Aaron, my simple mind is never troubled by the examples you give. When vector quantities increase or decrease it is always their magnitude that changes. Directions can be positive or negative but they cannot increase or decrease, they just are.
A vector quantity in two dimensions, such as displacement or velocity, can indeed be increasing in time even though one of its components is decreasing in time. The other component, of course, must be increasing in time at a rate sufficient to overcome the effect of the decreasing component.
I don't believe it is necessary to add the word magnitude when speaking about a changing vector quantity. Unless you specifically use the word component, it is understood that you are referring to the entire vector quantity.
Unless the ratio of the components of a changing two-dimensional vector quantity remains fixed, the quantity is changing in direction as well as in magnitude. You can speak of changing direction but not of increasing or decreasing direction.
poj
Original Message:
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From: Aaron Titus titus@NCAT.EDU
Date: Thu, 03 Jan 2002 16:28:37 -0500
To: PHYS-L@lists.nau.edu
Subject: increasing, decreasing...
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?
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?
Often, this is encountered when analyzing velocity component vs. time
graphs (note that I didn't say velocity vs. time graphs because we don't
plot velocity vs. time graphs except for one-dimensional motion--we always
plot a velocity component vs. time). An object may be slowing down (this
refers to speed) yet have an "increasing velocity component" (this refers
to the velocity component including direction--basically the velocity
component has a positive derivative with respect to time). Alternatively,
an object may be speeding up yet have a "decreasing velocity component".
I personally like to use "increasing" and "decreasing" to refer to the
magnitude of a vector component, always being careful to say "magnitude"
although it's easy to forget. That way, I can also use the same
terminology for the magnitude of the vector itself. Note that we cannot
refer to an "increasing velocity" since velocity is a vector (although one
can imply that whenever we refer to an increasing vector we are talking
about the magnitude of the vector and not the vector itself, but that's
confusing to students I'm sure).
I'm curious what you prefer and practice.
AT
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Dr. Aaron Titus
Department of Physics
316 Marteena Hall
North Carolina A&T State University
Greensboro, NC 27411