Newton’s three laws

A 1,200 kg car needs a net force of 3,600 N to speed up at 3 m/s².

First law: things keep doing what they are doing

Slide a book across a table and it stops. For a long time people concluded that moving things naturally come to rest, and that keeping something moving needs a constant push. Galileo saw it differently. In Two New Sciences (1638) he imagined a ball rolling on a perfectly smooth, endless horizontal plane and argued that it would keep going forever. The book stops because friction is acting on it, not because stopping is natural.

Isaac Newton made this the first of three laws in his Principia of 1687. In the wording used by OpenStax: a body at rest remains at rest, or, if in motion, remains in motion at a constant velocity unless acted on by a net external force. This tendency to keep doing the same thing is called inertia, and mass is the measure of it. A full shopping trolley is harder to start and harder to stop than an empty one because it has more inertia. Seat belts exist because of the first law: when a car stops suddenly, your body keeps moving forward until something pushes back.

Second law: F = m a

The second law says how much an object accelerates when the forces on it do not balance. The acceleration is in the direction of the net force, proportional to it, and inversely proportional to the mass: a = F_net ÷ m, more often written F_net = m a. Push a 2 kg cart with a net force of 10 N and it accelerates at 5 m/s². Push a 1,200 kg car to make it accelerate at 3 m/s² and you need 3,600 N. The net force is what counts: if you push a 5 kg box with 50 N while friction pushes back with 20 N, the net force is 30 N and the box accelerates at 6 m/s².

The second law also explains why all objects fall with the same acceleration. A heavier object feels a bigger gravitational force, but it also has more mass to accelerate, and the two effects cancel exactly: a = m g ÷ m = g.

Third law: forces come in pairs

Whenever one object pushes or pulls on a second, the second pushes or pulls back on the first with a force of the same size in the opposite direction. A swimmer pushes water backwards and the water pushes the swimmer forwards. A rocket pushes hot gas out of its nozzle and the gas pushes the rocket up; it needs no air to push against, which is why rockets work in space. When you walk, your foot pushes the ground backwards and the ground pushes you forwards.

The two forces in a pair act on different objects, so they never cancel each other. That is the usual trap. When a horse pulls a cart, the cart pulls back on the horse equally hard, yet they still move, because whether the horse speeds up depends on all the forces acting on the horse, including the ground pushing on its hooves.

You can see all three laws in one kick of a football. Before the kick the ball sits still, because nothing gives it a net force (first law). During the brief contact your foot pushes the ball, and the harder the push, the bigger the ball’s acceleration (second law). At the same moment the ball pushes back on your foot just as hard, which you feel as a thump on your toes (third law). After the ball leaves your foot, only gravity and air act on it, and its path is the projectile motion from the Motion course.