Expert: Richard J. Raridon - 4/22/2004

Question
Hello,
Recently in Physics class, we were working with moment of inertia I=MR^2. We did an experiment and then graphed I versus R. This produced a nonlinear graph (exponential); is this because I is proportional to R^2 but not proportional to R? Or is it because the slope of I versus R is the sqrt of M? Or both? To get a linear graph we would have to graph I versus R^2?

Something about this is confusing to me. What's the point of taking the square root of one side of the equation and not the other and what does the exponential graph say about the relationship between I and R?

Thanks a bunch! :)

Answer
Obviously, if you plot I vs. R you're going to get a non-linear relationship since that's the equation for a parabola.  If you plot I vs. R^2 you should get a straight line if your data are good.  The slope of that line will give you a value for M.  You can compare that with your measured value of M.  You're not taking the square root of one side by doing that.  The exponential graph just shows you that I vs. R is not a linear relationship.