Inertial Frame of Reference

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Inertial Frame of Reference

a frame of reference in which the law of inertia is valid: a mass point is at a state of rest or uniform linear motion when it is not acted on by any forces (or when it is acted on by balanced forces). Any frame of reference that is moving translationally, uniformly, and rectilinearly with respect to an inertial frame of reference is also an inertial frame of reference. Consequently, in theory any number of fully valid inertial frames of reference may exist with the important property that in all such frames the laws of physics are identical (the so-called relativity principle). In addition to the law of inertia, in any inertial frame of reference Newton’s second law and the laws of conservation of momentum and of angular momentum, as well as the law of motion of the center of inertia (or center of mass), are also valid for closed systems (systems not subject to external influences).

If a frame of reference does not move uniformly and linearly with respect to an inertial frame of reference, it is a noninertial frame, and neither the law of inertia nor the other laws mentioned above are observed within it. This is because even in the absence of acting forces a mass point will have an acceleration with respect to a noninertial frame of reference as a result of the accelerated translatory or rotational motion of the frame of reference itself.

The concept of an inertial frame of reference is a scientific abstraction. A real frame of reference is always connected with some specific body, such as the earth or the body of a ship or aircraft, with respect to which the motion of various objects is studied. Since there are no stationary bodies in nature (a body that is stationary with respect to the earth will move together with it under acceleration with respect to the sun and stars), any real frame of reference may be considered as an inertial frame of reference only to various degrees of approximation. The so-called heliocentric (stellar) system, with its reference point at the center of the sun (or, more accurately, at the center of mass of the solar system) and its coordinate axes directed toward three stars, may be considered an inertial frame of reference to a very high degree of accuracy. Such a frame of reference is used primarily in problems of celestial mechanics and astrogation. In practice a frame rigidly connected to the earth or, in cases that require greater accuracy (such as gyroscopy), a system with its origin at the center of the earth and its axes oriented toward the stars may serve as an inertial frame of reference for the solution of most technical problems.

In converting from one inertial frame of reference to another, Galilean transformations are valid for spatial coordinates and time in classical Newtonian mechanics, and Lorentz transformations are used in relativistic mechanics (that is, for rates of motion close to the speed of light).

S. M. TARG

References in periodicals archive ?
in the direction of the velocity of the material particle, remains invariant under the action of the Lorentz-Einstein transformations and is, therefore, constant in all inertial reference frames.
In the way we have chosen the inertial reference frames S and S', the transformations of the coordinates in the four-dimensional spacetime are given by the set of equations
The equations of this paragraph express the fact that in every inertial reference frame the velocity of the selfvariations remains constant as a vector with magnitude [parallel]u[parallel] = c.
Starting from equation (2) we get [parallel]v/c[parallel] = 1 for every inertial reference frame.
We are then introduced to inertial reference frames and told that, for objects in motion, time slows, length contracts and mass increases.
2 Defining two Instantaneous Inertial Reference Frames
To define the two instantaneous inertial reference frames to accomplish, simply, the effect of the Earth rotation, we, firstly, write down the rotation velocities of the points [?
Already fifty years ago, Frank Robert Tangherlini, an American theoretical physicist, suggested an original procedure which, targeting the synchronization of clocks located in two different inertial reference frames of the space, was different from that Einstein had introduced.
In his PhD thesis [1], Tangherlini suggested also another method how to synchronize the clocks: this is so-called the "external synchronization", where the clocks, distantly located from each other, become synchronized in a resting ("preferred") inertial reference frame, then these already synchronized clocks are used for synchronization of the other clocks, which are located in the moving inertial reference frames distant from each other.
During more than the hundred years after the Special Theory of Relativity was constructed, the most researchers were filled in belief that the Lorentz transformations originate in two postulates of the Special Theory of Relativity: the equality of all inertial reference frames, and the isotropy of the velocity of light in all inertial reference frames, including the independence of the velocity of light from the velocity of the source of light.
The anisotropy of the coordinate velocity of light c' = c in the inertial reference frame K' is the fee paid for the absolute simultaneity in all inertial reference frames [18].

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