Frame of Reference: Definition & Explanation

[fog37]

Hello,
My understanding is that a a frame of reference is a theoretical framework that is used to describe the motion of an object allowing for measurements of position, distance and time. A frame of reference always implicitly includes a coordinate system (cartesian, spherical, cylindrical, etc). A coordinate system has an origin O.

Is it correct to think that two reference frames, both at rest relative to each other and using the same coordinate system (Cartesian) but having their origins at different locations, represent different and distinct frames of reference?
thanks,
fog37

 

[phinds]

Hello,
My understanding is that a a frame of reference is a theoretical framework that is used to describe the motion of an object allowing for measurements of position, distance and time. A frame of reference always implicitly includes a coordinate system (cartesian, spherical, cylindrical, etc). A coordinate system has an origin O.

That's probably an overly strict, but correct, way of looking at it. Often when we talk able frames of reference, we don't think all that much about the coordinate system, just that it is a framework in which an object of interest's motion can be specified. Yes, to give a velocity vector you need a coordinate system but often we are simply concerned w/ whether or not an object is at rest in the frame or not.

Is it correct to think that two reference frames, both at rest relative to each other and using the same coordinate system (Cartesian) but having their origins at different locations, represent different and distinct frames of reference?

Yes although for some types of issues, it's just as convenient to consider only one such frame of reference since the other is offset by only a distance coordinate. When frames are moving relative to each other, the relativity of simultaneity complicates things.