Question

Why are constant linear velocity reference frames not absolute while constant angular velocity reference frames are?

Answer 1

If we observe Newton's force law, F = ma = m d/dt (v), then in case of linear velocity transform, v' = v + dv, where dv is a constant, F = m d/dt (v' - dv) = m d/dt (v'), which leaves us with the same form of physics. For rotating transforms, however, v' = v + r w cos( w t), which gives d/dt ( r w cos(w t)) != 0, and we will not obtain F=ma again in a new rotating coordinate. Therefore we can find a coordinate system where there is no extra terms in force law and recognize it as non-rotating. Such is impossible for linear frames.