Tuesday, November 28, 2006

Balancing Act

Today in calculus I taught the last of the content, using integrals to calculate the center of mass of a region below y = f(x) between x=a and x=b.

Before class I used Grapher to make a graph of my function, and I printed it out (to show the students something more accurate than my hand-drawn graph on the board). I also had Grapher print a larger version of the region -- but still large enough to fit on letter paper. I took my large region, plotted the centroid, glue-sticked the region to a manilla folder, and cut it out. In class I was able to get my region to balance on the eraser of my pencil.

On the exam I will ask the students, "What is a physical interpretation of the center of mass?"