Speaker
Description
The Centripetal Force Experiment is a standard experiment for physics student labs in which a mass is attached is rotated in a circle at different angular velocities. The mass is attached to a string that goes around a pulley and is attached a force sensor by a string over a pulley so that the length of the string to the pulley is the radius $R$ of the circular motion, and so the centripetal force is measured. In this experiment, that mass is assumed to be a point mass, but in reality, it is a disk whose radius some fraction of $R$, which introduces a systematic error. We have calculated the centripetal force due to a disk and have found a factor $\chi(b/R)$, where $b$ is the radius of the disk, which is written in terms of Complete Elliptic Integrals of the First and Second Kind. The centripetal force is then $F_c=m \omega^2 R \chi(b/R)$. The correction factor is always less than 1.13. The factor could be one of the contributions to the systematic error that account for the theoretical value of the centripetal force always being considerably less than the centripetal force measured in the experiment.
