Force and Newton's Laws of Motion

What Is Force?

A force is any push or pull that acts on an object. Forces change an object's speed, direction, or shape. You cannot see a force, but you can always observe its effect — a football flies off your foot, a spring stretches, a car slows down.

Scientists measure force in Newtons (N), named after Sir Isaac Newton. One Newton is roughly the force needed to hold a small apple in the air against gravity.

Forces are vector quantities. That means every force has both a size (magnitude) and a direction. A 10 N force pushing right is completely different from a 10 N force pushing left — always state both when you write an answer in an exam.

Types of Forces You Need to Know

• Gravity (Weight): pulls every object toward Earth's centre. Weight = mass × gravitational field strength (W = mg).
• Normal (Contact) Force: a surface pushes back on any object resting on it — always acts perpendicular to the surface.
• Friction: opposes motion between surfaces in contact. It acts in the direction opposite to movement.
• Air Resistance (Drag): a form of friction between a moving object and the air around it.
• Tension: the pulling force transmitted through a rope, string, or cable.
• Applied Force: any force you directly exert on an object by pushing or pulling it.

In most exam questions, you draw a free-body diagram first. Label every force with an arrow showing its direction and write the magnitude beside it. This one habit prevents the most common calculation mistakes.

Newton's First Law of Motion — The Law of Inertia

Statement: An object remains at rest, or continues moving in a straight line at constant speed, unless an unbalanced (net) force acts on it.

The key word is unbalanced. If all forces on an object cancel out, the object behaves as though no force acts on it at all — it either stays still or keeps moving at the same speed in the same direction.

What Is Inertia?

Inertia is an object's resistance to any change in its motion. A heavier object has more inertia and therefore needs a larger force to start, stop, or turn it. Think of pushing an empty shopping trolley versus a full one — the full trolley "fights back" more. That resistance is inertia at work.

Real-Life Examples

• Passengers lurch forward in a braking car. The car decelerates, but the passengers' bodies want to keep moving forward (inertia). Seat belts provide the backward force needed to slow them safely.
• A ball rolling across a field slows down and stops. Friction and air resistance act as unbalanced forces, removing energy and reducing speed. On a perfectly frictionless surface, the ball would roll forever.
• A book resting on a table stays still. Gravity pulls it down; the normal force from the table pushes it up. The two forces balance, so the net force is zero — the book does not move.
• Astronauts drift in space. In the near-vacuum of space, almost no friction or air resistance acts on a moving astronaut. A small push keeps them moving in a straight line indefinitely — a dramatic demonstration of the First Law.

Balanced vs. Unbalanced Forces

When forces balance, the net force = 0 N and the object's velocity does not change. When forces are unbalanced, the net force is non-zero and the object accelerates (speeds up, slows down, or changes direction). Examiners love asking you to distinguish between these two situations — practice identifying them quickly.

Newton's Second Law of Motion — Force, Mass, and Acceleration

Statement: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

Written as a formula:

F = m × a

Where:

• F = net force in Newtons (N)
• m = mass in kilograms (kg)
• a = acceleration in metres per second squared (m/s²)

Understanding the Relationship

Two key patterns emerge from this equation:

• More force → more acceleration (if mass stays the same). Push a trolley harder and it speeds up faster.
• More mass → less acceleration (if force stays the same). A loaded lorry takes far longer to reach 60 km/h than an empty one with the same engine force.

Rearranged Forms of the Formula

Depending on which quantity the question asks you to find, rearrange the equation before substituting numbers:

• Finding force: F = m × a
• Finding mass: m = F ÷ a
• Finding acceleration: a = F ÷ m

A quick tip many students find helpful: cover the quantity you want with your thumb on the triangle F | m × a. Whatever remains visible is the calculation you perform.

Always Use Net Force

The "F" in Newton's Second Law always refers to the net (resultant) force — the single combined force after you add all forces with their directions. If a 20 N force acts right and a 5 N friction force acts left, the net force is 20 − 5 = 15 N to the right. Use 15 N in your calculation, not 20 N.

Newton's Third Law of Motion — Action and Reaction

Statement: For every action force, there is an equal and opposite reaction force. These forces act on different objects.

This law trips students up because the two forces are equal in size. You might wonder: "If the forces are equal, why does anything move?" The answer is that they act on different objects, so they cannot cancel each other out. Each object experiences only the force acting on it.

How to Identify Action–Reaction Pairs

Always describe both forces using this template: "Object A exerts a force on Object B; Object B exerts an equal and opposite force on Object A." If both forces act on the same object, they are not a Newton's Third Law pair.

