PHYSICAL REVIEW PHYSICS EDUCATION RESEARCH 16, 010112 (2020) Students’ understanding of non-inertial frames of reference S. Küchemann,1,* P. Klein,1 H. Fouckhardt,2 S. Gröber,1 and J. Kuhn1 1Department of Physics, Physics Education Research Group, Technische Universität Kaiserslautern, Erwin-Schrödinger-Strasse 46, 67663 Kaiserslautern, Germany 2Department of Physics, Integrated Optoelectronics and Microoptics Research Group, Technische Universität Kaiserslautern, Erwin-Schrödinger-Strasse 46, 67663 Kaiserslautern, Germany (Received 26 February 2019; accepted 4 March 2020; published 24 March 2020) The concepts of the Coriolis and the centrifugal force are essential in various scientific fields and they are standard components of introductory physics lectures. In this paper, we explore how students understand and apply concepts of rotating frames of reference in the context of an example lecture demonstration experiment. We found in a predict-observe-explain setting that after predicting the outcome prior to the demonstration, only one out of five physics students correctly reported the observation of the trajectory of a sphere rolling over a rotating disc. Despite this low score, a detailed analysis of distractors revealed a significant improvement in the distractor choices during the observation of the experiment. In this context, we identified three main preconceptions and learning difficulties: The centrifugal force seems to be only required to describe the trajectory if the object is coupled to the rotating system, the inertial forces cause a reaction of an object on which they act, and students systematically mix up the trajectories in the stationary and the rotating frame of reference. Furthermore, we captured students’ eye movements during the predict task and found that physics students with low confidence ratings focused longer on relevant task areas than confident students despite having a comparable score. Consequently, this metric is a helpful tool for the identification of preconceptions using eye tracking. Overall, the results help us to understand the complexity of concept learning from demonstration experiments and provide important implications for instructional design of introductions to rotating frames of reference. DOI: 10.1103/PhysRevPhysEducRes.16.010112 I. INTRODUCTION derive the equation of motion of objects in non-inertial frames of reference [14–22] or contain a descriptive Rotating frames of reference play an important role in approach to the topic [23–27]. However, there are several a variety of fields in physics. Accordingly, Coriolis and shortcomings and false accounts outlined below, potentially centrifugal terms need to be considered for an accurate causing incoherent conceptions and complications in stu- account of the theoretical description of the motion of dents’ understanding. an object in rotating reference frames. While the Coriolis In this paper, we explore how students understand and force was originally introduced to describe the energy apply concepts of rotating frames of reference in the direct transfer in water wheels, nowadays it is applied to problems context of an example lecture demonstration experiment. in meteorology [1,2], oceanography [3], astrophysics [4], Therefore, we identify and study relevant preconceptions, optics [5], and nuclear physics [6]. Given this wide range of the non-obvious learning effect of experiment observation, applications, the Coriolis and the inertial centrifugal force and the relationship between response security and duration (ICF) are sometimes topics in introductory physics courses of focus on relevant areas (as measured by eye tracking). in college-level education and, accordingly, there are a The paper is structured in the following way. After this large number of experiments and open online materials – introduction, an overview of the current state of research and [7 13] which intend to demonstrate the Coriolis effect, i.e., the preliminary work follows in the second section and the the apparent deflection of an object by the Coriolis force. third section explains the materials and methods used in Moreover, there are several mechanics textbooks which this work. The subsequent section contains the results of the predict-observe-explain (POE) test including self-confidence *[email protected] ratings, student interviews, and eye-tracking data in the context of an example demonstration experiment of rotating Published by the American Physical Society under the terms of frames of reference. Then, these results are discussed in the the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to context of previous literature and, eventually in the final the author(s) and the published article’s title, journal citation, section, we conclude the manuscript with the main conse- and DOI. quences of the results for physics education research. 