Welcome to the cornerstone of classical mechanics! Whether you are looking at a rocket launching into space or a book sitting quietly on a desk, the forces involved and the resulting motion are entirely governed by three fundamental rules formulated by Sir Isaac Newton.

What you'll learn:

• How to state and apply Newton's three laws of motion.
• How to use the equation $F=ma$ to solve problems involving constant mass.
• How to draw and interpret free-body diagrams to find resultant forces.
• How to identify genuine Newton's third law force pairs (and spot the fakes!).

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The foundation: Newton's First Law

Before we look at how things accelerate, we need to look at how they behave when left alone.

Newton's First Law tells us what happens when this resultant force is exactly zero.

Newton's First Law: An object will remain at rest, or continue to move at a constant velocity, unless acted upon by a resultant force.

This means that "constant velocity" and "stationary" are essentially the same state mechanically: they both mean the forces are perfectly balanced. If a car is cruising down the motorway at a steady 70 mph, the driving force from the engine is exactly balanced by the resistive forces (air resistance and friction). There is no resultant force.

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The core equation: Newton's Second Law

If the forces aren't balanced, the object's velocity will change. It will accelerate.

Newton's Second Law: The acceleration of an object is proportional to the resultant force acting on it and inversely proportional to its mass.

For situations where the mass of the object is constant (which applies to almost all A-Level mechanics problems, unless you are dealing with rockets burning fuel), we write this as a famous equation:

$$F=ma$$

Where:

• $F$ is the resultant force in newtons (N).
• $m$ is the mass in kilograms (kg).
• $a$ is the acceleration in metres per second squared (${m\; s}^{-2}$).

Free-body diagrams

To correctly find the resultant force, you should draw a free-body diagram. This is a simplified sketch showing only the object in question and the forces acting directly on it.

We usually draw the object as a simple box or a dot. The forces are drawn as arrows pointing away from the centre of the object.

In the diagram above, the vertical forces (Weight and Normal Contact Force) balance out, so there is no vertical acceleration. Horizontally, the Driving Force is larger than the Friction, creating a resultant force to the right. Therefore, the car accelerates to the right.

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Action and reaction: Newton's Third Law

Newton's Third Law is often poorly understood. You have probably heard the phrase: "Every action has an equal and opposite reaction." While catchy, this phrasing can be dangerous in physics exams because it leaves out crucial details.

Newton's Third Law: If body A exerts a force on body B, then body B exerts a force of the same type, equal in magnitude and opposite in direction, on body A.

For two forces to be a genuine "Newton's Third Law pair", they must meet four strict criteria:

1. They must act on two different bodies.
2. They must be strictly equal in magnitude (size).
3. They must act in opposite directions.
4. They must be forces of the same type (e.g., both gravitational, or both electrostatic, or both contact forces).

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Verifying Newton's Second Law in the lab

You will likely carry out a core practical to verify $F=ma$. This is usually done using a trolley on a track, pulled by a falling mass hanging over a pulley.

By keeping the total mass of the system ($m$) constant, you can vary the pulling force ($F$) by moving small slotted masses from the trolley to the weight hanger. You then use light gates or a ticker-timer to measure the resulting acceleration ($a$).

When you plot a graph of Acceleration against Resultant Force, you should get a straight line passing through the origin. This proves that $a\propto F$, verifying Newton's Second Law.

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