Isaac Newton's three laws, published in 1687, describe how forces change motion. They work extremely well for everyday speeds and sizes, which is why they are the foundation of introductory physics.
First law: inertia
An object at rest stays at rest, and an object in motion keeps moving at the same speed in the same direction, unless a net force acts on it. A hockey puck glides a long way on ice because there is very little friction to slow it down. Motion does not need a force; changes in motion do.
Second law: F = ma
The net force on an object equals its mass times its acceleration: Fnet = m·a, with force in newtons (N), mass in kilograms, and acceleration in m/s².
- A 2 kg cart pushed with a 10 N net force:
a = 10 / 2 = 5 m/s². - A 1,200 kg car accelerating at 2.5 m/s² needs
F = 1,200 × 2.5 = 3,000 Nof net force.
With friction: you push a 20 kg box with 100 N and friction resists with 40 N. The net force is 100 − 40 = 60 N, so a = 60 / 20 = 3 m/s².
Third law: action and reaction
When object A pushes on object B, B pushes back on A with a force equal in size and opposite in direction. A swimmer pushes water backward and the water pushes the swimmer forward. These paired forces never cancel each other, because they act on different objects.
Mass versus weight
Mass is the amount of matter (kg) and does not change from place to place. Weight is the gravitational force on that mass: W = m·g, with g ≈ 9.8 m/s² near Earth's surface. A 50 kg student weighs about 50 × 9.8 = 490 N on Earth, but only about a sixth of that on the Moon.
Common mistakes
- Using one applied force in F = ma instead of the net force.
- Thinking a moving object must have a force pushing it forward.
- Cancelling third-law pairs as if they acted on the same object.