Newton’s Laws of Motion

Why do you lurch forward when a bus brakes hard? Why does a small car surge away from the lights while a loaded van pulls off sluggishly? Why does a rocket climb skyward when its exhaust gases blast downward? The answers lie in the three laws of motion set out by Isaac Newton more than three hundred years ago — laws so dependable that they still guide everything from car safety to spaceflight. This lesson, part of Topic P2 (Forces) of OCR Gateway Combined Science A, brings all three together: Newton's First Law (balanced forces and inertia), Newton's Second Law (the equation $F = ma$ linking force, mass and acceleration), and Newton's Third Law (forces coming in equal and opposite pairs).

By the end of this lesson you should be able to state Newton's First Law and explain it using resultant force, describe inertia, state Newton's Second Law and use and rearrange $F = ma$ , state Newton's Third Law, and identify action–reaction force pairs.

This lesson is AO1 for stating the three laws and describing inertia, strongly AO2 for applying and rearranging $F = ma$ , and AO3 when you analyse a situation to identify a correct action–reaction pair or explain a motion using the resultant force.

Newton’s First Law

Newton's First Law states that an object will stay at rest, or keep moving at a constant velocity (constant speed in a straight line), unless a resultant force acts on it. In other words, an object's motion only changes if there is a non-zero resultant force.

The law has two halves, depending on the object's starting state:

A stationary object stays stationary if the resultant force on it is zero (its forces are balanced). A book resting on a table stays put because its weight down is balanced by the normal contact force up.
A moving object keeps moving at a constant velocity if the resultant force is zero. A car driving at a steady speed in a straight line has its driving force balanced by drag, so it neither speeds up nor slows down.

So a zero resultant force does not mean "no motion" — it means "no change in motion". To change an object's speed or direction, a resultant force is always needed.

A common misconception, going back to the ancient Greeks, is that a constantly applied force is needed just to keep something moving. In fact, once moving, an object would carry on forever at constant velocity if no resultant force acted. The reason a rolling ball slows and stops on Earth is friction (and air resistance) — a resultant force opposing its motion. Remove those forces (as in deep space) and the object would keep going indefinitely.

Exam Tip: A common misconception (dating back to the ancient Greeks) is that a moving object needs a constant forward force to keep going. Newton's First Law says otherwise: with zero resultant force, an object stays at rest or continues at constant velocity. A resultant force is needed to change motion, not to maintain it.

Inertia

Inertia is the tendency of an object to keep doing what it is already doing — to stay at rest if it is at rest, or to keep moving if it is moving. It is why you are thrown forward when a car brakes sharply: your body "wants" to keep moving at the old speed, and only the seatbelt provides the force to slow you with the car. Inertia is also why a massive object is hard to get moving, and once moving is hard to stop.

The more mass an object has, the more inertia it has, and so the harder it is to change its motion (to start it, stop it, speed it up, slow it down or change its direction). This is why a loaded lorry needs a much bigger force to accelerate or to stop than a bicycle does.

Exam Tip: Inertia is the tendency to resist a change in motion; the greater the mass, the greater the inertia. Inertia is a property of an object, not a force — never write "the force of inertia".

Newton’s Second Law

Newton's Second Law states that the acceleration of an object is proportional to the resultant force acting on it, and inversely proportional to its mass. In words: a bigger force gives a bigger acceleration, but a bigger mass gives a smaller acceleration for the same force. The law is written as the equation:

$F = ma$

where $F$ is the resultant force (in $\text{N}$ ), $m$ is the mass (in $\text{kg}$ ) and $a$ is the acceleration (in $\text{m/s}^2$ ).

Two points are worth stressing. First, $F$ is the resultant (overall) force — if several forces act, you must work out the resultant first. Second, the acceleration is in the same direction as the resultant force: push something to the right and it accelerates to the right.

The equation captures both parts of the law at once:

for a fixed mass, doubling the force doubles the acceleration (acceleration ∝ force);
for a fixed force, doubling the mass halves the acceleration (acceleration ∝ 1/mass).

