According to the book I am referring while working with non inertial frame of reference we have to apply a pseudo force equal to mass x acceleration in the opposite direction of the acceleration of the non inertial frame of reference with respect to the inertial frame of reference. But which frame is to considered to be absolutely inertial? Please don't say earth because Earth is not perfectly inertial its just inertial to good approximation. This can be justified while calculating the apparent weight of object due to earth's rotation.

  • $\begingroup$ The laws of Newton only apply in inertial frames. That's not a circular definition, because there are no pseudo-forces in inertial frames. It does not mean, however, that there is exactly one inertial frame. Every other frame that is moving at a constant velocity to an inertial frame is also an inertial frame. $\endgroup$ – CuriousOne Sep 8 '14 at 9:43
  • $\begingroup$ Please tell me any one inertial frame so that i can decide which frame is inertial and which is not $\endgroup$ – Rohan Sep 8 '14 at 9:48
  • $\begingroup$ @CuriousOne: how do you realize that a force is a pseudo-force? I mean, you can't discriminate 'pseudo' from 'real' forces without thinking about changing coordinates. I think that the two things are defined at the same time. "Real" forces are those forces which do not disappear by any global change of coordinate and frames of reference where only those forces exist are termed "inertial". $\endgroup$ – gatsu Sep 8 '14 at 10:35
  • $\begingroup$ @gatsu - In Newtonian mechanics, a real force has a third law counterpart acting on some other body. A fictitious force doesn't. Another test: Is the force proportional to mass? All fictitious forces are proportional to mass, and the only real force that is proportional to mass in Newtonian mechanics is gravitation. A non-gravitational force that is proportional to mass is a fictitious force. $\endgroup$ – David Hammen Sep 8 '14 at 11:10
  • $\begingroup$ @DavidHammen: In all generality, one can consider a system (or the motion of a system) without having access to the rest of the universe to verify that Newton's third law is satisfied (the Lorentz force is not reciprocal and yet it is a 'real' force I think). The mass argument doesn't quite work because in any complex distribution of masses in motion, it is quite an effort to figure out which term arises from gravitation and which doesn't. Also, the definition I give has absolutely no problem so it is at least a sufficient condition (maybe not necessary though). $\endgroup$ – gatsu Sep 8 '14 at 12:45

I'll frame my answer in terms of a comment by the original poster, because that comment asks the question most succinctly:

Please tell me any one inertial frame so that I can decide which frame is inertial and which is not.

Good question!

I'll start my answer from a Newtonian perspective and assume that a (possibly unknowable) Newtonian inertial frame does exist. Every frame of reference invented by humankind inevitably will have two non-inertial aspects to it:

  • The origin of the frame is accelerating with respect to an inertial frame, and
  • The axes of the frame are rotating with respect to an inertial frame.

Some of those accelerations and rotations are known. For example, a frame fixed with respect to the rotating Earth is accelerating toward the Sun and Moon (and also toward other masses in the solar system, and outside it), and it rotates. These known accelerations and rotations are easily dealt with. One can either ignore them or take them into account, yielding a non-inertial frame with fictitious forces.

What about the unknowns? Every so-called inertial frame has later been found to be a rotating frame. Even our best inertial frames are but approximations. Astronomers have developed and then later discarded a number of supposedly non-rotating frames over the last 100 years. Some recent ones:

  • The FK4 frame, also known as the B1950.0 frame, also known as the M50 frame.
    This frame used the fourth fundamental catalog of stars (FK4). There's a basic problem with using the "fixed stars" as the underlying mechanism for defining a non-rotating frame: The "fixed stars" aren't fixed. Astronomers try as best they can to deduce and then remove the effects of proper motion of the stars on the inferred frame of reference, but they can only go so far. The FK4 frame was later found to be rotating. That said, the FK4 frame got humanity to the Moon and the Voyager spacecraft to Jupiter, Saturn, and beyond. It also let astronomers peer ever deeper into the universe.

  • The FK5 frame, also known as the J2000 frame. This frame used the fifth fundamental catalog of stars, an update to the FK4 catalog. This frame let astronomers peer even deeper into the universe.

  • The International Celestial Reference Frame, also known as the ICRF.
    The improvements offered by the FK4 and FK5 frames let astronomers peer extremely deeply into the universe. Some of the very remote objects they found were very bright (after accounting for their remoteness). These pulsars provided a means to go beyond star catalogs. The very remoteness of the pulsars drastically reduces the problem of proper motion. After the fact, it has been found that the FK5 frame is rotating with respect to the ICRF by about 3 milliarcseconds per year. That's incredibly small, but it's also incredibly important to astronomers, who have been looking at the sub-milliarcsecond level for the last twenty years.

  • The second realization of the ICRF, also known as the ICRF2.
    Improvements to the pulsar database kept by astronomers inevitably meant that the ICRF would itself be found to be rotating. And it was. The ICRF was updated in 2009 as the ICRF2. That is currently the best guess as to what constitutes a non-rotating frame. It too will eventually be found to be rotating.

The above explicitly assumes a Newtonian inertial frame exists. There is no such thing. While the inertial frames listed above got humanity to the Moon and let astronomers see back to the near the beginning of the universe, they are not universal. They can't be, thanks to general relativity.

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Make it clear all frames are relative in the sense that the frame that is inertial to you is non-inertial to another observer. Suppose you are at rest on the ground and thus you are at inertial frame of reference;however an alien outside earth will observe you rotating along earth around its axis thus you,according to the alien,are in non-inertial frame . Thus everything is relative,nothing is absolute. But it will not bother you in classical physics. You can consider ground or anything attached to the ground at rest or uniformly moving body with respect to a stationery object as inertial frame of reference . Hope this helps.

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