A push, a pull, and an ancient puzzle
You use forces all day without naming them: you push a door, pull a drawer, lean on a wall, carry a bag. Physics starts by taking that everyday feeling and sharpening it. A force is simply a push or a pull that one object exerts on another. It always has a size and a direction — so a force is a vector, drawn as an arrow whose length is the strength and whose point shows which way it acts.
Here is the puzzle that stumped humanity for two thousand years. Roll a ball across the floor and it slows and stops. Aristotle concluded that motion needs a continuous cause — take the push away and motion dies. It feels obviously true. It is also completely wrong, and seeing why is the first great leap in mechanics.
Forces are vectors — add them into the net force
An object rarely feels just one force. A book on a table feels gravity pulling down and the table pushing up. In a tug-of-war the rope feels pulls from both teams. What actually governs motion is the single net force (淨力): the vector sum of every force acting on the object.
The net force is the vector sum of all individual forces on the object.
When two equal, opposite pulls cancel, the net force is zero even though forces are present — the tug-of-war stalemate. Use the widget below to push a block around: add or remove forces and watch how only their sum decides what happens next.
Newton's first law: the law of inertia
Newton swept Aristotle aside with one sentence. Newton's first law: an object at rest stays at rest, and an object in motion keeps moving in a straight line at constant speed, unless a nonzero net force acts on it. Constant velocity is the natural, effortless state — not rest.
The property that makes an object resist any change in its motion is inertia, and the amount of it is measured by mass. A loaded truck has more inertia than a bicycle: harder to start, harder to stop. In equilibrium, when the forces balance, the first law is captured by a single condition.
Zero net force means constant velocity (which includes staying at rest): this is translational equilibrium.
Where the law holds: inertial frames
There is a subtlety. Stand in a bus that suddenly brakes and you lurch forward, seemingly pushed by nothing. In that accelerating frame the first law appears to fail. A frame in which the first law does hold — where a force-free object really does coast in a straight line — is called an inertial reference frame. The lurch is just your inertia carrying you forward while the bus decelerates beneath you.
The first law tells us when motion changes (whenever the net force is nonzero) but not yet by how much. Pin down that quantitative link — force, mass, and acceleration — and you can predict the motion of almost anything. That is Newton's second law, and it is next.