2469-9896=20=16(1)=010112(17) 010112-1 Published by the American Physical Society S. KÜCHEMANN et al. PHYS. REV. PHYS. EDUC. RES. 16, 010112 (2020) In this work, we address three research questions: that points outwards from the center of rotation can (1) What is the influence of a lecture experiment be responsible for this effect. demonstrating the motion of objects in non-inertial frames of reference on learning about the outcome of B. Why does the concept of inertial forces potentially the demonstration? cause problems for students? (2) What are the prevailing preconceptions of physics In some depictions of RFR the centrifugal force is students in the field of non-inertial frames of neglected when an object, which is moving in a RFR, reference? does not experience an interaction to the RFR. For instance, (3) Is there a specific eye-movement pattern that relates in Ref. [28], the author states that “the centrifugal effect is to the performance or confidence of physics students eliminated if there is no interaction between the rotating within a POE setting? disk and the body, like a ball rolling on the disk without friction.” This preconception that the centrifugal force only II. CURRENT STATE OF RESEARCH AND occurs, when the object is somehow coupled (e.g., by PRELIMINARY WORK friction or a rope) to the rotating system [28] is potentially guided by empirical experiences, such as the feeling of a A. Simplified conceptions of the Coriolis effect force pointing outwards when sitting in a carousel or in a and the centrifugal force car driving through a turn, i.e., the body reacts to the force A theoretical framework containing the equation of motion because the person is actually partially coupled to the of an object described in a rotating frame of reference (RFR) rotating system. This seems to be in conflict with the (also termed non-inertial frame of reference) is provided in characteristic that fictitious forces do not occur as a action- Sec. A1. In simplified depictions of a curved trajectory of an reaction pair with another force [29]. This cognitive object in a RFR, the Coriolis force is often presented as the dissonance can be resolved by discriminating between only cause for the deflection [7–13]. However, according to the centrifugal force which occurs as a consequence to a Eq. (A2) (see Appendix), the ICF also acts on the object in a centripetal force (here termed “reactive centrifugal force,” vector sum with the Coriolis force. The fact that the ICF is a RCF, see Appendix, Sec. A3for an example of the RCF) necessary quantity to describe the trajectory of an object in and the one which occurs as a fictitious force in a RFR “ ” a rotating frame of reference can be understood from two ( inertial centrifugal force, ICF) [30] which occurs as a arguments of a thought experiment. consequence of a description from a rotating frame of (I) Let us imagine a situation where a plane flies in a reference. Sometimes textbooks and scientific articles lack uniform motion over a large rotating disc starting this helpful linguistic distinction between RCF and ICF from the center of rotation. If an observer located on [14,17,28,31,32]. The reason for this could be that the the disc used the Coriolis force for the description mathematical equations are the same, only the situations in of the curved trajectory only, they would calculate which they occur and how they are perceived are different. that the plane returns to the center of rotation at some For the occurrence of the RCF, a coupling to the RFR is point in time because the Coriolis force is always indeed required so it occurs when a centripetal force occurs. perpendicular to the direction of motion thus leading For the occurrence of the ICF, a coupling to the RFR is not to a circular trajectory. For an observer in an required. Accordingly, the occurrence of a centripetal force stationary frame of reference (SFR), however, it is can be perceived (and might be related to the occurrence of obvious that this case would not occur because the the RCF) when driving through a turn or sitting in a merry plane flies in a uniform motion due to the absence of go round, whereas the occurrence of the ICF, for instance, any real force. In reality, the plane would pursue a for a passenger in an airplane flying in a uniform motion spiral trajectory for the observer in the RFR which is over a rotating disc, cannot be felt. the consequence of the vector sum of the inertial Apart from the RCF and ICF, a centrifugal force term ’ ’ centrifugal force and Coriolis force. may also occur as a d Alembert s force as pointed out by (II) During the aforementioned motion of the plane, the Kobayashi, which is an inertial resistance and occurs as a absolute value of the velocity jv⃗0j in the RFR would consequence of a coordinate transformation [30] to plane 0 “ increase according to Eq. (A1) because v⃗is a vector polar coordinates and has the form mass × centripetal ” sum of two perpendicular vectors, the velocity in the acceleration.