Conical Pendulum: Part 2 A Detailed Theoretical and Computational Analysis of the Period, Tension and Centripetal Forces

Abstract

This paper represents a continuation of the theoretical and computational work from an earlier publication, with the present calculations using exactly the same physical values for the lengths L (0.435 m – 2.130 m) for the conical pendulum, mass m = 0.1111 kg, and with the local value of the acceleration due to gravity g = 9.789 ms-2. Equations for the following principal physical parameters were derived and calculated: period T, angular frequency , orbital radius R, apex angle , tension force FT and centripetal force FC (additional functions were calculated when required). Calculations were performed over a wide range of values of the apex angle (0 85), corresponding to a calculated tension force FT range of approximately (mg FT 12 N) or alternatively (mg FT 11 mg) for the string. A technique is demonstrated to determine an accurate value of an unknown pendulum mass, by using a graphical analysis. Intercepts and asymptotic lines with respect to both the horizontal and vertical axes are described and fully explained. The main emphasis for this paper is to present highly detailed graphical charts for the calculated theoretical functions and appropriate physical parameters. Theoretical analysis is presented in comprehensive detail, showing full mathematical derivations and alternative equations when this approach is considered to be advantageous for both understanding and computational presentation.