Pub Date : 2024-06-05DOI: 10.1088/1361-6404/ad44f8
Vladimir Ivchenko
We consider the features of pellet motion under the elastic force acting from a decompressing spring of a finite mass. The muzzle speed of the pellet decreases as the ratio between spring and pellet mass increases. In the general case, the pellet loses contact with the spring as it is stretched. This effect occurs due to the fact that the peak of elastic displacement wave, propagating from the fixed end, reaches the opposite end of the spring. With a large relative mass of the pellet, it accelerates along a quarter of the sinusoid. At the limit of a very small pellet mass, it moves nearly all the time along with the end of the spring at an almost constant speed, approximately equal to the speed of sound propagation in the spring. In this case, after the initial compression, the pellet passes the equilibrium position, and comes off after moving a similar distance beyond the equilibrium.
{"title":"The internal ballistics of a spring gun","authors":"Vladimir Ivchenko","doi":"10.1088/1361-6404/ad44f8","DOIUrl":"https://doi.org/10.1088/1361-6404/ad44f8","url":null,"abstract":"We consider the features of pellet motion under the elastic force acting from a decompressing spring of a finite mass. The muzzle speed of the pellet decreases as the ratio between spring and pellet mass increases. In the general case, the pellet loses contact with the spring as it is stretched. This effect occurs due to the fact that the peak of elastic displacement wave, propagating from the fixed end, reaches the opposite end of the spring. With a large relative mass of the pellet, it accelerates along a quarter of the sinusoid. At the limit of a very small pellet mass, it moves nearly all the time along with the end of the spring at an almost constant speed, approximately equal to the speed of sound propagation in the spring. In this case, after the initial compression, the pellet passes the equilibrium position, and comes off after moving a similar distance beyond the equilibrium.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"24 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141550634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-27DOI: 10.1088/1361-6404/ad44f6
Timothy H Boyer
Electromagnetic quantities at a spacetime point have tensor Lorentz transformations between relatively-moving inertial frames. However, since the Lorentz transformation of time between inertial frames depends upon both the time and space coordinates, averages of electrodynamic quantities at a single time will in general depend upon the inertial frame, and will differ between inertial frames. Here we illustrate how the use of continuous charge and current distributions rather than point-charge distributions can lead to physically mystifying and even inaccurate results for electromagnetic quantities and physical phenomena. The discrepancy noted between the average electric field values in different inertial frames is particularly striking because it is first order in the relatative velocity between the frames.
{"title":"Point-charge models and averages for electromagnetic quantities considered in two relativistic inertial frames","authors":"Timothy H Boyer","doi":"10.1088/1361-6404/ad44f6","DOIUrl":"https://doi.org/10.1088/1361-6404/ad44f6","url":null,"abstract":"Electromagnetic quantities at a spacetime point have tensor Lorentz transformations between relatively-moving inertial frames. However, since the Lorentz transformation of time between inertial frames depends upon both the time and space coordinates, averages of electrodynamic quantities at a single time will in general depend upon the inertial frame, and will differ between inertial frames. Here we illustrate how the use of continuous charge and current distributions rather than point-charge distributions can lead to physically mystifying and even inaccurate results for electromagnetic quantities and physical phenomena. The discrepancy noted between the average electric field values in different inertial frames is particularly striking because it is first order in the relatative velocity between the frames.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"18 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141167915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-27DOI: 10.1088/1361-6404/ad3ca4
Ana Susac, Stefan Küchemann, Maja Planinic and Jochen Kuhn
The recognition and distinction of typical interference and diffraction patterns are among the expected learning outcomes of studying wave optics. Previous studies have reported high school students’ difficulties with this task. In this study, we investigated university students’ ability to distinguish typical wave optics patterns obtained by the double slit, single slit, and diffraction grating. We also used eye tracking to obtain an insight into the distribution of students’ visual attention during the task. The results showed that university students had similar difficulties in recognizing wave optics patterns as high school students. They mostly struggled with identification of the double-slit interference patterns and diffraction grating patterns of monochromatic light while they were more successful in recognition of the diffraction pattern of white light on an optical grating and single-slit diffraction patterns. The eye-tracking data also revealed that students spent more time attending colourful than grey patterns in questions regarding diffraction of white light on an optical grating, thus suggesting that they were aware that the diffraction grating separates white light into colours. In questions regarding monochromatic light patterns, students overall mostly attended the single-slit diffraction pattern probably because of its distinct central maximum. Furthermore, the longer fixation duration for patterns compared to the text implies that students found it easier to extract information from the text than from the patterns. No prior research has compared the number of transitions during problem solving with the accuracy of the answers. In this study, we observed that students who incorrectly solved a task demonstrated a significantly higher number of gaze transitions between the question and the options, as well as among different options. The results of this study indicate that the recognition of typical wave optics patterns is also difficult for university students, thus suggesting that more attention should be paid to systematic observation and identification of key features of basic wave optics phenomena in lecture demonstrations and student laboratories.
