Newton's Laws of Motion

Three laws from 1687 that still govern everything from a falling apple to a rocket launch. Learn them, draw the forces, and calculate what happens next.

  • State Newton's three laws of motion
  • Use F = ma to calculate force, mass and acceleration
  • Explain everyday situations with the third law
  • Distinguish mass from weight

A universe with rules

In 1687 Isaac Newton published three laws that describe how objects move. They aren't obvious — it took humanity thousands of years to get them right — but once you have them, you can predict everything from a braking car to a satellite's orbit.

Definition: force

A force is a push or a pull. It is measured in newtons (N) and always has both a size and a direction. Forces change motion: they speed things up, slow them down, or change their direction.

The key idea running through all three laws is the resultant force — what you get when all the forces on an object are added together (as arrows). If the resultant force is zero, the forces are balanced. If not, they're unbalanced — and the motion changes.

Newton's first law: keep doing what you're doing

Newton's 1st law

An object keeps its velocity unless a resultant force acts on it.

A hockey puck sliding on ice keeps sliding — it doesn't need a force to keep moving, only to change its motion. This property is called inertia: the tendency of objects to resist changes to their motion. More mass means more inertia.

Why does a passenger lurch forward when a bus brakes? The bus slows, but the passenger's body keeps its velocity (first law) until the seatbelt provides the force to slow them too.

Newton's second law: F = ma

Newton's 2nd law

F = m × a

The resultant force on an object equals its mass times its acceleration. Bigger force → bigger acceleration. Bigger mass → smaller acceleration for the same force.

Worked example

A 2 kg trolley accelerates at 3 m/s². What is the resultant force?

Maths
F = m × a
F = 2 kg × 3 m/s²
F = 6 N

And in reverse: a 1200 kg car experiences a resultant force of 3000 N. Its acceleration is a = F/m = 3000/1200 = 2.5 m/s².

Mass vs weight — don't mix them up

Mass (kg) is how much matter an object contains — the same everywhere. Weight (N) is the force of gravity on that mass: weight = mass × gravitational field strength. On Earth, g ≈ 10 N/kg, so a 2 kg bag weighs about 20 N. On the Moon it would weigh less but its mass wouldn't change.

objectreactionweightfrictionpush
Free-body diagram: draw every force on the object as an arrow before you calculate.

Newton's third law: every action has a reaction

Newton's 3rd law

For every action there is an equal and opposite reaction.

Push on a wall and the wall pushes back on you — that's why your hand hurts, not the wall. The two forces act on different objects, which is why they don't cancel out.

How rockets work

A rocket pushes exhaust gases backwards (action). The gases push the rocket forwards with an equal and opposite force (reaction). Notice: no air is needed to "push against" — rockets work perfectly in the vacuum of space.

Swimming, walking, birds flying — all third-law stories. You push water back; water pushes you forward.

Practice

State Newton's three laws in your own words.
Think: keep going / F = ma / action–reaction.
  1. Objects maintain their velocity unless a resultant force acts. 2) F = ma — resultant force equals mass × acceleration. 3) Every action has an equal and opposite reaction.
A 5 kg object accelerates at 4 m/s². Find the resultant force.
F = ma.

F = 5 × 4 = 20 N.

Explain why a rocket can accelerate in empty space.
What does it push on?

The rocket expels gas backwards (action); by the third law the gas pushes the rocket forwards (reaction). No surrounding air is required.

A car (1200 kg) brakes with a resultant force of 6000 N. Find its deceleration.
Rearrange F = ma to a = F/m.

a = 6000/1200 = 5 m/s² (deceleration).

Quick check

Newton's laws — quick check

A puck slides across frictionless ice at constant velocity. The resultant force on it is…

Constant velocity means no change in motion, so (1st law) the resultant force is zero.

A 10 N resultant force acts on a 2 kg mass. The acceleration is…

a = F/m = 10/2 = 5 m/s².

When you walk, the force that pushes you forward comes from…

Your foot pushes backwards on the ground (action); the ground pushes you forwards (reaction) — Newton's third law.

An astronaut's mass is 80 kg on Earth. On the Moon it is…

Mass measures amount of matter — it doesn't change. Weight changes; mass doesn't.
Key takeaways
  • 1st law: objects keep their velocity unless a resultant force acts (inertia).
  • 2nd law: F = ma — link force, mass and acceleration, and rearrange confidently.
  • 3rd law: every action has an equal and opposite reaction, acting on different objects.
  • Mass (kg) is matter; weight (N) is gravity's pull on it: weight = m × g.
  • Draw free-body diagrams before calculating — arrows first, numbers second.