Hooke's law

Lore & Background

The law is the fundamental principle behind the spring scale, manometer, galvanometer, and balance wheel of the mechanical clock.

Reader's Guide

Hooke's law is a first-order linear approximation to the real response of springs and other elastic bodies to applied forces. It holds for many situations where an elastic body is deformed, but fails once forces exceed certain limits, as no material can be compressed beyond a minimum size or stretched beyond a maximum size without permanent deformation. The modern theory of elasticity generalizes Hooke's law to say that strain is proportional to stress, with the proportionality factor becoming a tensor for complex objects. This generalization allows deduction of the relation between strain and stress for complex objects in terms of intrinsic material properties, such as a homogeneous rod with uniform cross section behaving like a simple spring with stiffness directly proportional to its cross-section area and inversely proportional to its length.

Did You Know?

• The law applies to torsional springs, with torque proportional to angular displacement.