{"title":"University students’ recognition of typical wave optics patterns","authors":"Ana Susac, Stefan Küchemann, Maja Planinic and Jochen Kuhn","doi":"10.1088/1361-6404/ad3ca4","DOIUrl":"https://doi.org/10.1088/1361-6404/ad3ca4","url":null,"abstract":"The recognition and distinction of typical interference and diffraction patterns are among the expected learning outcomes of studying wave optics. Previous studies have reported high school students’ difficulties with this task. In this study, we investigated university students’ ability to distinguish typical wave optics patterns obtained by the double slit, single slit, and diffraction grating. We also used eye tracking to obtain an insight into the distribution of students’ visual attention during the task. The results showed that university students had similar difficulties in recognizing wave optics patterns as high school students. They mostly struggled with identification of the double-slit interference patterns and diffraction grating patterns of monochromatic light while they were more successful in recognition of the diffraction pattern of white light on an optical grating and single-slit diffraction patterns. The eye-tracking data also revealed that students spent more time attending colourful than grey patterns in questions regarding diffraction of white light on an optical grating, thus suggesting that they were aware that the diffraction grating separates white light into colours. In questions regarding monochromatic light patterns, students overall mostly attended the single-slit diffraction pattern probably because of its distinct central maximum. Furthermore, the longer fixation duration for patterns compared to the text implies that students found it easier to extract information from the text than from the patterns. No prior research has compared the number of transitions during problem solving with the accuracy of the answers. In this study, we observed that students who incorrectly solved a task demonstrated a significantly higher number of gaze transitions between the question and the options, as well as among different options. The results of this study indicate that the recognition of typical wave optics patterns is also difficult for university students, thus suggesting that more attention should be paid to systematic observation and identification of key features of basic wave optics phenomena in lecture demonstrations and student laboratories.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"64 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141168048","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-05-16DOI: 10.1088/1361-6404/ad44f7
Justo Pastor Lambare
The Sagnac effect is an interferometric phenomenon produced by rotation. It has a rich history and presently has numerous technological applications. Despite some persistent claims to the contrary, we explain why the Sagnac effect does not prove relativity either incorrect or inconsistent. Analyzing such misunderstandings has didactic value because it allows us to review some subtle relativity concepts. It also reveals the importance of basing scientific reasoning on rigorous logical thinking to avoid confusion derived from prejudices based on our limited everyday human experience.
{"title":"On the Sagnac effect and the consistency of relativity theory","authors":"Justo Pastor Lambare","doi":"10.1088/1361-6404/ad44f7","DOIUrl":"https://doi.org/10.1088/1361-6404/ad44f7","url":null,"abstract":"The Sagnac effect is an interferometric phenomenon produced by rotation. It has a rich history and presently has numerous technological applications. Despite some persistent claims to the contrary, we explain why the Sagnac effect does not prove relativity either incorrect or inconsistent. Analyzing such misunderstandings has didactic value because it allows us to review some subtle relativity concepts. It also reveals the importance of basing scientific reasoning on rigorous logical thinking to avoid confusion derived from prejudices based on our limited everyday human experience.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"69 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-17DOI: 10.1088/1361-6404/ad399a
Amir Aghamohammadi
We study various physical quantities of objects with petal shapes. N-petal shapes exhibit N-fold rotational symmetry. Furthermore, they might have an additional characteristic: the equation defining their boundaries could be represented by F(Nθ). We will show that physical quantities of objects with these characteristics may show strange properties. By ‘physical quantities’, we refer to aspects such as electric potential and electric field due to a charged petal-shaped plate or cylinder on the rotation axis, their mass and moment of inertia. We are going to show that for such objects, these physical observables do not depend on the number of petals, N. This intriguing result has a simple reason.
