Let’s Treat Position and Velocity As Nothing Special

I have come to believe that the terminology and notation used in introductory physics should be as precise and as descriptive as possible. Music terminology and notation are both of those things and this makes learning to read music easier than learning physics. Play what the notation says, and the notation says what to play. There are ver few, if any, ambiguities. I want to harp on two things that irritate me about the treatment of vectors in introductory physics.

The first thing is a terminology issue. We know that there are, loosely speaking, vector quantities and scalar quantities in introductory physics. We talk about a particle’s momentum vector, and we say “magnitude of the particle’s momentum” when we want to refer to the magnitude of the momentum vector. We usually tell  students that we will always otherwise assume that “momentum” means “momentum vector” but then we sometimes  proceed to create confusion by using the term to mean a scalar magnitude in, say, a one dimensional problem. Okay, but that’s not my gripe. My point is that we say “magnitude of X” where X is a vector quantity. Well, that is, except for velocity. Velocity is the only quantity I can think of for which we have a separate name for the magnitude. The word “speed” is problematic because it can mean either the magnitude of average velocity, which is the magnitude of a vector comparison of displacement and duration, or it can mean a comparison of actual distance traveled to duration. These quantities are not the same thing, and this really confuses students. I think we should eliminate use of the word “speed” to mean “magnitude of velocity” and simply say “magnitude of velocity” as we do with momentum, force, and angular momentum. Then we could use “speed” to mean only a comparison of distance traveled to duration.

The second thing is a notation issue. In introductory physics we almost always work in Cartesian coordinate systems with directions loosely called x, y, and z. We use these labels as subscripts on the unadorned (no arrow) symbol for a vector to indicate that vector’s coordinate components (as in, for example, B_x,B_y,B_z). Well, that is, except for position vectors. We almost always simply use x, y, and z to denote the actual components (as in x,y,z instead of r_x,r_y,r_z). While I’ve never had a student speak out about this, it’s not the convention we use with other vector quantities, and it breaks conventions that we attempt to instill later on in the course.

So I guess my bottom line is that I’d like to see us use the same notation and terminology conventions with position and velocity that we use with other vector quantities. It’s a small, dare I say picky, thing, but I think it would help the music flow.





Comments 2

  • I think that the speed thing actually has little ambiguity; you’re looking at instantaneous speed vs. average speed, and we do look at instantaneous vs. average velocity and acceleration. The unique word is different, for sure. I always thought that of the positions as the fundamental quantities, so x and y are appropriate, while the others are operators that you do to the positions, so v_x is what happens when you “velocitize” x.

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