Newton's Laws of Motion Explained, With Examples

Newton's laws of motion — three laws describing how forces change (or fail to change) the way objects move — are the foundation of classical mechanics. The first law says an object keeps its velocity unless a force acts on it. The second law says force equals mass times acceleration, F = ma. The third law says every force has an equal and opposite reaction force. Together they explain everything from why a seatbelt matters to why a rocket can accelerate in empty space.

What is Newton's first law of motion?

Newton's first law (the law of inertia) says an object at rest stays at rest, and an object moving stays moving at a constant velocity in a straight line, unless an unbalanced force acts on it. "Velocity" here matters: speed and direction both have to stay the same, so a car going round a bend at constant speed is still accelerating, because its direction is changing.

• Inertia is an object's resistance to a change in its motion — the more mass something has, the more inertia it has.
• A ball rolling across a frictionless floor never slows down on its own; it's friction and air resistance, not some "natural" tendency to stop, that brings real balls to rest.
• This is why a passenger without a seatbelt keeps moving forward when a car suddenly brakes — their body has no force acting on it to slow it down at the same rate as the car.

What is Newton's second law of motion?

Newton's second law says the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass:

F = ma

where F is the net force (newtons, N), m is mass (kg), and a is acceleration (m/s²). Doubling the force doubles the acceleration; doubling the mass halves it for the same force.

Worked example: pushing a trolley

A shopping trolley has a mass of 15 kg. You push it with a steady net force of 30 N. What is its acceleration?

a = F / m = 30 / 15 = 2 m/s²

If the trolley were loaded up to 45 kg and you pushed with the same 30 N force, the acceleration would drop to 30 / 45 ≈ 0.67 m/s² — the same force moves a heavier trolley more slowly.

Worked example: finding the force

A 1200 kg car accelerates from rest to 20 m/s in 8 seconds. What net force does this need?

First find the acceleration: a = Δv / Δt = 20 / 8 = 2.5 m/s²

Then F = ma = 1200 × 2.5 = 3000 N

What is Newton's third law of motion?

Newton's third law says that for every action force, there is an equal and opposite reaction force: if object A exerts a force on object B, object B exerts an equal force back on object A, in the opposite direction. These two forces act on different objects at the same time, which is why they don't cancel out and leave everything motionless.

• A swimmer pushes backward on the water; the water pushes the swimmer forward with equal force.
• A rocket engine pushes exhaust gas downward; the gas pushes the rocket upward — this works even in the vacuum of space, because it needs no air to push against, only its own exhaust.
• Standing on the ground, you push down on the floor with your weight; the floor pushes up on you with an equal normal force, which is why you don't fall through it.

How do the three laws work together?

A common exam example shows all three laws at once: a book resting on a table.

Law	What it explains here
First	The book stays still because the forces on it are balanced
Second	Net force on the book is zero, so F = ma gives zero acceleration
Third	The book's weight pushes down on the table; the table pushes up on the book with an equal normal force

Note that the book's weight and the table's normal force are not a Newton's third law pair, even though they're equal and opposite — a third law pair always acts on two different objects (book-on-table and table-on-book), never on the same object twice.

Common mistakes with Newton's laws

• Confusing balanced forces with no forces. The first law needs zero net force, not zero forces — a book on a table has two forces acting on it (weight and normal force) that happen to cancel out.
• Mixing up a third law pair with balanced forces on one object. A third law pair acts on two different objects; balanced forces act on the same object.
• Forgetting mass and weight are different. Mass (kg) is how much matter an object has; weight (N) is the force of gravity on that mass, W = mg. F = ma always uses mass, not weight.
• Ignoring direction. Force and acceleration are vectors — a force opposing motion causes deceleration, which is just a negative acceleration.

For how forces combine when they don't all point the same way, see vectors explained. To see conservation laws applied to collisions, see conservation of momentum.

Frequently asked questions

What is Newton's second law formula?

Newton's second law is F = ma, where F is the net force in newtons, m is mass in kilograms, and a is acceleration in metres per second squared. It means the acceleration of an object depends on both the size of the net force acting on it and how much mass it has — a bigger force or a smaller mass both produce a bigger acceleration.

Why doesn't a rocket need air to push against?

A rocket's third law pair is between the rocket and its own exhaust gas, not between the rocket and the surrounding air. The engine pushes burning gas out backwards, and the gas pushes the rocket forwards with equal force — this works just as well in the vacuum of space, which is why rockets (not propellers or jets) are used for space travel.

What is an unbalanced force?

An unbalanced force is a net force that isn't cancelled out by other forces acting on the same object, so it causes a change in velocity (an acceleration). If all the forces on an object sum to zero, the forces are "balanced" and the object's velocity stays constant, per Newton's first law.

How is weight different from mass?

Mass is the amount of matter in an object, measured in kilograms, and doesn't change with location. Weight is the force of gravity pulling on that mass, measured in newtons, calculated as W = mg (g ≈ 9.8 m/s² on Earth). An astronaut has the same mass on the Moon as on Earth, but weighs about a sixth as much, because the Moon's gravity is weaker.

Try it yourself

Open Forces & Newton's Laws and add several forces to the same object. Watch how the free body diagram and the resulting acceleration change as you adjust each force's size and direction — then try making the forces balance exactly, and see the object move at constant velocity just as the first law predicts.