我们研究具有花瓣形状的物体的各种物理量。N 花瓣形状具有 N 倍旋转对称性。此外，它们可能还有一个额外的特征：定义其边界的方程可以用 F(Nθ) 表示。我们将证明，具有这些特征的物体的物理量可能会显示出奇特的性质。我们所说的 "物理量 "是指旋转轴上带电花瓣形板或圆柱体的电动势和电场、它们的质量和惯性矩。我们将证明，对于这些物体，这些物理观测量并不取决于花瓣的数量 N。
{"title":"Strange property of physical quantities of some petal shape objects","authors":"Amir Aghamohammadi","doi":"10.1088/1361-6404/ad399a","DOIUrl":"https://doi.org/10.1088/1361-6404/ad399a","url":null,"abstract":"We study various physical quantities of objects with petal shapes. N-petal shapes exhibit N-fold rotational symmetry. Furthermore, they might have an additional characteristic: the equation defining their boundaries could be represented by F(Nθ). We will show that physical quantities of objects with these characteristics may show strange properties. By ‘physical quantities’, we refer to aspects such as electric potential and electric field due to a charged petal-shaped plate or cylinder on the rotation axis, their mass and moment of inertia. We are going to show that for such objects, these physical observables do not depend on the number of petals, N. This intriguing result has a simple reason.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"58 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140798555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-17DOI: 10.1088/1361-6404/ad358b
L N Simpfendoerfer, Meagan Sundstrom, Matthew Dew, N G Holmes
Research suggests that interacting with more peers about physics course material is correlated with higher student performance. Some studies, however, have demonstrated that different topics of peer interactions may correlate with their performance in different ways, or possibly not at all. In this study, we probe both the peers with whom students interact about their physics course and the particular aspects of the course material about which they interacted in six different introductory physics courses: four lecture courses and two lab courses. Drawing on social network analysis methods, we replicate prior work demonstrating that, on average, students who interact with more peers in their physics courses have higher final course grades. Expanding on this result, we find that students discuss a wide range of aspects of course material with their peers: concepts, small-group work, assessments, lecture, and homework. We observe that in the lecture courses, interacting with peers about concepts is most strongly correlated with final course grade, with smaller correlations also arising for small-group work and homework. In the lab courses, on the other hand, small-group work is the only interaction topic that significantly correlates with final course grade. We use these findings to discuss how course structures (e.g. grading schemes and weekly course schedules) may shape student interactions and add nuance to prior work by identifying how specific types of student interactions are associated (or not) with performance.
{"title":"What topics of peer interactions correlate with student performance in physics courses?","authors":"L N Simpfendoerfer, Meagan Sundstrom, Matthew Dew, N G Holmes","doi":"10.1088/1361-6404/ad358b","DOIUrl":"https://doi.org/10.1088/1361-6404/ad358b","url":null,"abstract":"Research suggests that interacting with more peers about physics course material is correlated with higher student performance. Some studies, however, have demonstrated that different topics of peer interactions may correlate with their performance in different ways, or possibly not at all. In this study, we probe both the peers with whom students interact about their physics course and the particular aspects of the course material about which they interacted in six different introductory physics courses: four lecture courses and two lab courses. Drawing on social network analysis methods, we replicate prior work demonstrating that, on average, students who interact with more peers in their physics courses have higher final course grades. Expanding on this result, we find that students discuss a wide range of aspects of course material with their peers: concepts, small-group work, assessments, lecture, and homework. We observe that in the lecture courses, interacting with peers about concepts is most strongly correlated with final course grade, with smaller correlations also arising for small-group work and homework. In the lab courses, on the other hand, small-group work is the only interaction topic that significantly correlates with final course grade. We use these findings to discuss how course structures (e.g. grading schemes and weekly course schedules) may shape student interactions and add nuance to prior work by identifying how specific types of student interactions are associated (or not) with performance.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"49 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140613820","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-08DOI: 10.1088/1361-6404/ad2fd7
Alexander M Gabovich, Volodymyr I Kuznetsov
The recent proposition to eliminate eponyms from physical publications is discussed. The role of eponyms in research and education is analyzed. We show that eponyms constitute an integral part of physical texts and ensure the continuity of scientific research. Their proposed elimination is dangerous for science and the entire human culture and must be rejected.
