inertie

Inertia, or inertie, is the property of matter to resist changes in its state of motion or rest. In classical physics, inertia is quantified by mass, and the term derives from the Latin inertia, meaning laziness or idleness. The concept is central to Newton’s laws and the description of motion.

Linear inertia states that a body at rest remains at rest, and a body in uniform straight-line motion continues with the same speed and direction unless acted upon by a net external force. This principle holds in inertial reference frames—frames in which Newton’s laws are valid without additional forces.

Mathematically, inertia is linked to the relation between force and acceleration. The net force acting on an object equals the rate of change of its momentum, F = dp/dt. For constant mass, F = m a, showing that acceleration is proportional to applied force. The proportionality constant is the inertial mass, experimentally found to equal the gravitational mass, a fact that underpins the equivalence principle.

Rotational inertia, or moment of inertia, extends the concept to rotation. It quantifies a body's resistance to changes in its rotational motion and depends on how mass is distributed relative to the rotation axis. For a discrete system, I = Σ m_i r_i^2; for continuous bodies, I = ∫ r^2 dm. Common results include I = 1/2 M R^2 for a solid disk and I = 1/3 M L^2 for a rod about one end.

Non-inertial frames, which accelerate, require fictitious forces (such as centrifugal or Coriolis forces) to account for observed motion. In social sciences, inertie describes resistance to change in systems, institutions, or cultural norms, a usage distinct from the physical sense yet related in metaphor.