Newton's Laws of Motion — Quick Summary

Mr Toogood's Physics · Mechanics

AQA 3.4.1.5
F = ma
2nd law
W = mg
Weight
ΣF = 0
1st law condition
Equal, opposite, same type
Newton pair

Newton's 1st Law

Galileo's thought experiment with a ball rolling down slopes of decreasing steepness

On a frictionless flat surface, the ball would roll forever at constant velocity.

"Every body continues in its state of rest, or of uniform motion in a straight line, unless acted on by some external resultant force."

Forces change motion, they don't sustain it — Galileo's thought experiment shows a frictionless ball keeps rolling forever on a flat surface. ΣF=0 → constant velocity (or rest).

Law of inertia: mass is a measure of an object's reluctance to change its motion — a larger mass needs a larger force for the same change in velocity.

Newton's 2nd Law

"The rate of change of momentum of a body is directly proportional to the resultant external force acting on it, and takes place in the direction of that force."

F ∝ d(mv)/dt  →  F = ma  (constant mass)
F is always the resultant force — identify every force acting on the body first, usually with a free-body diagram, before applying F=ma.

A common application: weight is simply the resultant force due to gravity, W = mg.

Newton's 3rd Law

A book resting on a table, showing the weight and normal contact force on the book, and the true Newton pair of contact forces between book and table

Weight and normal force are NOT a Newton pair — the true pair is the two contact forces.

"If a body A exerts a force on a body B, then B exerts an equal and oppositely directed force on A." More precise than "equal and opposite reaction" — these are Newton pairs.

Checklist for a genuine Newton pair:

  1. Equal in size, along the same line of action.
  2. Act on two different bodies — never the same one.
  3. Always the same type of force.
Classic trap: a book's weight and the table's normal contact force are not a Newton pair — both act on the same body (the book) and are different force types (gravitational vs. contact). They simply happen to balance.

The three laws at a glance

In shortKey idea
1stVelocity won't change unless a resultant force acts.Balanced forces → constant velocity
2ndA resultant force causes acceleration.F=ma
3rdForces come in equal, opposite, same-type pairs on different bodies.Newton pairs never cancel

Exam essentials

Key equations

  • F=ma
  • W=mg
  • ΣF=0 (equilibrium)

Spotting a Newton pair

  • Equal size, same line of action.
  • Different bodies.
  • Same type of force.

Common slips

  • Weight & normal force are never a Newton pair — same body, different force types.
  • F in F=ma is always the resultant, not any single force.
  • Accelerating lift test: N≠W the instant it accelerates, proving they were never a Newton pair.