'It Has to Go Down A Little, In Order to Go Around'- Following Feynman on the Gyroscope

In this paper we show that with the help of accessible, teaching quality equipment, some interesting details of the motion of a gyroscope, typically overlooked in introductory courses, can be measured and compared to theory. We begin by deriving a simple relation between the asymptotic dip angle of a gyroscope released from rest and its precession velocity. We then describe an experiment which measures these parameters. The data gives excellent agreement with the model. The idea for this project was suggested by the discussion of gyroscopic motion in The Feynman Lectures on Physics. Feynman's conclusion (stated in colloquial terms and quoted in the title) is confirmed and, in addition, conservation of angular momentum, which underlies this effect, is quantitatively demonstrated.Comment: 6 pages, 4 figure

Energy in one dimensional linear waves in a string

We consider the energy density and energy transfer in small amplitude, one-dimensional waves on a string, and find that the common expressions used in textbooks for the introductory physics with calculus course give wrong results for some cases, including standing waves. We discuss the origin of the problem, and how it can be corrected in a way appropriate for the introductory calculus based physics course.Comment: 5 page

Parametric resonance in a linear oscillator at square-wave modulation

Abstract The phenomenon of parametric resonance in a linear torsion spring oscillator caused by a square-wave modulation of its moment of inertia is explained and investigated both analytically and with the help of a computer simulation. Characteristics of parametric resonance and regeneration are found and discussed in detail. Ranges of frequencies within which parametric excitation is possible are determined. Stationary oscillations at the boundaries of these ranges and at the threshold conditions are investigated

Had the planet mars not existed: Kepler's equant model and its physical consequences

We examine the equant model for the motion of planets, which has been the starting point of Kepler's investigations before he modified it because of Mars observations. We show that, up to first order in eccentricity, this model implies for each orbit a velocity which satisfies Kepler's second law and Hamilton's hodograph, and a centripetal acceleration with an inverse square dependence on the distance to the sun. If this dependence is assumed to be universal, Kepler's third law follows immediately. This elementary execice in kinematics for undergraduates emphasizes the proximity of the equant model coming from Ancient Greece with our present knowledge. It adds to its historical interest a didactical relevance concerning, in particular, the discussion of the Aristotelian or Newtonian conception of motion

Stability boundary approximation of periodic dynamics

We develop here the method for obtaining approximate stability boundaries in the space of parameters for systems with parametric excitation. The monodromy (Floquet) matrix of linearized system is found by averaging method. For system with 2 degrees of freedom (DOF) we derive general approximate stability conditions. We study domains of stability with the use of fourth order approximations of monodromy matrix on example of inverted position of a pendulum with vertically oscillating pivot. Addition of small damping shifts the stability boundaries upwards, thus resulting to both stabilization and destabilization effects.Comment: 9 pages, 2 figure

Parametric resonance for vibration energy harvesting with design techniques to passively reduce the initiation threshold amplitude

A vibration energy harvester designed to access parametric resonance can potentially outperform the conventional direct resonant approach in terms of power output achievable given the same drive acceleration. Although linear damping does not limit the resonant growth of parametric resonance, a damping dependent initiation threshold amplitude exists and limits its onset. Design approaches have been explored in this paper to passively overcome this limitation in order to practically realize and exploit the potential advantages. Two distinct design routes have been explored, namely an intrinsically lower threshold through a pendulum-lever configuration and amplification of base excitation fed into the parametric resonator through a cantilever-initial-spring configuration. Experimental results of the parametric resonant harvesters with these additional enabling designs demonstrated an initiation threshold up to an order of magnitude lower than otherwise, while attaining a much higher power peak than direct resonance

The impact of tides on the capillary transition zone

The capillary transition zone, also known as the capillary fringe, is a zone where water saturations decrease with height above the water table/oil–water contact as a result of capillary action. In some oil reservoirs, this zone may contain a significant proportion of the oil in place. In groundwater assessments, the capillary fringe can profoundly affect contaminant transport. In this study, we investigated the influence of a tidally induced, semi-diurnal, change in water table depth on the water saturation distribution in the capillary fringe/transition zone. The investigation used a mixture of laboratory experiments, in which the change in saturation with depth was monitored over a period of 90 days, and numerical simulation. We show that tidal changes in water table depth can significantly alter the vertical water saturation profile from what would be predicted using capillary–gravity equilibrium and the drainage or imbibition capillary pressure curves

Using a smartphone acceleration sensor to study uniform and uniformly accelerated circular motions

The acceleration sensor of a smartphone is used for the study of the uniform and uniformly accelerated circular motions in two experiments. Data collected from both experiments are used for obtaining the angular velocity and the angular acceleration, respectively. Results obtained with the acceleration sensor are shown to be in good agreement with alternative methods, like using video recordings of both experiments and a physical model of the second experiment.Castro-Palacio, JC.; Velazquez, L.; Gómez-Tejedor, JA.; Manjón Herrera, FJ.; Monsoriu Serra, JA. (2014). Using a smartphone acceleration sensor to study uniform and uniformly accelerated circular motions. Revista Brasileira de Ensino de Fisica. 36(2):2315-2315. doi:10.1590/S1806-11172014000200015S2315231536