Spring-Mass Correction in Uniform Circular Motion

IntroductionThe simplest model of circular locomotion is a point mass moving uniformly on a circle. To produce circular motion, a centripetal force is generated. This study investigated contributions of individual limbs to the net centripetal force in horses trotting on a circle.MethodsSix horses trotted on a 6 m diameter circle at their preferred speed. Optical motion capture (Motion Analysis Corp) recorded kinematics, while six force plates (AMTI) recorded ground reaction forces (GRF). Whole body center of mass (CoM) was computed using a 23‐segment rigid body model. The GRF of each limb was expressed at the CoM in cylindrical coordinates centered at a best‐fit circle of the ground path of the CoM. Average vertical, tangential and radial force components were computed for each limb over the whole stride duration. Forces were analyzed using ANOVA with Tukey HSD post‐hoc tests.ResultsThe maximum ground‐path deviation of the CoM from the best‐fit circle among all trials was only 2.8% of the radius. The forelimbs contributed an average centripetal (radial) force of 0.49 ± 0.16 N/kg (mean ± SD, normalized to body mass), which was significantly greater (P<0.001) than the hind limb contribution of 0.36 ± 0.13 N/kg. There was no significant difference between inside and outside limbs.ConclusionsThe contribution of individual limbs to the centripetal force provided a direct indication of their role in circular locomotion. The forelimbs generated significantly more centripetal force, possibly in direct relation to their greater support of the body mass against gravity.Ethical Animal ResearchThe study was approved by the MSU Institutional Animal Care and Use Committee, protocol #06/11‐112‐00. Sources of funding: This study was funded by the McPhail Endowment. SD Starke's collaborative research visit for this project was funded by the British Society for Animal Science, Murray Black Award. Competing interests: none.

The suspension characteristics of a 10 ton truck with a highly non-linear leaf spring suspension have been investigated. The acceleration transmissibility frequency response characteristics of the truck were first investigated. Results showed that whereas the bounce (sprung mass) resonant frequency was quite close to that expected, the wheel-hop (unsprung mass) resonant frequencies were roughly twice that expected. As no obvious mechanism for this effect was evident, the static stiffness characteristics of the suspension were measured in an attempt to understand this phenomenon. A simple plot of the resulting suspension-generated force against suspension deflection showed that two distinct stiffness regimes were present; the first, which was associated with small suspension deflections of between 2 and 4 mm, was significantly greater than the second, which was associated with larger suspension deflections. A state-variable linear 5 degree-of-freedom spring mass damper model of the vehicle was created within MATLAB in an attempt to predict the frequency response characteristics of the vehicle. The state-variable model predictions were close to those seen experimentally for the sprung mass at frequencies below 3 Hz, but were quite incorrect for both the sprung and unsprung masses above this frequency. The state-variable model was then used again with increased values of suspension stiffness and results showed that using these higher values led to a more accurate predicted response for both the sprung and unsprung masses above 3 Hz, whereas below this frequency their responses were clearly incorrect. Comparison of experimental and predicted results showed that the vehicle frequency response was dominated above 3 Hz by the low suspension deflection-high stiffness regime identified in the static stiffness results, whereas below this frequency, the high suspension deflection- low stiffness regime tended to dominated the response. To overcome the problem of the transition from the low to the high stiffness regimes when predicting the frequency response characteristics, a non-linear model was created using MATLAB and SIMULINK. Results showed that the model was able to capture this transition, with resulting frequency response curves for both the sprung and unsprung masses being very similar to the experimental results. Further refinements to the model were able to account for additional discrepancies between predictions and experimental results. The non-linear nature of the spring stiffnesses, resulting in a very useful hysteresis damping effect at the sprung mass resonant frequency, meant that for most normal road conditions the vehicle would ride on a near solid suspension. The apparent advantages of the extra damping would therefore be o set by a significant decrease in ride quality, and this was especially evident in respect to road noise and vibration-a finding borne out in practice. This paper establishes the principal characteristics of the truck suspension and goes on to describe the linear state-variable and non-linear models created to simulate the frequency response characteristics of the vehicle suspension.

