Normal Force
Definition
The push a surface exerts on an object resting on it, always directed perpendicular (normal) to the surface.
Symbol: · Unit: N
Technical definition
A contact force arising from electromagnetic repulsion between surface atoms. Denoted N or F_N, directed perpendicular to the contact surface. On a horizontal surface with no other vertical forces, N = mg; on an incline, N = mg·cosθ.
Example
You feel the normal force as the floor pushing up on your feet. On a bathroom scale, it is the normal force — not gravity directly — that the scale measures.
The normal force is not always equal to mg. On an incline it is mg·cosθ, in a rising elevator it is m(g+a), and it adjusts to whatever is needed to prevent the object passing through the surface — it is a reactive force, not a fixed one.