{"title":"Eponyms in physics: useful tools and cultural heritage","authors":"Alexander M Gabovich, Volodymyr I Kuznetsov","doi":"10.1088/1361-6404/ad2fd7","DOIUrl":"https://doi.org/10.1088/1361-6404/ad2fd7","url":null,"abstract":"The recent proposition to eliminate eponyms from physical publications is discussed. The role of eponyms in research and education is analyzed. We show that eponyms constitute an integral part of physical texts and ensure the continuity of scientific research. Their proposed elimination is dangerous for science and the entire human culture and must be rejected.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"100 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140617794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-19DOI: 10.1088/1361-6404/ad2cf6
Orion Ciftja, Cleo L Bentley Jr
The calculation of the electrostatic potential and/or electrostatic field due to a continuous distribution of charge is a well-covered topic in all calculus-based undergraduate physics courses. The most common approach is to consider bodies with uniform charge distribution and obtain the quantity of interest by integrating over the contributions from all the differential charges. The examples of a uniformly charged disk and ring are prominent in many physics textbooks since they illustrate well this technique at least for special points or directions of symmetry where the calculations are relatively simple. Surprisingly, the case of a uniformly charged annulus, namely, an annular disk, is largely absent from the literature. One might speculate that a uniformly charged annulus is not extremely interesting since after all, it is a uniformly charged disk with a central circular hole. However, we show in this work that the electrostatic potential created by a uniformly charged annulus has features that are much more interesting than one might have expected. A uniformly charged annulus interpolates between a uniformly charged disk and ring. However, the results of this work suggest that a uniformly charged annulus has such electrostatic features that may be essentially viewed as ring-like. The ring-like characteristics of the electrostatic potential of a uniformly charged annulus are evident as soon as a hole is present no matter how small the hole might be. The solution of this problem allows us to draw attention to the pedagogical aspects of this overlooked, but very interesting case study in electrostatics. In our opinion, the problem of a uniformly charged annulus and its electrostatic properties deserves to be treated at more depth in all calculus-based undergraduate physics courses covering electricity and magnetism.
{"title":"Electrostatic potential of a uniformly charged annulus","authors":"Orion Ciftja, Cleo L Bentley Jr","doi":"10.1088/1361-6404/ad2cf6","DOIUrl":"https://doi.org/10.1088/1361-6404/ad2cf6","url":null,"abstract":"The calculation of the electrostatic potential and/or electrostatic field due to a continuous distribution of charge is a well-covered topic in all calculus-based undergraduate physics courses. The most common approach is to consider bodies with uniform charge distribution and obtain the quantity of interest by integrating over the contributions from all the differential charges. The examples of a uniformly charged disk and ring are prominent in many physics textbooks since they illustrate well this technique at least for special points or directions of symmetry where the calculations are relatively simple. Surprisingly, the case of a uniformly charged annulus, namely, an annular disk, is largely absent from the literature. One might speculate that a uniformly charged annulus is not extremely interesting since after all, it is a uniformly charged disk with a central circular hole. However, we show in this work that the electrostatic potential created by a uniformly charged annulus has features that are much more interesting than one might have expected. A uniformly charged annulus interpolates between a uniformly charged disk and ring. However, the results of this work suggest that a uniformly charged annulus has such electrostatic features that may be essentially viewed as ring-like. The ring-like characteristics of the electrostatic potential of a uniformly charged annulus are evident as soon as a hole is present no matter how small the hole might be. The solution of this problem allows us to draw attention to the pedagogical aspects of this overlooked, but very interesting case study in electrostatics. In our opinion, the problem of a uniformly charged annulus and its electrostatic properties deserves to be treated at more depth in all calculus-based undergraduate physics courses covering electricity and magnetism.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"2020 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140311731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-19DOI: 10.1088/1361-6404/ad2ec1
Luiz G M Ramos, Antonio S de Castro
The stationary states of a particle under the influence of a delta potential confined by impenetrable walls are investigated using the method of expansion in orthogonal functions. The eigenfunctions of the time-independent Schrödinger equation are expressed in closed form by using a pair of closed-form expressions for series available in the literature. The analysis encompasses both attractive and repulsive potentials with arbitrary couplings. Confinement significantly impacts the quantum states and introduces a scenario of double degeneracy including the ground state. Analysis extends to discuss the transition to unconfinement. This research holds particular significance for educators and students engaged in mathematical methods applied to physics and quantum mechanics within undergraduate courses, offering valuable insights into the complex relationships among profiles of potentials, boundary conditions, and the resulting quantum phenomena.
