Newton's Laws of Motion

Newton's first law — an object stays at rest, or keeps moving at a constant velocity in a straight line, unless a resultant force acts on it.

This is less obvious than it sounds. It says that motion needs no force to keep it going — only a change in motion does. A puck sliding on ice keeps going because almost nothing opposes it, not because something keeps pushing.

Newton's second law — the acceleration of an object is proportional to the resultant force and inversely proportional to its mass:

F = m a

with force in newtons, mass in kilograms and acceleration in m/s². This is the equation to reach for whenever a question gives you two of the three.

Newton's third law — for every action there is an equal and opposite reaction. More precisely: if A exerts a force on B, then B exerts an equal and opposite force on A.

The third-law trap. The two forces in a third-law pair act on different objects, so they never cancel each other out. A book's weight and the table's normal contact force are not a third-law pair — they act on the same object and happen to be equal because the book is in equilibrium. The third-law partner of the book's weight is the pull of the book on the Earth.

Mass and weight are different quantities:

Mass — the amount of matter in an object, in kilograms. It is the same everywhere.

Weight — the force of gravity on that mass, in newtons:

W = m g

where g is the gravitational field strength, about 10 N/kg on Earth. A 60 kg student has a mass of 60 kg on the Moon as well as on Earth, but weighs about 600 N here and about 100 N there.

Example: a 1200 kg car with a resultant driving force of 3600 N accelerates at F/m = 3600 ÷ 1200 = 3 m/s². Double the mass and the same force gives half the acceleration, which is what "inversely proportional to mass" means in practice.