Newton's Second Law

Newton's second law is the engine of mechanics: the net force on an object equals its mass times its acceleration, F = ma. Read it as a recipe for acceleration. Add up the forces, divide by the mass, and you have how the velocity is changing, in both size and direction. Two details trip people up before the algebra even starts. The law takes mass in kilograms, not weight in newtons, so a value in newtons has to become a mass before it goes on the right side. And the forces you add up come from a free-body diagram, not from habit: the normal force, in particular, is the perpendicular push the surface supplies, set by the free-body diagram and the motion, which is rarely just mg.

Three habits bleed points here. One treats mass and weight as the same number, dropping the factor of g so a 20 N weight becomes a 20 kg mass. Another reaches for N = mg as a fixed identity, when the normal force has to come from the free-body diagram and shifts on an incline, in an accelerating elevator, or whenever another vertical force is in play. The last is inherited from the first law: aiming the net force along the velocity instead of the acceleration. F = ma settles all three at once — a vector equation about acceleration, written in terms of mass.