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A bicycle wheel that was initially spinning freely was placed in contact with a rough surface and a digital film was made of its motion. Using Tracker software for video analysis, we obtained the velocity vectors for several points on the wheel, in the frame of reference of the laboratory as well as in a relative frame of reference having as its origin the wheel`s center of mass. The velocity of the wheel`s point of contact with the floor was also determined obtaining then a complete picture of the kinematic state of the wheel in both frames of reference. An empirical approach of this sort to problems in mechanics can contribute to overcoming the considerable difficulties they entail.
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We describe a study on the conceptual difficulties faced by college students in understanding hydrodynamics of ideal fluids. This study was based on responses obtained in hundreds of written exams and oral interviews, which were held with first-year Engineering and Science university students. Their responses allowed us to identify a series of misconceptions unreported in the literature so far. The study findings demonstrate that the most important difficulties arise from the students inability to establish a link between the kinematics and dynamics of moving fluids, and from a lack of understanding regarding how different regions of a system interact.
The problem of a disc or cylinder initially rolling with slipping on a surface and subsequently transitioning to rolling without slipping is often cited in textbooks. The following experiment serves to clearly demonstrate the transition from rolling with slipping to rolling without slipping. In the experiment, a rotating bicycle wheel was placed in contact with a horizontal surface and the wheel in motion was tracked using Tracker video analysis software [8]. The software created linear velocity plots for the centre of mass and a point on the circumference as well as a plot of the angular velocity of the rotating wheel. The time evolution plots created by Tracker clearly illustrate the transition between the two types of motion.
The motion of submerged magnetic microspheres rolling at a glass-water interface has been studied using magnetic rotation and optical tweezers combined with bright-field microscopy particle tracking techniques. Individual microspheres of varying surface roughness were magnetically rotated both in and out of an optical trap to induce rolling, along either plain glass cover slides or glass cover slides functionalized with polyethylene glycol. It has been observed that the manipulated microspheres exhibited nonlinear dynamic rolling-while-slipping motion characterized by two motional regimes: At low rotational frequencies, the speed of microspheres free-rolling along the surface increased proportionately with magnetic rotation rate; however, a further increase in the rotation frequency beyond a certain threshold revealed a sharp transition to a motion in which the microspheres slipped with respect to the external magnetic field resulting in decreased rolling speeds. The effects of surface-microsphere interactions on the position of this threshold frequency are posed and investigated. Similar experiments with microspheres rolling while slipping in an optical trap showed congruent results.
Students in interviews on a wave physics topic give answers through embodied actions which connect their understanding of the physics to other common experiences. When answering a question about wavepulses propagating along a long taut spring, students gestures help them recruit information about balls thrown the air. I analyze gestural, perceptual, and verbal information gathered using videotaped interviews and classroom interactions. I use conceptual blending to describe how different elements combine to create new, emergent meaning for the students and compare this to a knowledge-in-pieces approach.
We report on several specific student difficulties regarding the Second Law of Thermodynamics in the context of heat engines within upper-division undergraduates thermal physics courses. Data come from ungraded written surveys, graded homework assignments, and videotaped classroom observations of tutorial activities. Written data show that students in these courses do not clearly articulate the connection between the Carnot cycle and the Second Law after lecture instruction. This result is consistent both within and across student populations. Observation data provide evidence for myriad difficulties related to entropy and heat engines, including students struggles in reasoning about situations that are physically impossible and failures to differentiate between differential and net changes of state properties of a system. Results herein may be seen as the application of previously documented difficulties in the context of heat engines, but others are novel and emphasize the subtle and complex nature of cyclic processes and heat engines, which are central to the teaching and learning of thermodynamics and its applications. Moreover, the sophistication of these difficulties is indicative of the more advanced thinking required of students at the upper division, whose developing knowledge and understanding give rise to questions and struggles that are inaccessible to novices.
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