Newton's Laws of Motion

Newton's three laws form the foundation of classical mechanics, describing how objects move under the influence of forces.

The Three Laws

First Law (Law of Inertia)

An object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted on by a net external force.

Second Law

Newton's Second Law

\vec{F} = m\vec{a}

Net force equals mass times acceleration. F in Newtons (N), m in kg, a in m/s².

Third Law

For every action, there is an equal and opposite reaction.

$\vec{F}_{AB} = -\vec{F}_{BA}$

Free body diagram: block on surface with weight, normal force, and applied force

A 5 kg box is pushed with a net force of 20 N. Find acceleration.

$a = F/m = 20/5 = 4 \text{ m/s}^2$

Note

Weight is a force: $W = mg$ . On Earth, $g \approx 9.81 \text{ m/s}^2$ .

Real world: seatbelts — First Law

When a car travelling at 60 km/h brakes suddenly, the car decelerates — but by the First Law, passengers tend to keep moving forward at 60 km/h. Without a seatbelt, a passenger would continue forward and hit the windscreen. The seatbelt provides the backward (decelerating) force needed to slow the passenger at the same rate as the car.

Real world: lorry vs. sports car — Second Law

A sports car has mass 1 200 kg; a loaded lorry has mass 20 000 kg. If both have the same net forward force of 12 000 N:

Sports car: $a = 12\,000 / 1\,200 = 10 \text{ m/s}^2$

Lorry: $a = 12\,000 / 20\,000 = 0.6 \text{ m/s}^2$

The same force produces far less acceleration in the heavier vehicle. This is why lorries need much more powerful engines to achieve useful acceleration from traffic lights.

Real world: rocket exhaust — Third Law

A rocket engine burns fuel and expels exhaust gases downward at high speed (action). By the Third Law, the exhaust gases exert an equal and opposite force on the rocket upward (reaction) — this is thrust. Crucially, the rocket does not need air to push against; the reaction works even in a vacuum, which is why rockets can travel in space.

Tip

Where do you see Newton's Laws? Seatbelts (1st Law), pushing a supermarket trolley (2nd Law), swimming strokes (3rd Law), airbags in cars, football kicks, and spacecraft launches — all can be explained using Newton's three laws.

Practice Problems

A 10 kg object accelerates at 5 m/s². What net force acts on it?

Show answer

F = ma = 10 × 5 = 50 N

A force of 30 N produces acceleration of 6 m/s². What is the mass?

Show answer

m = F/a = 30/6 = 5 kg