Rectilinear vs Curvilinear Motion: Explained

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Discussion Overview

The discussion revolves around the concepts of rectilinear and curvilinear motion, particularly in the context of different reference frames, including Galilean and accelerated frames. Participants seek to clarify how motion appears differently depending on the observer's frame of reference, exploring both theoretical and conceptual aspects of motion in physics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant states that an object performing rectilinear motion in a Galilean reference frame appears to perform curvilinear motion in an accelerated reference frame.
  • Another participant suggests that due to spacetime contraction, an accelerating body must curve light, leading to the perception of curvilinear motion.
  • A participant asks for clarification on specific terms related to the statement, including reference frames and types of motion.
  • One participant rephrases the original question, presenting a scenario involving three people and questioning the motion of one person with respect to another, concluding that it would appear as a curve in the x-y plane.
  • A follow-up question is raised about whether the motion of an accelerating body would still appear curvilinear if it accelerates in the same direction as another body moving at constant velocity.
  • A suggestion is made to use a spacetime diagram to illustrate the differences in motion between inertial and accelerating frames.

Areas of Agreement / Disagreement

Participants express varying interpretations of how motion is perceived in different reference frames, indicating that multiple competing views remain. The discussion does not reach a consensus on the implications of these interpretations.

Contextual Notes

Some assumptions about the nature of reference frames and the effects of acceleration on perceived motion remain unresolved. The discussion also highlights the dependence on definitions of rectilinear and curvilinear motion.

Who May Find This Useful

This discussion may be of interest to students and enthusiasts of physics, particularly those exploring concepts of motion, reference frames, and relativistic effects.

SpaceExplorer
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If an object O is performing rectilinear motion w.r.t a Galilian body of reference K then w.r.t an accelerated body of reference K', O performs 'curvilinear' motion... What I ask for is a detailed explanation of this statement.
 
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I don't have a detailed explanation but instinctively, I would say that since the spacetime is contracting, the body passing by the other body as no place to go but to go before you. In that case, that body accelerating cannot do anything but to curve light and from your point of view, it's a "curvilinear' motion.
 
What part of the statement are you having problems with?
body of reference (=reference frame)?
Galilean reference frame?
rectilinear motion?

For example, if you have a trajectory x=vt, y=0 in an inertial reference frame, how would it look in the frame t'=t, x'=x, y'=y-a/2*t² (which is an accelerated frame in pre-relativistic mechanics)?
 
Hope you don’t mind if I put the question in my own words first.

Given:
Three people start out together. Person ‘B’ is traveling at constant velocity in the x-direction with respect to Person ‘A’. Person ‘C’ is accelerating in the y-direction with respect to Person ‘A’.

Question:
What will the motion of Person ‘C’ be with respect to Person ‘B’?

Answer:
A curve in the x-y plane. (as you probably already suspect)
 
Thanks 'Mikelizzi', for your reply which changed my interpretation of the statement... My prev's interp'n was that the body 'C' is accelerating in the same dir'n as is the motion of body 'B' w.r.t A... So for my 1st interpretation, would the movement of C would still look Curvilinear to B, or will it be rectilinear?
 
Draw a spacetime diagram, i.e. a graph of distance against time. If you have a straight-line graph relative to an inertial frame, you'll have a curved graph relative to an accelerating frame.
 

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