Determination of gravitational acceleration g using a uniform circular motion

Abstract

A lead sphere is suspended on a fishline attached to the vertical shaft of an electric motor which forces the sphere into uniform circular motion, making a conical pendulum. A mathematical treatment which considers the tension in the fishline and the gravitational force and their geometry reveals a critical length for the fishline. Using a length in excess of the critical allows a measurement of a distance which, when multiplied by the square of the angular velocity, gives g. Results agreeing to better than 1% with the accepted value of g are easily obtained. The equipment is inexpensive. The experiment is presented for demonstration purposes primarily, but can be expanded in scope to be a laboratory experiment.