American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines. Introduction The use of centrifugal force to separate fluids is a proved process that has been applied by many industries. The force is explained in college physics textbooks under uniform circular motion where Newton's laws of motion are discussed. A classic textbook example describes an object of known weight that is held in a circular path by a string of known length, and the weight is moving at a constant speed. The inward force that is developed is known as the centripetal force. The equal and opposite reaction that is in the outward direction is known as the centrifugal force. This is the force that we use to separate gas well fluids in a centrifugal-type separator. The flowing pressure at the wellhead furnishes the energy for the process. Upon expansion to a lower pressure at the wellhead choke, the natural gas, condensate, and water flow to the centrifugal separator for rotation and subsequent separation. The fluids tend to separate in layers of uniform density. Water collects on the internal surface of the separator, condensate flows on the water, and the gas flows in a circular pattern in the center of the vessel. FUNDAMENTALS The following formula for centripetal - force summarizes the process. 2WVFc = ———,gR where Fc = centripetal force, lbW = weight of the fluids, lbV = velocity, ft/secg = gravity constant, 32 ft/sec/secR = radius of the circle, ft The centripetal force, Fc, is that force in the inward direction, expressed in pounds, that is developed when the fluids are directed in a circular path in the separator. The centrifugal force is an equal and opposite reaction to the centripetal force; therefore, calculated values for Fc are vend for the centrifugal forces in the outward direction. The weight of the fluids can be calculated from the fixed dimensions of the internals of the vessel, the operating pressure, and temperature in the separator, and the gas-condensate ratio and gas-water ratio of the flowing stream.

In this undergraduate laboratory experiment we measure the centripetal force acting on a bob in uniform circular motion. As the experiment was originally designed, it consistently yielded large errors due to a subtle twist of the bob as the mass was increased incrementally. This error is due to the fact that the center of mass changes relative position as the mass is incremented; therefore, the spring that provides the centripetal force for the apparatus causes an unintended torque on the bob. A solution to the problem consists of positioning the incremental masses so that the center of mass does not change position. This simple correction provides a useful lesson on redesigning an undergraduate laboratory experiment to obtain better agreement with theory.

Uniform circular motion is one of the key mechanics topics in Physics that students fail to comprehend and master. In South Africa, uniform circular motion is currently not taught to Physical Sciences Matriculate learners and thus students are only introduced to it at university level. It is appreciated that poor comprehension of fundamental concepts and tenets of uniform circular motion leads to difficulties in understanding related topics such as Rotational Kinematics and Rotational Dynamics. This study investigated student teachers’ misconceptions about uniform circular motion and its pertinent underlying concepts such as tangential acceleration and centripetal acceleration. The study also attempted to figure out the source(s) of the ensuing misconceptions. The sample of the study consisted of 41 second-year Physical Sciences student teachers at a South African university. A multiple-choice test consisting of 20 questions on uniform circular motion was administered. Simple and explanatory statistical techniques were employed to analyse the data and appropriate intervention methods were proposed to curtail the identified misconceptions. The study revealed that factual misconceptions and conceptual misunderstandings were prevalent amongst the student teachers who took part in the research exercise.

When a vibrating thin structure moves in a heavy flow field, the effect of sound waves on the structure cannot be ignored. This effect is especially pronounced when the relative velocity of the structure and the flow field increases. The hybrid numerical method of finite element method (FEM) and convective boundary element method (BEM) is proposed to solve acoustic-structural interaction problems in uniform relative motion between structure source and fluid. Besides, an acoustic-analogy Lorentz transform is proposed to handle the direct convective boundary integral equation (BIE), which makes the convective BIE has the same form as traditional BIE so that there are no more convective terms and extra singular integrals. The continuity condition at the fluid-structure interface is also proposed to generate the coupling equation. Compared with the traditional FEM, this hybrid method has the advantages of greatly reducing the number of finite elements outside the structure as well as automatically satisfying the radiation condition at far field. And compared with the direct convective BIE, this method reduces the computational complexity and time. It is potential to deliver a solver with higher accuracy and less memory consumption. Some numerical examples are designed to study the influence of the convective effect. Keywords: Acoustic-structural interaction, Finite element method, Boundary element method, FEM-BEM coupling

