The principle of inertia

Here is the statement, followed by an explanation of why it is counterintuitive:

If the forces acting on an object cancel each other out, then that object is either at rest or moving in a straight line at a constant speed — and vice versa.

‘Uniform rectilinear’ means: in a straight line, at a constant speed.

What’s puzzling

Intuition tells us that you have to keep pushing for an object to keep moving forward. Stop pedalling, and the bike stops: so surely a force is needed to maintain the motion, isn’t it?

No. The bike stops because forces are acting on it: friction and air resistance. These forces no longer balance each other out.

Remove these frictions — on ice, or in the vacuum of space — and the object continues indefinitely. The Voyager probes have had no engines since 1977 and are still travelling on.

The correct formulation

A force does not sustain motion. A force changes motion.

forces compensees   ->  vitesse constante (possibly zero)
forces non compensees ->  la vitesse change

This shift is one of the major turning points in the history of science. For twenty centuries, Aristotelian physics asserted the opposite, and this seemed obvious to everyone.

A surprising example

Does a car taking a bend at a constant speed experience forces that cancel each other out?

No. Its speed does not change in magnitude, but its direction does. The motion is not rectilinear: the forces therefore do not balance each other out. It is the grip of the tyres that provides the force needed to take the bend — and on black ice, this force disappears, and the car continues straight ahead. Exactly what the principle predicts.

The principle of inertia is also what propels you forwards during sudden braking: your body carries on moving forwards whilst the car slows down. The seatbelt is precisely the force that was missing.