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19 October 2001
A Look at Where We Are
by George E. Hrabovsky, President of MAST
News from MAST
Howdy! It looks like I will be going out tomorrow to get some soil samples for microbiology experiments. MAST has also developed a funding proposal for the tornado spotter network and we arehoping that this will bring us some income.
Continuing from last week I will begin to develop the principles of motion from first principles. I will also be introducing a new feature that I call the Theory Challenge. This will be a task to challenge the readership in a specific way, directly related to the column.
What is Motion?
We all know what motion is right? Right? Try to define motion. What is your answer? Here is my stab at it: "Any change in the position of an object in time is motion." There are only four things wrong with this as a definition; we do not know what is meant by change, position, object, or time.
For this column we will treat objects as particles (see the last column). So to proceed we choose to begin this column by addressing the notion of position. What is it? Think about it, and try to develop a notion for what it is. The first thing to realize is that we cannot identify the position of anything without knowing what the position is relative to. In other words, we have to identify some arbitrary reference point. We will call this point O. This is classical for origin.
Now we have to draw a line from O to the location of our object. From the last column we will treat the object as a particle. In this way we can treat its location as another point (since a particle has no size, we can treat it as a geometrical object having no size, a point). We will call this point, from tradition, P. This gives us the segment
as the distance from O to P.
To measure the distance we must choose a unit of length. Once we have such a unit, we count the number of units and their fractions in
. This is the length of the segment. We can't ever discuss a length without including the unit of distance we are using. The length becomes an algebraic quantity with the number of units being the coefficient of the symbol for the unit. We might say four feet, or ten meters, or six light years, etc.
Once we know the distance to P from O then we need to determine the direction. One way is to choose an arbitrary direction as 0° and then measure the angle of
counterclockwise to the 0° line. Once we have done this
is then called a directed line segment. Another word for a directed line segment is vector. In this case we have a specific type of vector called a position vector. A position vector is classically denoted by the symbol r. Writing it by hand you might use either
or
.
Theory Challenge
I have described the process of locating an object. Can you develop a geometrical justification for the validity of my method?
I will present my own "proof" to this next time.
Books That I Like
The best book on this subject is not a physics book:
John Roe (1993), Elementary Geometry, Oxford University Press. The chapters related to this subject are 1-3. This is a very interesting and challenging book on geometry.
Converted by Mathematica October 18, 2001