In this study, we demonstrate an interesting relationship between simple harmonic motion and uniform circular motion trough a simple experiment. The experiment requires a low cost-easily found materials and free software, Tracker. To represent uniform circular motion, we use a tape that is stick on a fan moving with the constant angular speed. Meanwhile, spring and pendulum motion are used to represent simple harmonic motion. Through Video Tracker analysis, we have shown that the positions (x and y coordinates) of an object undergoes uniform circular motion fit to the sinusoidal function of time, as same as shown in simple harmonic motion. This simple experiment can be used in high school physics course to lead students in developing a conceptual understanding of uniform circular motion with a less mathematical approach.

Numerous approaches to seismic detection have been proposed. Usual methods to sense seismic vibrations use either accelerometers to measure the ground acceleration or geophones based on electro-dynamic actuator velocimeters. In this paper, we present the design and the development of a polarimetric transducer using a single-mode optical fiber for low level and low frequency vibration measurements such as those encountered in seismology. Polarimetric sensors can be optimized to have a reduced sensitivity to temperature. The mechanical part of our one-dimensional seismic sensor is based on a spring-mass device. A small section of the fiber is squeezed between a substrate connected to the ground and the sprung mass. The resulting force acts along a vertical direction onto a small section of the optical fiber. The elastooptic effect induces stress birefringence which varies temporally with the frequency of the applied force. We used a polarized and single-mode laser diode source to couple light in the fiber. The induced polarization modulation measured at the output of the fiber gives information of the seismic signals. The physical model of the developed inertial seismometer has been considered as a mass-and-spring system with viscous damping. Firstly, we expose the principle behind our optical fiber seismic sensor. Next, we computed the dynamic characteristics of the seismic sensor. Physical simulation results obtained using the analytical model are presented and discussed. Finally, we present experimental results measured with our seismic fiber sensor. Both model and experimental results demonstrate the potential of the sensor for low level and low frequency vibrations characterization.

An extension of Kirchoff’s theory of the motion of solid bodies in irrotationally moving liquids to the case of motion in liquids in which a vorticity is present does not exist. Only a few isolated cases of such motion are known. Bearing on the consideration of this paper, there is an important work by Taylor which expresses the additional pressure effect on a system of cylinders moving in a perfect liquid without rotation when the whole system is rotated uniformly about an axis. Taylor’s theory reduces the problem of such motion to one of irrotational motion. In the present paper the motion of a perfect liquid having constant vorticity, and in which a cylinder of any cross-section is moving in any manner, has been considered. The pressure integral can be obtained in a simple form, referred to axes fixed in the body, which is very suitable for calculation. It is shown, whenever the pure potential motion of the liquid for the rotation of the cylinder and the solution of a definite potential problem or the corresponding Green’s function can be found, the formula can be applied to calculate the motion of the cylinder in liquids with constant vorticity. Two important cases of constant vorticity are uniform shear motion along a direction and uniform rotation about an axis. In the present paper the former case is considered in detail for an elliptic cylinder. The case of uniform rotation being covered by Taylor’s result it is only verified that the present method gives the same result as Taylor’s formulae. There are some simple free motions of an elliptic cylinder in a liquid with uniform shear motion which have been discussed in the paper. 2—Equations of Motion Referred to Axes Fixed in the Body and the Pressure Integral It is first necessary to write down the equations of motion referred to a system of axes fixed in the body having both translation and rotation. These equations are obtained below following a method of Taylor.

