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An inertial frame of reference is a frame of reference which is not accelerating. All laws of physics are the same measured from an inertial frame of reference. A rest frame is a frame of reference where a particle is at rest.

Does this mean that a rest frame could possibly be non-inertial (that is, accelerating), but the particle with respect to his rest frame would have a velocity of $0$? What kind of velocity? And what exactly would it mean to be at rest with respect to a possibly accelerating frame of reference?

What are the differences and relations between rest frame and inertial reference frame?

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  • $\begingroup$ Yes, the rest frame can be non inertial. To be at rest is to not change position, your reference frame just move along with the particle. There is nothing deeper to understand $\endgroup$ – user126422 May 16 '17 at 12:30
  • $\begingroup$ Vocabulary that might help "instantaneous co-moving frame" or equivalently "momentarily co-moving frame". $\endgroup$ – dmckee --- ex-moderator kitten Mar 11 '18 at 18:14
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Yes, a rest frame can be accelerated. Right at this moment I am seat at rest with respect to the Earth. However Earth itself is accelerated.

A rest frame associated to a particle will be inertial if the particle is free, i.e. it does not interact with anything. This is actually the first Newton's law and it gives a definition of an inertial frame.

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Consider your own personal rest frame, one with its origin at your center of mass. The acceleration of your center of mass with respect to your personal rest frame is tautologically zero. From this narcissist perspective, it's the Earth that is accelerating toward you when you parachute out of an airplane or bungee jump off of a bridge. Similarly from this perspective, the road accelerates backwards underneath you when you punch the accelerator on your car, and accelerates forwards when you hit the breaks.

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An inertial frame of reference is a frame of reference which is not accelerating

This is wrong: an inertial frame of reference is, by definition, a reference frame where a particle not subject to external forces moves along straight lines.

A rest frame is a frame of reference where a particle is at rest.

A rest frame is a frame integral to the particle, namely a frame with respect to which $p(t)=0$ however you choose $t$.

This said, a frame might obviously be non-inertial and integral to some particle somewhere in the universe. Velocity, position and acceleration are all measures that depend exactly on what system the observer chooses and any combination thereof is possible, for some frame of references (as long as they do not violate basic relativity or derivatives rules).

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  • $\begingroup$ Whenever you say "it is not accelerating" you have to specify with respect to what: with respect to a non-inertial accelerating observer your inertial reference frame is indeed accelerating. The only difference is that in the former a body not subject to external forces does not move along straight lines, whereas in yours it does. $\endgroup$ – gented May 16 '17 at 13:50
  • $\begingroup$ In the above I am not stating any connection among different frames: I am just defining what a reference frame is (whether or not they are accelerating with respect to other inertial frames is outside the scope). $\endgroup$ – gented May 16 '17 at 14:08

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