Three laws, published in 1687, and essentially all of classical mechanics follows from them. They are also, and this is worth saying early, almost never what people remember. What they actually say is subtler and more useful than "things stay put, things go faster when pushed, and things push back".
First law: inertia, and the word that does the work
An object remains at rest, or in motion at constant velocity, unless acted on by a non-zero net external force.
The load-bearing word is net. Forces do not need to be absent for an object to stay at rest — they need to cancel. A book on a table is pulled down hard by gravity and pushed up equally by the table, and the sum is zero, so the book stays put. Slide a book across a table and friction opposes the motion; eventually friction and drag balance out and the book stops, and where it stops is exactly where the net force reached zero.
The everyday consequence is why seat belts, non-slip mats and helmets work. A crash does not need a sustained force to injure you — the change in velocity is what hurts, and that change is produced by a force acting over a very short time. A seat belt lengthens the stopping time, which lowers the force on your chest. The momentum guide covers the arithmetic of exactly this.
Second law: F = ma, and the net force again
Net force = mass × acceleration.
Everything important about the second law is contained in the word net. Acceleration is not caused by "force" in general; it is caused by the unbalanced force. Three equal forces at 120° apart produce a net force of zero, and an object under all three does not accelerate at all.
Worked examples:
1. What force accelerates a 1,200 kg car at 3 m/s²? F = ma = 1200 × 3 = 3,600 N. Mass is what makes cars feel heavy — the same force on a bicycle produces an acceleration fifteen times larger.
2. A 5 kg block with 20 N of force, frictionless. What is the acceleration? a = F ÷ m = 20 ÷ 5 = 4 m/s².
3. Gravity on a 2 kg object near Earth's surface? F = mg = 2 × 9.81 ≈ 19.6 N downward.
Note the direction: F = ma with a downward positive gives a downward force. Signs are not decoration in this equation; they carry the direction, which is why the force calculator reports the value alongside the sense it applies in.
Third law: action and reaction, and why it does not cancel
For every action there is an equal and opposite reaction, and these two forces act on different bodies.
That final clause is where most people go wrong. It is not a paradox that a book rests on a table "despite" an equal downward force: the weight acts on the book and the normal force acts on the table. They live on different objects, so they never cancel for any one body. The book has a net upward force on it, so it accelerates upward — until it lifts off, which is exactly what happens when the table is removed.
Applied examples, all the same pattern:
- Walking: your foot pushes backward on the ground; the ground pushes you forward. You are not propelled by your own muscles, you are propelled by the ground.
- Rocket: the exhaust leaves downward, the rocket goes up. The exhaust has its own upward momentum, which is the reason the pairing matters.
- Swimming: hands push water backwards, water pushes hands forwards.
- Friction: a box slides right, friction acts left — on the box. The box's forward push is a different force, acting on the box too, and it is the difference between the two that accelerates it.
Putting the three together
Consider a 1,500 kg car braking from 20 m/s to rest in 4 s. The first law says the car will not stop on its own — a net force is required. The second law gives it: a = (0 − 20)/4 = −5 m/s², so F = 1500 × (−5) = −7,500 N, i.e. 7.5 kN backwards. The third law says the road pushes the car backwards with 7.5 kN, and the tyres push the road forwards with the same amount.
Every real motion problem is this: find the net force from the second law, identify which individual force is responsible from the diagram, and check the pairing with the third.
Weight, mass and the distinction worth keeping
Mass is how much matter there is, in kilograms, and it is the same everywhere. Weight is the gravitational force on that mass, W = mg, in newtons, and it changes with location — an object weighs about 1/6 as much on the Moon (g ≈ 1.63) as on Earth, while its mass is unchanged. Astronauts are not weightless because they have no mass; they are weightless because both they and everything around them are in free fall, so the scale reads zero.
Three traps
Friction as a force you must overcome. Friction is not a fixed "penalty" — it depends on the normal force (F = µN) and, in air, roughly on the square of speed. A force calculation with the wrong friction assumption will be wrong by an order of magnitude on a slippery surface.
Weight as a force that "does work". On a table, weight does zero work because the displacement is zero. Work needs movement, and a force applied over no distance contributes nothing.
Adding forces without a diagram. Especially with angles. Two 10 N forces at 90° give a net of about 14.1 N, not 20 N, and at 180° give zero. Draw the diagram, resolve into components, then add.
A reliable method for any force problem
Three steps, always in this order: draw the object as a dot with every force as a labelled arrow from it; resolve any angled force into horizontal and vertical components; solve with ΣF = ma in each direction separately, then convert back to magnitude and direction. Skipping the diagram is the reliable way to a wrong answer with confident arithmetic, because most errors are missing a force rather than miscalculating one.
Frequently asked questions
What is Newton's first law really saying?
An object keeps its state of motion — at rest it stays at rest, moving at constant velocity it continues — unless a net external force acts. The word net is the whole point: forces that cancel each other out change nothing.
What does F = ma actually mean?
The net force on an object equals its mass multiplied by its acceleration. Acceleration is determined by net force and mass, not by any single force in isolation.
Is action-reaction the same as balanced forces?
No. Action-reaction pairs act on different bodies, so they never cancel on any one object. Balanced forces on a single object are what produce zero acceleration.
Why do heavier objects fall at the same rate?
Gravity pulls harder on a heavier object (F = mg) but its inertia is proportionally larger too. The mass cancels in F = ma, giving every object the same 9.81 m/s² in a vacuum. Air resistance is what makes the difference in everyday life.