Compound pendulum pivot force

The force at the pivot of a simple pendulum and the acceleration of the bob have been the subject of a number of papers. The present paper extends this analysis to a compound pendulum, which requires an extra torque to rotate the pendulum about its center of mass. The dependence of the pivot force on κ = k/a, the ratio of the radius of gyration k to the center of mass position a, is investigated. The pivot force on an ideal compound pendulum is shown to be the same as that for a lighter simple pendulum plus a mass located at the pivot.