Although the spherical underwater robot has the advantage of 0 radius for the turning locomotion, a variable radius of turning locomotion is also necessary for the path planning and obstacle avoidance of an underwater robot. This paper focused on the turning locomotion with variable radius for the forthgeneration spherical underwater robot (SUR IV) with the hybrid propulsion device. The hybrid propulsion device could be controlled by PWM signals to modify the thrust and linear velocity. The motion state of the turning locomotion was developed in different radius. The centripetal force of curve motion is also analyzed by Newton's first law. The relationship between the centripetal force and turning radius was proposed. In order to verify the turning locomotion with different turning radius, the experiment was carried out in the swimming pool. The experimental results show that the change of the turning radius can be achieved by adjusting the control input PWM signal of the main thruster and the assist thruster.

The Sagnac effect, named after its discoverer, is the phase shift occurring between two beams of light, traveling in opposite directions along a closed path around a moving object. A special case is the circular Sagnac effect, known for its crucial role in GPS and fiber-optic gyroscopes. It is often claimed that the circular Sagnac effect does not contradict special relativity theory (SRT) because it is considered an accelerated motion, while SRT applies only to uniform, non-accelerated motion. It is further claimed that the Sagnac effect, manifest in circular motion, should be treated in the framework of general relativity theory (GRT). We counter these arguments by underscoring the fact that the dynamics of rectilinear and circular types of motion are completely equivalent, and that this equivalence holds true for both non-accelerated and accelerated motion. With respect to the Sagnac effect, this equivalence means that a uniform circular motion (with constant w) is completely equivalent to a uniform rectilinear motion (with constant v). We support this conclusion by convincing experimental findings, indicating that an identical Sagnac effect to the one found in circular motion, exists in rectilinear uniform motion. We conclude that the circular Sagnac effect is fully explainable in the framework of inertial systems, and that the circular Sagnac effect contradicts special relativity theory and calls for its refutation.

Classical electrodynamics basically assumes that a charged particle is a point charge, whose size is infinitesimal. This assumption caused a lot of problems with the radiation reaction (also called the self-force), by which a radiating particle feels friction. For example, Lorentz-Abraham-Dirac (LAD) model, which is the earliest theory about radiation reaction based on a point charge, leads to unphysical solutions such as runaway solutions and preacceleration. It has been tried to modify LAD model, and the most successful result was Landau-Lifshitz (LL) model, which also interpret well the recent experimental data of radiation reaction from laser-plasma interactions. However, even LL model has some problems, and particularly it cannot explain the radiation reaction of a uniformly accelerated charge. In this talk, we assume that the size of a particle is finite but the particle itself is completely indistinguishable from a point charge. By this assumption, we calculate the self-force of this particle undergoing uniform acceleration and uniform circular motion. The calculations show that the self-force of uniform acceleration can increase the effective mass of the particle, and it explain why a uniformly accelerated particle needs more energy to radiate. The calculations also indicate that the self-force of uniform circular motion only depends on the acceleration at the retarded time. In addition, we propose that there is a classical limit of the acceleration, and by combining it with the Schwinger limit we suggest that the classical radius of a particle is somehow related to the reduced Compton wavelength.

A biologically inspired method for estimating 2D high-speed translational motion

Transmission error investigation of gearbox using rigid-flexible coupling dynamic model: Theoretical analysis and experiments

Students' argumentation ability is very important in the learning process. Argumentation activity is an effective teaching-learning process that becomes an important in learning today and a major concern in many countries over the past decade. The aim of the research is to show the effect of problem-based learning using circle share activity on students' argumentation ability. Problem-Based learning using circle share activity is the learning model where problem-based learning with the use of two steps circles shares discussion. The first step, the discussion of the problem among student was conducted in each group which consisted of three or four students. The second step, the student discussion was conducted between groups by circle share. The discussion among students between groups will result in more explanation about problem-solving than each group. For control class, students learn using classroom discussion. The data was collected using two-tier tests on uniform circular motion, student reasoning of choosing the answer was considered as argumentation that was analyzed with Toulmin Model Argumentation. The results of the research showed that the student argumentation ability in the experimental class was better than the control class.