Inertial frame of reference

In such a frame, an object with zero net force acting on it, is perceived to move with a constant velocity, or, equivalently, Newton's first law of motion holds.

Some physicists, like Isaac Newton, originally thought that one of these frames was absolute — the one approximated by the fixed stars.

[1][2] Viewed from the perspective of general relativity theory, the fictitious (i.e. inertial) forces are attributed to geodesic motion in spacetime.

[4] The principle of simplicity can be used within Newtonian physics as well as in special relativity:[5][6] The laws of Newtonian mechanics do not always hold in their simplest form...If, for instance, an observer is placed on a disc rotating relative to the earth, he/she will sense a 'force' pushing him/her toward the periphery of the disc, which is not caused by any interaction with other bodies.

Newton posited an absolute space considered well-approximated by a frame of reference stationary relative to the fixed stars.

[15] Some historical background including Lange's definition is provided by DiSalle, who says in summary:[16] The original question, "relative to what frame of reference do the laws of motion hold?"

, by simple addition or subtraction of coordinates: where r0 and t0 represent shifts in the origin of space and time, and v is the relative velocity of the two inertial reference frames.

Newton viewed the first law as valid in any reference frame that is in uniform motion (neither rotating nor accelerating) relative to absolute space; as a practical matter, "absolute space" was considered to be the fixed stars[18][19] In the theory of relativity the notion of absolute space or a privileged frame is abandoned, and an inertial frame in the field of classical mechanics is defined as:[20][21] An inertial frame of reference is one in which the motion of a particle not subject to forces is in a straight line at constant speed.Hence, with respect to an inertial frame, an object or body accelerates only when a physical force is applied, and (following Newton's first law of motion), in the absence of a net force, a body at rest will remain at rest and a body in motion will continue to move uniformly—that is, in a straight line and at constant speed.

If the rule is interpreted as defining an inertial frame, then being able to determine when zero net force is applied is crucial.

[23] A possible issue with this approach is the historically long-lived view that the distant universe might affect matters (Mach's principle).

It shares the special principle of the invariance of the form of the description among mutually translating reference frames.

Einstein's theory of special relativity, like Newtonian mechanics, postulates the equivalence of all inertial reference frames.

The invariance of the speed of light leads to counter-intuitive phenomena, such as time dilation, length contraction, and the relativity of simultaneity.

We stand on the side of the road and start a stop-clock at the exact moment that the second car passes us, which happens to be when they are a distance d = 200 m apart.

For a simple example involving only the orientation of two observers, consider two people standing, facing each other on either side of a north-south street.

For a more complex example involving observers in relative motion, consider Alfred, who is standing on the side of a road watching a car drive past him from left to right.

In his frame of reference, Alfred defines the spot where he is standing as the origin, the road as the x-axis, and the direction in front of him as the positive y-axis.

[32] Support for this principle is found in the Eötvös experiment, which determines whether the ratio of inertial to gravitational mass is the same for all bodies, regardless of size or composition.

[34] Einstein's general theory modifies the distinction between nominally "inertial" and "non-inertial" effects by replacing special relativity's "flat" Minkowski Space with a metric that produces non-zero curvature.

This phenomenon of geodesic deviation means that inertial frames of reference do not exist globally as they do in Newtonian mechanics and special relativity.

[37] "Local" can encompass, for example, the entire Milky Way galaxy: The astronomer Karl Schwarzschild observed the motion of pairs of stars orbiting each other.

These observations allowed him to conclude that inertial frames inside the galaxy do not rotate with respect to one another, and that the space of the Milky Way is approximately Galilean or Minkowskian.

In Newton's time the fixed stars were invoked as a reference frame, supposedly at rest relative to absolute space.

[41] The concept of inertial frames of reference is no longer tied to either the fixed stars or to absolute space.

An answer might explain the shape of the Milky Way galaxy using the laws of physics,[44] although other observations might be more definitive; that is, provide larger discrepancies or less measurement uncertainty, like the anisotropy of the microwave background radiation or Big Bang nucleosynthesis.

However, if rotation were found, interpretation of observations in a frame tied to the universe would have to be corrected for the fictitious forces inherent in such rotation in classical physics and special relativity, or interpreted as the curvature of spacetime and the motion of matter along the geodesics in general relativity.

These equations allow transformations between the two coordinate systems; for example, Newton's second law can be written as When there is accelerated motion due to a force being exerted there is manifestation of inertia.

But in a frame rotating about a fixed axis, the object appears to move in a circle, and is subject to centripetal force.

For linear acceleration, Newton expressed the idea of undetectability of straight-line accelerations held in common:[25] If bodies, any how moved among themselves, are urged in the direction of parallel lines by equal accelerative forces, they will continue to move among themselves, after the same manner as if they had been urged by no such forces.This principle generalizes the notion of an inertial frame.

[54] The outer casing of the gyrocompass device is held in such a way that it remains aligned with the local plumb line.

Figure 1 : Two frames of reference moving with relative velocity . Frame S' has an arbitrary but fixed rotation with respect to frame S . They are both inertial frames provided a body not subject to forces appears to move in a straight line. If that motion is seen in one frame, it will also appear that way in the other.
Figure 1 : Two cars moving at different but constant velocities observed from stationary inertial frame S attached to the road and moving inertial frame S′ attached to the first car.
Figure 2 : Simple-minded frame-of-reference example
Figure 2 : Two spheres tied with a string and rotating at an angular rate ω. Because of the rotation, the string tying the spheres together is under tension.
Figure 3 : Exploded view of rotating spheres in an inertial frame of reference showing the centripetal forces on the spheres provided by the tension in the tying string.