Taking the fear out of vector addition by concentrating on the superimposed axes

Abstract

Introductory physics students often express fears regarding graphical vector addition. To ameliorate student trepidation of possibly making a mistake when moving the second vector to its new position at the head of the first vector before being added, as is most often advised by physics teachers, an alternative method is detailed here. This subtly different method instead concentrates student effort on using ‘sensing personification’ to identify a ‘center of the universe’ position that shifts for each vector by considering the initial axes choice when drawing the first vector, then superimposing a new axes for the second vector onto the same graph at the head of the first vector before drawing in the second vector. The vector is then drawn to-scale onto the new axes. This process then allows students to render the vector correctly without worry of inadvertent error of vector rotation and/or accidental elongation or truncation of the vector. A simple example is given to demonstrate this alternative method and how it also better aligns with analytical vector addition which uses vector equations. Use of sensing personification in vector addition can also set the stage for its use in other physics problems the student will encounter later, such as remembered experiences on amusement park rides.