noninertial

Noninertial refers to a reference frame that is accelerating relative to an inertial frame. Inertial frames are those moving at constant velocity in straight lines, in which Newton's laws hold in their simplest form. In noninertial frames, Newton's laws do not apply without modification unless fictitious forces are introduced to account for the frame's acceleration.

A fictitious force is an apparent force that arises from the acceleration of the reference frame rather than from a physical interaction. If a frame accelerates with a0, the relation between observed and real motion is a_inertial = a_noninertial + a0, and a fictitious force F_fict = -m a0 acts on a body of mass m in that frame. Common examples include the centrifugal force in a rotating frame and the Coriolis force that affects moving objects in rotating systems. The Euler force appears when the rotation rate itself changes with time.

Noninertial frames are ubiquitous in everyday life. A spinning playground carousel, a car turning a corner, or an elevator that accelerates upward all define noninertial frames in which observers must include fictitious forces to apply Newtonian dynamics correctly. The Earth itself is effectively noninertial due to its rotation and orbital motion, leading to measurable effects in meteorology and gyroscope experiments.

In the context of relativity, the concept connects to the equivalence principle: locally, a gravitational field is indistinguishable from acceleration, so gravity can be treated as a fictitious force in a noninertial frame. Nevertheless, in general relativity gravity is not a force but a manifestation of spacetime geometry, and locally free-falling frames serve as inertial frames.