What Are Newton's Three Laws of Motion?

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1. 01

   Draw the object alone and mark every force acting on it

   A free-body diagram is where these questions are won or lost. Isolating one object stops forces acting on other things from creeping into the working, and it makes the third law manageable later — a force whose partner acts elsewhere cannot appear on this diagram at all.

2. 02

   Combine the forces into a single resultant

   Forces are vectors, so direction is part of the quantity and opposing forces subtract rather than add. Every one of the three laws is a statement about the resultant, not about the individual forces, which is why nothing can be decided until the arrows have been combined into one.

3. 03

   Apply the first law as a test on that resultant

   If the resultant is zero, the velocity does not change — the object stays at rest or keeps moving at constant speed in a straight line. This is the law students most often reverse, assuming that steady motion needs a steady force. A car at constant speed on a motorway has zero resultant force acting on it.

4. 04

   Apply the second law when the resultant is not zero

   A non-zero resultant produces acceleration in the direction of that resultant, with size given by F = ma. Mass appears as the resistance to that change, which is why the same push produces a smaller acceleration on a heavier object. Rearranging to a = F/m makes the relationship easier to read.

5. 05

   Use the third law to name the partner force

   Every force has an equal and opposite partner acting on the other object. Keeping the partner on that other object is the whole point — it is why the pair never cancels, and why a book resting on a table is explained by the first law rather than the third.

01

The first law: no resultant force, no change in velocity

An object at rest stays at rest, and an object in motion keeps moving at the same speed in the same straight line, unless a resultant external force acts on it. The property that makes this true is inertia, and mass is the measure of it.

The law is counter-intuitive because everyday motion always involves friction and air resistance, so things do slow down when you stop pushing. What the law says is that the slowing is caused by those forces, not by the absence of a push. A puck sliding on frictionless ice would keep going, and this is what makes it the more useful description.

02

The second law: F = ma

The acceleration of an object is directly proportional to the resultant force acting on it, in the same direction as that force, and inversely proportional to its mass. In symbols, F = ma, where force is in newtons, mass in kilograms and acceleration in metres per second squared.

The units follow from the equation rather than being separate facts: one newton is the force that accelerates one kilogram at one metre per second squared, so 1 N = 1 kg m/s². A resultant force of 3600 N on a 1200 kg car gives an acceleration of 3600 ÷ 1200 = 3 m/s².

Weight is the everyday example. A mass of 1 kg in Earth's gravitational field of roughly 9.8 N/kg has a weight of about 9.8 N. Mass is a quantity of matter and does not change with location; weight is a force and does.

03

The third law: pairs act on different objects

For every action there is an equal and opposite reaction. The phrasing is familiar and the meaning is routinely mistaken, because the two forces in a third-law pair never act on the same object. They are equal in size, opposite in direction, of the same type, and applied to two different bodies.

A book resting on a table is the standard test. The book's weight pulls down on the book; the table's normal contact force pushes up on the book. These two balance, which is why the book does not move — but they are not a third-law pair, because both act on the book. The partner of the book's weight is the book's gravitational pull on the Earth, and the partner of the table's push is the book's push down on the table.

The distinction matters in practice as well as in exams. If third-law pairs did cancel, nothing could ever accelerate: a swimmer pushes water backwards and the water pushes the swimmer forwards, and the swimmer moves precisely because those two forces act on different things.

• Equal in magnitude
• Opposite in direction
• The same type of force — both gravitational, both contact, both friction
• Acting on two different objects, which is why they never cancel

04

How we teach this

We start with free-body diagrams and stay with them longer than most schemes of work do. Almost every error in this topic — forces from other objects appearing on the wrong diagram, third-law pairs believed to cancel — is a diagram problem before it is a physics problem.

The book-on-a-table question is used as a diagnostic in our Grade 9 and 10 classes. A student who can explain why the two balanced forces on the book are not a third-law pair has understood the third law properly, and a student who cannot has usually memorised the phrase without it.