Re: increasing, decreasing...

[Joe Heafner <heafnerj@VNET.NET>]

> From: Aaron Titus <titus@NCAT.EDU>
>
> Lately I've been considering the terminology we use in introductory physics
> and how it is sometimes confusing and vague and interpreted differently by
> physicists.  For instance, when you talk about a vector component and
> whether it is constant, increasing, or decreasing, are you referring to the
> vector component with its sign or the magnitude of the vector component?
We should refer specifically to the vector's magnitude. How can a *direction* increase or decrease? Well, it could possibly change in *the direction that we have arbitrarily named positive*, and we could call this an increase. It could also change in *the direction that we have named negative* (assuming we've already defined the positive direction, we've also implicitly defined the negative direction as well) and this could be called a decrease.

The concepts of *positive* and *negative* only make sense once we've defined a coordinate system. Vector quantities exist independent of any coordinate system and they have properties that can be explained in geometric terms without a coordinate system.

This came as a rather sudden, and enlightening, realization to me only recently as a result of using Matter & Interactions (Chabay and Sherwood, 1997. Wiley).

> Consider a somewhat typical introductory question where an object has a
> negative velocity component and a positive acceleration.  Would you say
> that the velocity component is increasing or decreasing, and when you use
> this terminology are you referring to the velocity component or the
> magnitude of the velocity component, being careful to say "magnitude" of
> course?
I would refer specifically the magnitude.




Cheers,
Joe

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