Conical pendulum

Abstract: In this article we refer to the somewhat surprising fact that questions connected with the mechanics of such popular physical models as the simple and conical pendulum seem to be difficult not only for secondary school students but even for those taking introductory university courses in physics. Two tests concerning both the simple pendulum and the conical pendulum were examined by groups of 50 students. We give a brief analysis of their unsatisfactory results as well as a correct presentation of the problem at the secondary school level.

Abstract: The present invention relates to an electric vibration motor built according to the so-called "conical pendulum" principle, which principle is explained and exemplified in such patents as that to Svenson, No 2,194,410, dated March 19, 1940 In known vibration motors generally constructed

Abstract: The rolling friction phenomenon is encountered in a wide range of applications and when two different materials are involved, quantitative characterization is necessary. The parameter to be determined is the coefficient of rolling friction, for whose estimation a methodology is proposed, based on the damped oscillation of a conical pendulum. The pure rolling contact between a sphere and a plane is obtained when a steel ball is the bob of the pendulum, which rolls on an inclined plate made from a second material from the contacting pair. The mathematical model of the motion of a conical pendulum constructed from a revolution body supported on an inclined plane in the presence of the rolling friction is developed. The dynamic equations of the rigid body with fixed point are applied and the differential equation of motion of the pendulum is obtained together with the expressions of the reaction forces in the contact point. For different pairs of materials, tests are performed on a laboratory device. The damped oscillatory motion of the conical pendulum is video-captured for the estimation of the angular amplitude variation. A program for image processing is developed for measuring the values of angular elongations from the analysis of each frame of the video and, finally, the coefficient of rolling friction is obtained. For all the materials tested, a linear decrease in angular amplitude is detected and the slope of angular amplitude can be considered as a characteristic parameter related to the coefficient of rolling friction between the two materials.

Abstract: We study the turning point problem of a spherical pendulum. The special cases of the simple pendulum and the conical pendulum are noted. For simple initial conditions the solution to this problem involves the golden ratio, also called the golden section, or the golden number. This number often appears in mathematics where you least expect it. To put our result in perspective we briefly discuss its relevance in physics.