Inertial and Non-Inertial Frames of Reference

A frame of reference is simply a set of coordinates with a chosen origin used to describe the position of objects. Whether an object is 'in motion' depends entirely on which frame you use: a passenger standing on a railway platform sees a departing train as moving, while a passenger inside that train sees the platform (and the standing observer) as moving backward -- both descriptions are correct in their own frame.

An INERTIAL FRAME of reference is, in its simplest sense, any frame in which Newton's first law holds true: if there is no net force on a body, it shows no acceleration in that frame (it moves with constant velocity, possibly zero). A NON-INERTIAL frame is one in which a body can show an acceleration even though no real net force acts on it.

Illustration: imagine sitting inside a car with opaque windows, so you cannot see outside, with a pendulum hanging inside (not swinging). If the car suddenly starts moving, you feel a jerk (an acceleration) even though no real force is acting on you -- during this phase the car is a NON-inertial frame, and the pendulum string tilts away from vertical though not oscillating. Once the car settles into constant velocity, the jerky feeling disappears, the pendulum hangs vertical again, and the car becomes (for practical purposes) an inertial frame once more.

Measurements made in one inertial frame can be converted to another inertial frame using a simple velocity transformation (the relative velocity between the two frames). …