Physics 2015: Rolling Motion and Moment of Inertia Purpose  Investigate which factors affect moments of inertia (such as length, mass, and shape).  Calculate moments of inertia for various shapes to check our results.

Physics 2015: Rolling Motion and Moment of Inertia Equipment Inclined board on which you can place round objects at the top of the board and let them accelerate towards the bottom:

Physics 2015: Rolling Motion and Moment of Inertia Activity I: Data Collection  Note that for constant acceleration (like in out setup today) the velocity increases linearly with time. Therefore, where  To measure v average, all you need is a stopwatch (time t) and a ruler (distance d).  By the way, the acceleration is

Physics 2015: Rolling Motion and Moment of Inertia Activity II: Calculating Moments of Inertia  Simply use conservation of energy, which we quickly see from the figure below is  Since we can’t measure , we use the fact that to see that

Physics 2015: Rolling Motion and Moment of Inertia  With this equation we can solve for I, which is the moment of inertia of the rolling object and calculate I from the measured data.  For many round objects I can be calculated as I = Kmr 2, where r is the radius, m is the mass, and K is a number dependent on the mass distribution and shape.  To compare your results to theory, write I as I = Kmr 2 in the equation above and then solve the equation for K. Then you will have an expression for K as a function of g, h, and v f.  Use this formula to calculate K for three different objects from your measured data.  Compare your experimental K-values to those in the literature. (e.g., for a disk K=1/2 as we saw in the “Rotational Motion” lab” last week).