inertialframe

An inertial frame is a reference frame in which a free particle moves with constant velocity if no net external forces act. In such a frame Newton's first law holds without invoking fictitious forces, and the equations of motion take their simplest form.

Under classical (Newtonian) mechanics, inertial frames are related by Galilean transformations: x' = x - vt, t' = t. Acceleration is invariant under these transformations, so Newton’s laws have the same form in all inertial frames.

Real laboratories on Earth are only approximately inertial, since Earth is rotating and orbiting the Sun. In non-inertial frames, fictitious or pseudo-forces appear, such as the centrifugal and Coriolis forces, which are needed to apply Newton's laws correctly within that frame.

In special relativity, inertial frames are frames moving at constant velocity relative to each other, and the laws of physics have the same form in all inertial frames. In general relativity, global inertial frames do not exist in curved spacetime; locally, freely falling frames approximate inertial behavior.

The concept is central to mechanics, astronomy, and engineering, providing a simple description of motion and a basis for transforming observations between observers in relative motion.