Newton's three laws of motion

Updated October 20, 2026

Newton's three laws describe how forces change motion. First: an object keeps its velocity, staying still or moving steadily in a straight line, unless a net force acts on it. Second: net force equals mass times acceleration, F = ma. Third: when one object pushes on another, the second pushes back with a force equal in size and opposite in direction.

Forces, mass and acceleration: the words you need

A force is a push or a pull, measured in newtons (N). Forces have a size and a direction, so two forces can add together or cancel out. The net force is what you get when you combine all the forces on an object.

Mass is the amount of matter in an object, measured in kilograms (kg). It also measures inertia, how hard the object is to speed up, slow down or turn. Weight is different: it is the force of gravity on that mass, W = mg, where g is about 9.8 N/kg on Earth. A 50 kg student has a weight of about 490 N on Earth and about 81 N on the Moon, but the same mass in both places.

Acceleration is any change in velocity: speeding up, slowing down or changing direction. It is measured in metres per second per second (m/s²).

The first law: inertia

An object at rest stays at rest, and an object in motion keeps moving at the same speed in the same direction, unless a net force acts on it. This tendency to keep doing what it is already doing is called inertia, and more mass means more inertia.

This is why you lurch forward when a bus brakes: the bus slows, but your body keeps moving until the seat belt or your feet push you back. It also explains why a hockey puck slides a long way on ice: with very little friction, there is almost no force to slow it.

The key point is that moving steadily needs no net force. A car cruising at a constant 100 km/h on a straight road has balanced forces: the push from the road on the tyres exactly matches air resistance and friction.

The second law: F = ma

The second law says how much an object accelerates: the net force on it equals its mass times its acceleration, F = ma. Rearranged, a = F/m. A bigger net force gives a bigger acceleration; a bigger mass gives a smaller one for the same force.

The units fit together: one newton is the force that gives a 1 kg mass an acceleration of 1 m/s², so 1 N = 1 kg m/s². Keep mass in kilograms and acceleration in m/s², and the force comes out in newtons.

The acceleration is always in the direction of the net force. Push a cart forward and it speeds up; apply the brakes and the backward net force slows it down.

ProblemWhat net force gives a $1200$ kg car an acceleration of $3$ m/s $2$ ?

$F$ $= m a$
Start from the second law.
$F$ $= 1200 kg \times 3 {m/s}^{2}$
Substitute the mass in kilograms and the acceleration in metres per second squared.
$F$ $= 3600 kg \cdot {m/s}^{2}$ $= 3600 N$
A kilogram metre per second squared is a newton.

Answer $3600 N$

Worked example: finding acceleration

The same equation works backwards. When you know the force and the mass, divide to find the acceleration.

ProblemA $90$ N kick acts on a $0.45$ kg soccer ball. What is its acceleration during the kick?

$a$ $= \frac{F}{m}$
Divide both sides of F = ma by m.
$a$ $= \frac{90 N}{0.45 kg}$
Substitute the force in newtons and the mass in kilograms.
$a$ $= 200 {m/s}^{2}$
90 divided by 0.45 is 200, and a newton per kilogram is a metre per second squared. The acceleration is huge but only lasts the instant the foot touches the ball.

Answer $200 {m/s}^{2}$

Worked example: a free-body diagram

A free-body diagram shows one object as a box or dot with an arrow for every force acting on it, each pointing the way the force acts. It is the best first step in any force problem, because F = ma only works with the net force, and you cannot find the net force until you have every force in front of you.

Handle each direction separately. Forces up and down combine with each other, and forces left and right combine with each other.

ProblemA rope pulls a $50$ kg crate across a floor with $200$ N. Friction is $120$ N. Find the acceleration $(g = 9.8$ N/kg $)$ .

$W$ $= m g$ $= 50 \times 9.8$ $= 490 N down$
Draw the crate. Its weight is an arrow straight down.
$N$ $= 490 N up$
The floor pushes up with a normal force. The crate does not sink or lift, so the vertical forces balance.
$F_{n e t}$ $= 200 N - 120 N$ $= 80 N$
Horizontally, the 200 N pull points forward and the 120 N friction points backward, so they partly cancel.
$a$ $= \frac{F_{n e t}}{m}$ $= \frac{80 N}{50 kg}$ $= 1.6 {m/s}^{2}$
Use only the net force, not the 200 N pull, and the acceleration points the way the rope pulls.

Answer $1.6 {m/s}^{2}$

The third law: action and reaction

Forces always come in pairs. If object A pushes on object B, then B pushes on A with a force of the same size in the opposite direction. The two forces act on different objects, which is why they do not cancel.

When you walk, your foot pushes backward on the ground, and the ground pushes forward on you; that forward push is what moves you. A rocket pushes exhaust gases backward, and the gases push the rocket forward, even in space where there is no air to push against. When you lean on a wall, you push on the wall and the wall pushes back on you just as hard.

If the forces are equal, why does a bug splat on a windscreen while the car barely notices? The forces on the bug and the car are equal in size, but the second law says the effect depends on mass. The bug's tiny mass gets an enormous acceleration; the car's large mass gets almost none.

Common mistakes

These errors appear in almost every class:

Thinking motion needs a force. A steadily moving object needs no net force; a force is needed to change motion.
Putting a single applied force into F = ma. Use the net force, after friction, drag and any other forces are combined.
Saying third-law pairs cancel. They act on different objects, so they never cancel on one free-body diagram.
Mixing up mass and weight. Mass is in kilograms and does not change from place to place; weight is a force in newtons and depends on gravity.
Believing heavier objects fall faster. Without air resistance, every object falls with the same acceleration, about 9.8 m/s², because a bigger mass has a bigger weight in exact proportion.
Using grams or km/h in F = ma. Convert to kilograms and metres per second first, or the answer will not be in newtons.

How to practise and check your work

Start every problem with a free-body diagram, even a quick sketch. Label each arrow with what exerts it: the Earth, the floor, the rope, the air. If you cannot name what exerts a force, it is probably not there; there is no separate force of motion pushing a moving object along.

Check units at each step. If your force is not in newtons or your acceleration is not in m/s², a conversion is missing. Then check the size: a car accelerating at 50 m/s² or a person weighing 5 N signals a slip.

For the third law, practise naming pairs in the form "A pushes on B, B pushes on A". For the first law, explain everyday moments, like a tablecloth pulled from under dishes, in terms of inertia.

Questions

What are Newton's three laws in simple terms?

First, objects keep doing what they are doing unless a net force acts. Second, force equals mass times acceleration. Third, every force has an equal and opposite partner force on the other object.

What is the unit of force?

The newton, N. One newton is the force that gives a 1 kg mass an acceleration of 1 m/s², so 1 N = 1 kg m/s².

Why don't action and reaction forces cancel out?

They act on different objects. Forces cancel only when they act on the same object, so each object in the pair is affected by its own force.

What is the difference between mass and weight?

Mass is the amount of matter, in kilograms, and is the same everywhere. Weight is the force of gravity on that mass, in newtons, found with W = mg.

What is an example of Newton's first law?

Passengers lurch forward when a bus brakes suddenly, because their bodies keep moving forward until a force such as a seat belt stops them.

How do you calculate net force?

Add the forces acting in the same direction and subtract those acting in the opposite direction, treating up and down separately from left and right.