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In an inertial frame of reference (let's say a car moving with certain constant velocity in which I am sitting) If I observe the motion of another car through my frame of reference i.e.car, will I be at rest with my frame of reference or in motion?

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You're always at rest with respect to your own frame. It doesn't matter what else is going on.

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  • $\begingroup$ Is there any reason for this or it is presumed? $\endgroup$ – Atharav Karhad Jul 29 at 15:05
  • $\begingroup$ @AtharavKarhad I guess presumed? Your own reference frame is the frame where you are at rest. I am not sure how else to describe it. $\endgroup$ – Aaron Stevens Jul 29 at 15:22
  • $\begingroup$ Ok so if i am an observer then i will always be at rest with respect to my frame even if i am in motion in my frame. I will actually not realise that i am in motion but i will feel that everything in the surrounding is in motion and those objects which are at rest wrt ground will be felt in motion having my velocity in opposite direction. $\endgroup$ – Atharav Karhad Jul 30 at 4:14
  • $\begingroup$ Also i am moving with velocity 5m/s and another person person is is moving towards me with 3m/s then how will i exactly know that he will be moving with speed 8m/s only ?or is it that mathematically he will be moving with velocity 8m/s towards me but i will in real world will only feel that he is moving towards me at a faster rate? $\endgroup$ – Atharav Karhad Jul 30 at 4:22
  • $\begingroup$ @Atharav Karhad "...even if i am in motion in my frame" Bad idea here. You are at rest in your own inertial frame. You cannot be moving in your inertial frame. It's fine to say you are moving relative to some other inertial frame, but not your own frame which is defined as the frame your are at rest in. $\endgroup$ – Aaron Stevens Jul 30 at 4:29
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If we model you as a "disembodied spatial tangent vector" (i.e. a point particle with a preferred spatial direction to represent your line of sight), then you'll need to spin in place to keep an eye on the other guy, but that doesn't count as motion.

If we think of you as three dimensional, then parts of your body will have to move, but there's no need for your center of mass to move.

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If I observe the motion of another car through my frame of reference i.e.car, will I be at rest with my frame of reference or in motion?

You will always be "at rest" in your own frame of reference. You will not be at rest with respect to the frame of reference of the person in the other car. Nor will the person in the other car be "at rest" with respect to your frame of reference.

The terms "at rest" and "moving" only have meaning with respect to a particular reference frame. An object cannot be both at rest and moving in the same reference frame. The exception is the speed of light in a vacuum which is the same with respect to any inertial frame of reference.

Hope this helps.

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