Newton's Laws of Motion

Three rules for everything that moves

In 1687 Isaac Newton published the Principia, which set out three laws of motion.^[2] They connect forces (pushes and pulls with a size and a direction^[4]) to the way objects move.

The first law: inertia

An object at rest remains at rest, and an object in motion remains in motion at constant speed and in a straight line, unless acted on by an unbalanced force.^[1]

This tendency of objects to keep doing what they’re already doing is called inertia.^[2] It sounds obvious for things at rest, but less so for moving things: a rolling ball on Earth does slow down and stop. The first law says that’s because an unbalanced force acts on it,^[1] such as friction, which always opposes motion between surfaces.^[5]

Galileo had already seen part of this. He realised that a force is needed not just to start something moving, but also to slow it down, stop it, speed it up or change its direction.^[3]

The second law: force, mass and acceleration

The second law says that an object’s acceleration depends on its mass and on the force applied. For equal forces, a heavier object speeds up less than a lighter one.^[1] It’s usually written as:

F = m × a (force = mass × acceleration)^[1]

Newton put it as: the change of motion of a body is proportional to, and in the direction of, the force acting on it.^[2] Force is measured in newtons: one newton is the force that gives a 1 kg mass an acceleration of 1 metre per second, every second.^[4]

Worked example (optional). Push a 20 kg crate on wheels with an unbalanced force of 40 N. Rearranging F = m × a gives a = F ÷ m = 40 ÷ 20 = 2 m/s². Every second, the crate goes 2 m/s faster. Push the same way on a 40 kg crate and it only gains 1 m/s each second.

It’s the net force that counts, meaning all the forces on the object added together.^[4] If your push is exactly cancelled by friction, the net force is zero and nothing accelerates.

The third law: action and reaction

Whenever one object pushes on another, the second pushes back on the first with a force of equal size in the opposite direction.^[1]

Forces always come in pairs: whenever one object exerts a force on another, the second exerts an equal and opposite force on the first.^[1] The two forces act on different objects, which is why they don’t cancel each other out.

This is how jet engines and wings work. An engine produces thrust by pushing hot gas backwards, and the gas pushes the engine forwards. A wing deflects air downward, and the air pushes the wing up.^[1]

The laws in flight

An airplane shows all three laws at once:^[1]

• First law: an airplane’s motion stays steady until the pilot changes the throttle setting.
• Second law: the aerodynamic forces and the engine’s thrust decide how the airplane accelerates.
• Third law: the engine’s thrust and the wing’s lift both come from pushing air or gas in the opposite direction.

Common misconceptions

• “Moving things need a force to keep moving.” No, they need a force to change their motion. A moving object keeps moving at a constant speed in a straight line unless an unbalanced force acts on it.^[1]
• “Action and reaction cancel out.” They act on different objects, so each object feels only one of them.^[1]
• “A force is needed just to keep something moving at a steady speed.” A force is needed to change speed or direction. At constant velocity the forces on an object are balanced.^[1]

Where to go next

Newton’s laws plus his law of Gravity explain the orbits of the planets. Follow the trail From falling apples to satellites to see how.