![]() ![]() In this paper, we perform full experimental and numerical analysis of the gee-haw whammy diddle. Recently in the work by Bhattacharjee 5, the problem was reconsidered by connecting it to the Kapitza pendulum and recalling the idea of synchronization between the motion of the stick and the propeller. In the experiment, recordings were performed with very low temporal resolution (30 fps), which apparently led to rather imprecise results of the motion of the stick. In the analytical part, no slip is assumed between the stick and the propeller, which makes the problem and its solution similar to the hula-hoop problem however, there is no experimental evidence for this assumption. However, this work has a few limiting factors embedded. He also presented the hypothesis that the frequency of rotation of the propeller is synchronized with the driving frequency of the notches. However, the presented experiment concluded only a one-sided implication of the hypothesis, namely that an elliptical movement of the stick causes a rotation of the propeller in the given direction, but did not show that this is the primary cause of the movement in the real toy.įurther analytical and experimental research was performed by Wilson 4, whose results partially contradict the previous work in claiming that the direction of rotation of the end of the stick does not necessarily define the direction of the propeller’s motion. ![]() They confirmed the validity of the original hypothesis – that the rotation direction is determined by the elliptical movement of the end of the stick and the speed of the propeller by the magnitude of the areal velocity of the end of the stick. 3 provided presumably the most complex analysis of the problem so far, from both a theoretical and an experimental point of view. Almost a decade later two other papers appeared on this topic. Authors also provide a basic numerical output given the possibilities of computers of that period. 2 where the direction of rotation is suggested to be related to the way the stick is being held by hand. This idea was further developed by Schlichting et al. In one of the first works on this topic, Leonard 1 suggests that the propeller vibrates due to an elliptical motion of the end of the stick and the direction of the motion is determined by the phase shift between the vertical and horizontal stick vibrations, caused by different rubbing directions. This is however not the case despite research on this topic lasting almost a century. ![]() Being a mechanical device, one would expect to be able to pinpoint a simple and clear explanation of why and how linear motion along the notches induces a circular motion of the propeller and what defines the direction of this motion. ![]()
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