Real-Life Examples

• Rocket propulsion: The rocket engine expels hot gases backward at high speed (action). The gases push the rocket forward with an equal force (reaction). This works even in the vacuum of space, where there is nothing to "push against" — the rocket pushes the gases, and the gases push the rocket.
• Walking: Your foot pushes backward against the ground (action). The ground pushes your foot forward (reaction). That forward reaction force is what moves you ahead. Without friction between your shoe and the ground, you cannot walk — as anyone who has stepped onto ice knows.
• Swimming: A swimmer's hand pushes water backward (action). The water pushes the swimmer forward (reaction). Competitive swimmers maximize this by pulling with a wide, curved stroke to move as much water as possible.
• A book on a table (revisited): Gravity pulls the book down onto the table (action). The table pushes the book upward with the same force — the normal force (reaction). These two forces act on different objects (Earth pulls book; table pushes book), so they are indeed a Third Law pair, even though the book does not move.

Fully Worked Exam Examples

Work through each example completely before checking the answer. Writing out every step — even when the numbers look simple — trains the habit that earns full marks in exams.

Example 1 — Find the Force

Question: A 4 kg box accelerates at 3 m/s². Calculate the net force acting on it.

Given: m = 4 kg, a = 3 m/s²

Formula: F = m × a

Substitution: F = 4 × 3

Answer: F = 12 N

Example 2 — Find the Acceleration

Question: A net force of 35 N acts on a 7 kg object. Find its acceleration.

Given: F = 35 N, m = 7 kg

Formula: a = F ÷ m

Substitution: a = 35 ÷ 7

Answer: a = 5 m/s²

Example 3 — Find the Mass

Question: A force of 60 N produces an acceleration of 4 m/s². What is the mass of the object?

Given: F = 60 N, a = 4 m/s²

Formula: m = F ÷ a

Substitution: m = 60 ÷ 4

Answer: m = 15 kg

Example 4 — Two Opposing Forces (Net Force)

Question: Two forces act on a 5 kg trolley: 30 N to the right and 10 N to the left. Calculate the trolley's acceleration and state its direction.

Step 1 — Find net force:

F_net = 30 − 10 = 20 N to the right

Step 2 — Apply Newton's Second Law:

a = F ÷ m = 20 ÷ 5

Answer: a = 4 m/s² to the right

Notice that step 1 comes before the formula. Many students plug numbers straight into F = ma and use 30 N instead of 20 N — that costs marks. Always calculate net force first.

Example 5 — Real-World Problem (Braking Car)

Question: A car of mass 1 200 kg brakes and decelerates at 6 m/s². Calculate the braking force.

Given: m = 1 200 kg, a = 6 m/s² (deceleration, so the force opposes motion)

Formula: F = m × a

Substitution: F = 1 200 × 6

Answer: F = 7 200 N (acting backward, opposing motion)

Always mention the direction of the braking force in your written answer. Examiners award a separate mark for direction in many marking schemes.

Common Mistakes and How to Avoid Them

• Using total force instead of net force. Always subtract opposing forces before applying F = ma.
• Leaving mass in grams. Convert grams to kilograms before substituting (divide by 1 000). The formula only works in SI units.
• Forgetting direction. Acceleration and force are vectors. Write "to the right," "upward," or use a sign (positive/negative) to show direction.
• Confusing mass and weight. Mass (kg) measures the amount of matter. Weight (N) is the gravitational force on that mass. They are not the same thing.
• Claiming Third Law pairs cancel each other. They act on different objects, so they never cancel. Only forces on the same object can cancel.

Exam Tips — Pick Up Every Mark

• Draw a free-body diagram for every force question, even if the mark scheme does not ask for one. It shows the examiner your thinking and helps you avoid missing forces.
• Calculate net force before anything else when two or more forces act on the same object.
• Always include units in your final answer (N, kg, m/s²). An answer without a unit is technically incomplete.
• State direction whenever the question involves vector quantities — force, acceleration, velocity, and displacement all have direction.
• Describe Third Law pairs in full sentences using the structure: "[Object A] exerts [force] on [Object B]; [Object B] exerts an equal and opposite force on [Object A]."
• Check your arithmetic by substituting your answer back into the formula to see whether both sides balance.

Quick Summary — Newton's Three Laws

• First Law (Inertia): Objects resist changes in motion. No net force means no change in velocity.
• Second Law (F = ma): Net force causes acceleration. Greater force or smaller mass produces greater acceleration.
• Third Law (Action–Reaction): Every force has an equal and opposite partner force acting on a different object.

Once you understand how these three laws connect, most mechanics problems in Class 6 through O Level become straightforward. Practise drawing free-body diagrams daily, always write out every step, and state both the magnitude and direction in every answer.