Re: Displacement

[Gene Mosca <mosca@USNA.EDU>]

Greg wrote:

> Suppose you exercise by walking for 15 minutes  on a treadmill that has a
> level track that moves at a velocity of -4km/hr.
> Remembering that the treadmill belt is a rubberized loop that returns to its
> original position after every full turn, what would be your total
> displacement relative to the treadmill track when you are finished exercising
> and you dismount off the belt from the same spot that you started your
> exercise ?
>
> Using the argument that dispalcement is final minus initial,
> would your dispalcement then be 1 km or zero km ?


One can modify this question slightly to obtain some insight into the issue
raised.  Consider the treadmill belt to consist of a large number of narrow
links, like the tread of a tank.  Each narrow link is rigid, and thus is
suitable for consideration as a reference frame.  Now consider the
displacement of the walker relative to one of the links. After 15 minutes of
walking, the magnitude of the walker's displacement relative to one of the
links is zero.

The treadmill belt does not remain rigid.  Thus the belt as a whole is
unsuitable for consideration as a reference frame. For the treadmill belt, a
sufficiently small spot on the belt is sufficiently rigid to be considered a
reference frame.

Gene