The equation rearranges to make the mass or the acceleration the subject:

$F = ma \qquad a = \dfrac{F}{m} \qquad m = \dfrac{F}{a}$

A formula triangle is a useful aid: cover the quantity you want, and the triangle shows the calculation.

Force sits at the top, so $F = ma$ ; mass and acceleration sit side by side at the bottom, so $a = \dfrac{F}{m}$ and $m = \dfrac{F}{a}$ .

Worked Example 1 — Finding the force

A car of mass $1200 \text{ kg}$ accelerates at $2 \text{ m/s}^2$ . Calculate the resultant force needed.

Step 1 — write the equation: $F = ma$ .

Step 2 — substitute: $F = 1200 \times 2$ .

Step 3 — calculate: $F = 2400 \text{ N}$ .

Answer: the resultant force is $2400 \text{ N}$ .

Worked Example 2 — Finding the acceleration

A resultant force of $6000 \text{ N}$ acts on a van of mass $1500 \text{ kg}$ . Calculate its acceleration.

Step 1 — rearrange for acceleration: $a = \dfrac{F}{m}$ .

Step 2 — substitute: $a = \dfrac{6000}{1500}$ .

Step 3 — calculate: $a = 4 \text{ m/s}^2$ .

Answer: the acceleration is $4 \text{ m/s}^2$ .

Worked Example 3 — Finding the mass

A resultant force of $200 \text{ N}$ gives a trolley an acceleration of $2.5 \text{ m/s}^2$ . Calculate the mass of the trolley.

Step 1 — rearrange for mass: $m = \dfrac{F}{a}$ .

Step 2 — substitute: $m = \dfrac{200}{2.5}$ .

Step 3 — calculate: $m = 80 \text{ kg}$ .

Answer: the mass of the trolley is $80 \text{ kg}$ .

Worked Example 4 — Using the resultant force

A box of mass $5 \text{ kg}$ is pushed with a force of $30 \text{ N}$ while friction of $10 \text{ N}$ opposes the motion. Calculate the acceleration.

Step 1 — find the resultant force first: $F = 30 - 10 = 20 \text{ N}$ .

Step 2 — rearrange for acceleration: $a = \dfrac{F}{m}$ .

Step 3 — substitute and calculate: $a = \dfrac{20}{5} = 4 \text{ m/s}^2$ .

Answer: the acceleration is $4 \text{ m/s}^2$ . Note that you must use the resultant force ( $20 \text{ N}$ ), not the applied force ( $30 \text{ N}$ ).

Exam Tip: $F = ma$ uses the resultant force in newtons, mass in kilograms, and acceleration in $\text{m/s}^2$ . When other forces (like friction) act, find the resultant force first, then put it into $F = ma$ . Convert any mass given in grams to kg before substituting.

The mass in $F = ma$ is really a measure of inertia: because $a = \dfrac{F}{m}$ , an object with a large mass gets only a small acceleration for a given force, so it strongly resists changes in its motion. This is exactly why a fully loaded lorry, with its huge mass, needs a very large force to accelerate or to brake, while a bicycle responds to a small force.

Newton’s Third Law

Newton's Third Law states that whenever two objects interact, they exert equal and opposite forces on each other. The forces are often described as action and reaction: for every action force, there is an equal and opposite reaction force.

The crucial detail — and the one examiners test hardest — is that the two forces in a Newton's Third Law pair act on different objects. If object A pushes on object B, then object B pushes back on object A with a force that is:

equal in size;
opposite in direction;
of the same type (e.g. both gravitational, or both contact);
but acting on the other object.

Newton’s Laws of Motion

Newton’s Laws of Motion

Newton’s First Law

Inertia

Newton’s Second Law

Worked Example 1 — Finding the force

Worked Example 2 — Finding the acceleration

Worked Example 3 — Finding the mass

Worked Example 4 — Using the resultant force

Newton’s Third Law

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