{"title":"Revisiting the bound states of a confined delta potential","authors":"Luiz G M Ramos, Antonio S de Castro","doi":"10.1088/1361-6404/ad2ec1","DOIUrl":"https://doi.org/10.1088/1361-6404/ad2ec1","url":null,"abstract":"The stationary states of a particle under the influence of a delta potential confined by impenetrable walls are investigated using the method of expansion in orthogonal functions. The eigenfunctions of the time-independent Schrödinger equation are expressed in closed form by using a pair of closed-form expressions for series available in the literature. The analysis encompasses both attractive and repulsive potentials with arbitrary couplings. Confinement significantly impacts the quantum states and introduces a scenario of double degeneracy including the ground state. Analysis extends to discuss the transition to unconfinement. This research holds particular significance for educators and students engaged in mathematical methods applied to physics and quantum mechanics within undergraduate courses, offering valuable insights into the complex relationships among profiles of potentials, boundary conditions, and the resulting quantum phenomena.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"31 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140311819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-19DOI: 10.1088/1361-6404/ad2b98
Chaelee Dalton, Brian Farlow, Warren M Christensen
Upper-division undergraduate physics coursework necessitates a firm grasp on and fluid use of mathematical knowledge, including an understanding of non-cartesian (specifically polar, spherical and cylindrical) coordinates and how to use them. A limited body of research into physics students’ thinking about coordinate systems suggests that even for upper-division students, understanding of coordinate system concepts is emergent. To more fully grasp upper-division physics students’ incoming understanding of non-cartesian coordinates, the prevalence of non-cartesian content in seven popular Calculus textbooks was studied. Using content analysis techniques, a coding scheme was developed to gain insight into the presentation of coordinate system content both quantitatively and qualitatively. An initial finding was that non-cartesian basis unit vectors were absent in all but one book. A deeper analysis of three of the calculus textbooks showed that cartesian coordinates comprise an overwhelming proportion of the textbooks’ content and that qualitatively the cartesian coordinate system is presented as the default coordinate system. Quantitative and qualitative results are presented with implications for how these results might impact physics teaching and research at the middle and upper-division.
{"title":"Multivariable calculus textbook representation of non-cartesian coordinates: a misalignment between multivariable calculus textbook content and upper-division physics application","authors":"Chaelee Dalton, Brian Farlow, Warren M Christensen","doi":"10.1088/1361-6404/ad2b98","DOIUrl":"https://doi.org/10.1088/1361-6404/ad2b98","url":null,"abstract":"Upper-division undergraduate physics coursework necessitates a firm grasp on and fluid use of mathematical knowledge, including an understanding of non-cartesian (specifically polar, spherical and cylindrical) coordinates and how to use them. A limited body of research into physics students’ thinking about coordinate systems suggests that even for upper-division students, understanding of coordinate system concepts is emergent. To more fully grasp upper-division physics students’ incoming understanding of non-cartesian coordinates, the prevalence of non-cartesian content in seven popular Calculus textbooks was studied. Using content analysis techniques, a coding scheme was developed to gain insight into the presentation of coordinate system content both quantitatively and qualitatively. An initial finding was that non-cartesian basis unit vectors were absent in all but one book. A deeper analysis of three of the calculus textbooks showed that cartesian coordinates comprise an overwhelming proportion of the textbooks’ content and that qualitatively the cartesian coordinate system is presented as the default coordinate system. Quantitative and qualitative results are presented with implications for how these results might impact physics teaching and research at the middle and upper-division.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":"54 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140316676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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