Editing Inertial frame of reference (section)

=== Additional example ===
[[File:Wikipage pic.PNG|thumb|250px|'''Figure 2''': Simple-minded frame-of-reference example]]
For a simple example involving only the orientation of two observers, consider two people standing, facing each other on either side of a north-south street. See Figure 2. A car drives past them heading south. For the person facing east, the car was moving to the right. However, for the person facing west, the car was moving to the left. This discrepancy is because the two people used two different frames of reference from which to investigate this system.

For a more complex example involving observers in relative motion, consider Alfred, who is standing on the side of a road watching a car drive past him from left to right. In his frame of reference, Alfred defines the spot where he is standing as the origin, the road as the {{math|''x''}}-axis, and the direction in front of him as the positive {{math|''y''}}-axis. To him, the car moves along the {{math|''x''}} axis with some [[velocity]] {{math|''v''}} in the positive {{math|''x''}}-direction. Alfred's frame of reference is considered an inertial frame because he is not accelerating, ignoring effects such as Earth's rotation and gravity.

Now consider Betsy, the person driving the car. Betsy, in choosing her frame of reference, defines her location as the origin, the direction to her right as the positive {{math|''x''}}-axis, and the direction in front of her as the positive {{math|''y''}}-axis. In this frame of reference, it is Betsy who is stationary and the world around her that is moving – for instance, as she drives past Alfred, she observes him moving with velocity {{math|''v''}} in the negative {{math|''y''}}-direction. If she is driving north, then north is the positive {{math|''y''}}-direction; if she turns east, east becomes the positive {{math|''y''}}-direction.

Finally, as an example of non-inertial observers, assume Candace is accelerating her car. As she passes by him, Alfred measures her [[acceleration]] and finds it to be {{math|''a''}} in the negative {{math|''x''}}-direction. Assuming Candace's acceleration is constant, what acceleration does Betsy measure? If Betsy's velocity {{math|''v''}} is constant, she is in an inertial frame of reference, and she will find the acceleration to be the same as Alfred in her frame of reference, {{math|''a''}} in the negative {{math|''y''}}-direction. However, if she is accelerating at rate {{math|''A''}} in the negative {{math|''y''}}-direction (in other words, slowing down), she will find Candace's acceleration to be {{math|1=''a′'' = ''a'' − ''A''}} in the negative {{math|''y''}}-direction—a smaller value than Alfred has measured. Similarly, if she is accelerating at rate ''A'' in the positive {{math|''y''}}-direction (speeding up), she will observe Candace's acceleration as {{math|1=''a′'' = ''a'' + ''A''}} in the negative {{math|''y''}}-direction—a larger value than Alfred's measurement.