What is the principle of inertia?

A simple but powerful idea

The principle of inertia, also called Newton's first law, states that every body persists in its state of rest or uniform rectilinear motion, unless external forces act on it and force it to change.

In other words, an object does not change speed (in magnitude and direction) on its own. An external cause is needed to make it accelerate, slow down, or change direction.

Modern formulation

A system is said to be pseudo-isolated if the forces acting on it cancel out, that is, if their vector sum is zero: sum F = 0 vector. The principle of inertia is then stated as follows:

If a system is isolated or pseudo-isolated, then its center of inertia is either at rest or moving with uniform rectilinear motion (constant speed in magnitude and direction).

Concrete example

A hockey puck sliding on very smooth ice continues almost indefinitely in a straight line at constant speed, because friction is very weak. On a normal table, friction slows the puck down: it is not the principle of inertia that is wrong, but rather that the puck is no longer isolated.

Situation	Forces cancel out?	Motion
Puck on smooth ice	Yes (nearly)	Uniform rectilinear
Puck on rough table	No	Slows down
Book resting on a table	Yes	At rest

Key takeaway

Constant speed means 0 m/s (rest) or a nonzero value in a straight line, with no change in direction. The principle of inertia connects an object's state of motion to the balance of forces acting on it.