The Normal Force

Set a book on a table and the table pushes up on it. That push exists because the table resists being compressed. At the atomic level the surface behaves like an incredibly stiff spring: the weight of the book squeezes the surface down by an amount too tiny to see, and the surface pushes back with exactly the force needed to stop further sinking. That reaction force, always perpendicular to the surface, is the normal force. The word normal here means perpendicular, not ordinary.

Because the normal force is a response, not a fixed quantity, it equals the object's weight only in the simplest case: a flat surface, nothing else pushing or pulling vertically. Add another vertical force and the normal force changes to keep the object in equilibrium. Push straight down on a book with your hand and the table must now support the book's weight plus your push, so the normal force grows. Lift up on the book instead and the normal force shrinks, since the table has less work to do. The rule is always the same: add up every vertical force and solve for whatever normal force makes the net force zero, given no vertical acceleration.

This sets up everything else in the unit. Normal force feeds directly into friction, since friction's maximum strength depends on how hard the surfaces press together. On inclines the normal force tilts with the surface and no longer equals weight at all. In circular motion, like a car cresting a hill, the normal force can drop below weight because some of gravity's pull is now busy supplying centripetal acceleration instead of being cancelled.