Can velocity of the free particle remain constant in non-inertial frame as contrast to free particle in an inertial frame? I know the answer is straightforward yes but taking a different perspective that non-inertial frames are frames where space is non-homogenous,and anistropic and time is non-homogenous. Then we can argue that lagrangian of free particle may/may not depend on coordinate of particle but definitely depend on velocity and time,which by Euler-Lagrange equations suggest velocity should not be constant,now how to answer the question?
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1$\begingroup$ The answer is obviously "yes" (just take a non-inertial reference frame fixed to the particle and its velocity in that frame is constant and zero!) but it's not clear what you are really trying to ask here. $\endgroup$– alephzeroCommented Jun 2, 2019 at 11:08
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$\begingroup$ Yes seeing this way it is looking obvious but let us take a different prespective that non inertial frames are frames where space is non-homogenous,and anistropic and time is non-homogenous.Then we can argue that lagrangian of free particle may/may not depend on coordinate of particle but defintely depend on velocity and time,which by Euler lagrange equations suggest velocity should not be constant $\endgroup$– Ashley ChrayaCommented Jun 2, 2019 at 11:23
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$\begingroup$ I think you want to change the phrasing of the question to include "free" particle (i.e. one on which there is no force). Even then - the answer is "yes", a stationary particle at the center of a rotating frame of reference is both free, and its velocity is constant (zero). Add "non-zero velocity" and it gets more challenging. The best questions get the best answers... $\endgroup$– FlorisCommented Jun 2, 2019 at 12:54
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$\begingroup$ " but let us take a different prespective that non inertial frames are frames where space is non-homogenous,and anistropic and time is non-homogenous" - well, if you wanted to ask about that, you should have put it in the question (and not in a comment which is likely to get deleted). I'm not a mind reader - most of what I do on my day job involves non-inertial frames, and I've never thought about them that way in the last 40 years or so! $\endgroup$– alephzeroCommented Jun 2, 2019 at 13:05
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Consider two objects falling from the same height. One is dropped without initial velocity. The second is thrown downwards with some initial vertical velocity vo. The velocity of the second object relative to the first one (non inertial frame) is vo during the entire fall.
