5.14:
Inertial Frames of Reference
The frame of reference in which Newton's laws are valid is called an inertial frame of reference. The object relative to this frame of reference continues to stay at rest or move with a constant velocity.
Consider a car in motion. The passenger is moving along with the car relative to the Earth. When the car stops suddenly, the passenger experiences a push forward despite no net force acting on her.
Although the passenger moves forward relative to the car, her velocity relative to the Earth is maintained.
The inertia of the passenger tends to maintain her velocity relative to the Earth due to Newton's first law of motion. Here, the frame of reference attached to the Earth can be considered as an inertial frame of reference.
Even though the Earth's velocity is not constant due to its rotation and revolution, it can be approximated as an inertial frame as its effects are negligible on objects' motion on Earth's surface.
5.14:
Inertial Frames of Reference
Newton’s first law is usually considered to be a statement about reference frames. It provides a method for identifying a special type of reference frame: the inertial reference frame. In principle, we can make the net force on a body zero. If its velocity relative to a given frame is constant, then that frame is said to be inertial. So, by definition, an inertial reference frame is a reference frame where Newton's first law holds valid. Newton's first law applies to objects with constant velocity. From this fact, we can infer the following:
A reference frame moving at constant velocity relative to an inertial frame is also inertial.
Are inertial frames common in nature? It turns out that well within experimental error, a reference frame at rest relative to the most distant, or "fixed," stars is inertial. All frames moving uniformly with respect to this fixed-star frame are also inertial. For example, a non-rotating reference frame attached to the Sun is, for all practical purposes, inertial, because its velocity relative to the fixed stars does not vary by more than one part in 1010. The Earth accelerates relative to the fixed stars because it rotates on its axis and revolves around the Sun; hence, a reference frame attached to its surface is not inertial. For most problems, however, such a frame serves as a sufficiently accurate approximation to an inertial frame because the acceleration of a point on the Earth's surface relative to the fixed stars is relatively small (< 3.4 x 10−2 m/s2). Thus, we consider reference frames fixed on the Earth to be inertial unless otherwise indicated . Finally, no particular inertial frame is more special than any other. As far as the laws of nature are concerned, all inertial frames are equivalent. When analyzing a problem, we choose one inertial frame over another simply based on convenience.
This text is adapted from Openstax, University Physics Volume 1, Section 5.2: Newton's First Law.