Principal physical parameters of the conical pendulum calculated directly from the orbital period

Abstract

The analysis, calculations and graphical charts presented here in this paper are based directly on a recently published paper by the first two of the above-named authors. In the present paper, it is clearly demonstrated that all of the following nine (or eleven including the centripetal acceleration and total mechanical energy) principal physical parameters can be calculated directly by using only the rotational period of a conical pendulum, assuming that the pendulum mass, string length and local gravitational acceleration are known precisely: string tension force, centripetal force (yielding the centripetal acceleration by simple direct calculation), orbital radius, orbital speed, apex angle, rotational moment, magnitude of the angular momentum, potential energy, kinetic energy and consequently the total mechanical energy. All of these physical parameters were calculated for a range of pendulum lengths 0.400 ⩽ L ⩽ 2.00 m (in nine equal interval steps of 0.200 m) and are illustrated with appropriate charts showing how these physical parameters vary as a function of the orbital period. The limiting values of the parameters as the multiple chart lines approach the horizontal and vertical exes (where this is appropriate) are explained in detail, along with any specifically interesting observations that can also be made, for example, axis intercept gradients and any points of curve inflexion (which are readily explained and calculated using calculus). For the three situations in which inflexions have been demonstrated, appropriate (and very simple) equations for the locus of points have been determined.