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However, this definition of inertial frames is understood to apply in the Newtonian realm and ignores relativistic effects. In practical terms, the equivalence of inertial reference frames means that scientists within a box moving with a constant absolute velocity cannot determine this velocity by any experiment.
In the inertial frame of reference (upper part of the picture), the black ball moves in a straight line. However, the observer (brown dot) who is standing in the rotating/non-inertial frame of reference (lower part of the picture) sees the object as following a curved path due to the Coriolis or centrifugal forces present in this frame.
An inertial reference frame (or inertial frame in short) is a frame in which all the physical laws hold. For instance, in a rotating reference frame, Newton's laws have to be modified because there is an extra Coriolis force (such frame is an example of non-inertial frame). Here, "rotating" means "rotating with respect to some inertial frame".
The center of momentum frame is defined as the inertial frame in which the sum of the linear momenta of all particles is equal to 0. Let S denote the laboratory reference system and S′ denote the center-of-momentum reference frame. Using a Galilean transformation, the particle velocity in S′ is
In an inertial reference frame S, let and denote the endpoints of an object in motion. In this frame the object's length is measured, according to the above conventions, by determining the simultaneous positions of its endpoints at =. Meanwhile, the proper length of this object, as measured in its rest frame S', can be calculated by using the ...
In special relativity, an observer is a frame of reference from which a set of objects or events are being measured. Usually this is an inertial reference frame or "inertial observer". Less often an observer may be an arbitrary non-inertial reference frame such as a Rindler frame which may be called an "accelerating observer".
The perifocal coordinate system may also be used as an inertial frame of reference because the axes do not rotate relative to the fixed stars. This allows the inertia of any orbital bodies within this frame of reference to be calculated. This is useful when attempting to solve problems like the two-body problem. [6]
Consider a stationary inertial frame of reference , and a non-inertial frame of reference ′, which is translating with velocity () and rotating with angular velocity () with respect to the stationary frame. The Navier–Stokes equation observed from the non-inertial frame then becomes