Newton's Three Laws of Motion Explained With Examples

Quick answer: Newton's first law says an object stays at rest or keeps moving at constant velocity unless a resultant force acts on it. The second law says resultant force = mass x acceleration, written F = ma. The third law says when two objects interact, each pushes the other with a force that is equal in size, opposite in direction, the same type, and acting on a different object.

For about a year I treated these as three sentences to memorise for a one-mark definition question. That is why I lost four marks in an IGCSE physics mock. I wrote "action and reaction are equal and opposite" for the third law and stopped. The mark scheme wanted four things and I had given one and a half. These laws are three different tools, and most of the marks come from knowing which one a question is actually asking for.

First law: it is about resultant force, not "no force"

The first law says an object keeps doing what it is doing — stationary, or moving in a straight line at constant speed — until a resultant force acts on it. The word that earns marks is resultant. A car cruising at a steady 30 m/s has a driving force, drag, weight and a normal contact force acting on it. They simply add to zero. If you write "no forces act on it", you are describing a spaceship in deep space, not a car on a motorway.

Real numbers help. A parachutist falling at a steady 5 m/s has 700 N of weight pulling down and 700 N of air resistance pushing up. Resultant = 700 - 700 = 0 N, so the velocity does not change. That is terminal velocity, and it is a first-law answer even though the object is moving fast.

The other half feels wrong at first: nothing has to push an object to keep it moving. A puck on ice slows down because friction acts, not because it runs out of force. There is no such thing as a force of motion, and drawing one loses marks.

Second law: F = ma, where F means the resultant

The second law is resultant force = mass x acceleration. The units line up so that 1 N = 1 kg m/s^2, which is worth remembering because it tells you the equation only works in kilograms, metres and seconds. Grams will quietly wreck an otherwise correct answer.

The trap is subtler than the first law's. The F in F = ma is the resultant force, not the force the question happened to mention. If a train's engine provides 12000 N against 4000 N of resistance, the number going into F = ma is 8000 N, not 12000 N.

Worked example. A 1200 kg car has a driving force of 4200 N and total resistive forces of 1800 N.

1. Resultant force = 4200 - 1800 = 2400 N, forwards.
2. Rearrange F = ma to a = F / m.
3. a = 2400 / 1200 = 2.0 m/s^2.
4. State the direction: 2.0 m/s^2 forwards.

Acceleration is a vector, so direction is part of the answer and often part of the mark. Now extend it. The driver holds 4200 N, the car speeds up, and drag rises with speed. When drag reaches 4200 N the resultant is zero and the car sits at top speed. Second law explains how it got there; first law explains why it stops speeding up.

Fully worked example: the lift question

This one appears at Cambridge IGCSE, AQA GCSE and AP Physics 1 in slightly different clothes, and it uses two laws at once.

A 60 kg student stands on a bathroom scale inside a lift that accelerates upwards at 1.5 m/s^2. What does the scale read? Take g = 9.8 N/kg — some papers give 10, so use whatever the front page tells you.

1. Draw the forces on the student only: weight down, normal contact force N up from the scale.
2. Weight = m g = 60 x 9.8 = 588 N.
3. The student accelerates upwards, so the resultant points upwards, so N must be bigger than 588 N.
4. Take up as positive: N - 588 = m a = 60 x 1.5 = 90 N.
5. So N = 588 + 90 = 678 N.
6. The scale reads the force the student pushes down on it with. By the third law that is 678 N, equal and opposite to the 678 N the scale pushes up with.

Two checks catch most errors. The answer is larger than the true weight, matching "accelerating upwards". And setting a = 0 gives exactly 588 N, the first law falling out of the same equation. Accelerating downwards instead gives 588 - 90 = 498 N, and you feel light. Getting the forces onto the right object is the hard part, and it is worth drilling on the physics hub.

Third law: the four-part test

Write the third law as four things, because that is how it is marked. When two objects interact, the forces they exert on each other are equal in magnitude, opposite in direction, of the same type, and act on different objects.

Test any suggested pair against all four parts. The classic wrong answer is a book on a table: students name the book's weight and the table's normal force as a pair. That fails two parts. Both act on the book rather than on different objects, and one is gravitational while the other is a contact force. They are balanced forces, a first-law idea.

The genuine pairs are these. The Earth pulls the book down and the book pulls the Earth up, both gravitational. The table pushes the book up and the book pushes the table down, both contact.

So why does the universe not cancel itself out? Because the two forces in a pair act on different objects, they never appear in the same F = ma calculation. Your push on a trolley goes into the trolley's equation; its push back goes into yours.

Which law is the question asking for?

• Phrases like "constant velocity", "steady speed", "terminal velocity", "at rest" or "moving at a constant 20 m/s" mean the resultant force is zero. First law.
• A mass plus a force, or a mass plus an acceleration, means F = ma. Second law.
• "Explain why the rocket moves forwards", "identify the reaction force", or anything describing two objects touching means third law. Name both objects, every time.
• If the command word is "explain", you need words as well as numbers. The explain tool helps you check whether your reasoning actually reaches the conclusion or just restates the question.

Test yourself

1. A 4 kg box is pushed with 30 N while friction acts backwards with 6 N. Calculate the acceleration.
2. A helicopter hovers perfectly still. What is the resultant force on it, and which law tells you?
3. A swimmer pushes backwards on the water. State the other force in the third-law pair, including which object it acts on.

FAQ

Are weight and the normal force a third-law pair?

No. They act on the same object and are different types of force, so they fail two parts of the test. They only happen to be equal when the object is not accelerating vertically, which is a first-law situation. The true partner to your weight is the upward gravitational pull you exert on the Earth.

Does F = ma still work if the force is not constant?

At GCSE, WASSCE and CBSE level you are only asked about constant or average forces, so F = ma as written is fine. At Cambridge International A-Level and AP Physics it holds at every instant, but the acceleration changes as the force changes, which is why those papers move on to impulse and momentum.

Why do I keep getting the signs wrong?

Because you have not chosen a positive direction before you start. Write "taking up as positive" at the top of the working, then give every opposing force a minus sign. It takes five seconds and removes most sign errors.

Do I have to quote the laws word for word?

You need the key phrases, not the exact sentence. Examiners look for "resultant force", "constant velocity", "equal and opposite", "different objects" and "same type of force". Missing phrases lose marks; different phrasing does not. Drilling those phrases with quick quizzes beats rereading the chapter.

In short

First law tells you what happens when the resultant force is zero. Second law tells you how much acceleration a non-zero resultant produces. Third law tells you forces come in pairs on two different objects. Decide which law a question is testing before writing, use the resultant rather than the first force you were handed, and always say which object each force acts on.