equations.
Friction (f)
Opposes motion, or attempted motion, between two touching surfaces. It always acts along the surface, pointing against the way the object is moving or trying to move.
Normal force (N)
The support push a surface gives back, always perpendicular to that surface. On a level floor with nothing extra pressing down, it is equal to the weight.
Weight (W = mg)
The pull of gravity on the object, in newtons. Not the same thing as mass — which is the second half of this section.
Why starting is harder than continuing
Push gently and friction politely matches you. Push past the surface's limit and it suddenly gives way. The graph below is the whole story — move the sliders and watch the dot travel along it.
Useful and harmful, both at once
Useful: walking, braking, holding a pencil, tyres gripping the road, striking a match. Without friction you could not start moving at all — the Third Law needs something to push against.
Harmful: it wears machine parts down, turns useful energy into waste heat, and slows things you wanted to keep moving. We reduce it with oil, ball bearings and wheels — and rolling friction is far smaller than sliding friction, which is the entire reason wheels were invented.
What friction does and does not depend on
It does depend on the two surfaces (through the coefficient μ) and on the normal force. Heavier object, more friction. Rougher surfaces, more friction.
It does not depend on the area of contact. Turn the crate on its side and the friction is the same — the weight is now spread over a different area, and the two effects cancel exactly.
Mass is not weight
These two words mean different things in physics, and mixing them up is one of the easiest marks to lose. Change your mass below and watch which column moves.
| Mass | Weight | |
|---|---|---|
| What it is | The amount of matter in an object | The force of gravity pulling on that matter |
| Unit | kilogram (kg) | newton (N) |
| Type of quantity | Scalar — no direction | Vector — always points down |
| Does it change? | Never, wherever you go | Yes — it depends on the local g |
| Measured with | A balance | A spring scale |
| Formula | — | W = mg |
The laws around you
Nine ordinary moments. Decide which law explains each one before you tap — guessing first is what makes the answer stick.
How to tell them apart quickly
Ask yourself what the situation is really about. Is something carrying on when you expected it to stop — or staying put when you expected it to go? That is the First Law. Is it about how much something speeds up, and does mass or force get mentioned? Second Law. Are there two objects pushing on each other? Third Law.
Sort it: which law is it?
Twelve situations, three bins. Drag one in, or tap the token and then tap a bin. Every correct drop tells you why.
Count the objects
If the situation only really involves one object and what it was already doing, it is the First Law. If it involves one object and a number — a force, a mass, an acceleration — it is the Second. If you can name two objects each pushing the other, it is the Third.
Real situations use all three
A rocket launch obeys every law at once — the gas pushes it up (third), that net force divided by its mass gives its acceleration (second), and it would coast forever in space if nothing acted on it (first). These items are chosen so that one law is the best answer, but noticing the others is a good sign, not a mistake.
Flashcard review
The words you need before the quiz. Tap a card to flip it. Cover the answer and say the definition out loud first — that is what makes it stick.
Practice quiz
Fifteen questions, a mix of ideas and calculations. You get an explanation after every answer — read it even when you get it right.
The questions shuffle
Every attempt reorders the items, so you cannot memorise the sequence — only the physics.
Compute before you tap
For the number questions, work it out on paper first. Every one of them can be done in two lines: find ΣF, then divide or multiply.
Aim for 13 / 15
Below that, go back to the solver and the flashcards, then try again.
Cheat sheet
Everything this lesson turns on, in one table. If you can read down this list and explain each line to somebody, you are ready.
| Idea | The rule | Remember |
|---|
Nothing changes on its own
At rest stays at rest. Moving keeps moving, same speed, same direction. Only an unbalanced force can change that. Mass measures how strongly an object resists the change.
How much it changes
ΣF = ma. Acceleration grows with net force and shrinks with mass, and it always points the way the net force points — not the way the object happens to be travelling.
You cannot push without being pushed
Equal, opposite, same type, different objects. They never cancel, because cancelling requires both forces to act on the same object.
Before you close this
On exam day, write these three lines at the top of your paper before you read a single item: ΣF = ma · W = mg, and g = 9.8 m/s² · a pair acts on two different objects. Then, for every problem, draw the free-body diagram before you write any numbers. Most of the marks are in that drawing.