We report on an investigation of student understanding of rigid body dynamics in which we asked students in introductory calculus-based physics to compare the translational motions of identical rigid bodies subject to forces that differed only in the point of contact at which they were applied. There was a widespread tendency to claim that forces that cause rotational motion have a diminished effect on translational motion. A series of related problems was developed to examine whether similar errors would be made in other contexts, and interviews were conducted to probe student thinking in greater depth. In this paper, we describe the results of our investigation and also describe a series of different interventions that culminated in the development of a tutorial that improves student ability to apply Newton's second law to rotating rigid bodies.
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For organizing our analysis of student thinking, here we draw a line between two major approaches to causality in classical mechanics: energy-type causality, and force-type causality. In this view, torques are force-type, in that they are instantaneous causal influences that combine as vectors and result in a change in motion that is inversely proportional to some kind of inertia. We do not mean “strictly Newtonian” in an historical sense, since Euler, not Newton, is responsible for formulating the relationship between torques and rotational motion.
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The uncertainties represent 95% confidence intervals based on Student's t-distribution for those cases in which the data were sufficient to establish that the distributions are normal.
22.
In this table, p-values were obtained through permutation tests, which are exact tests that do not require assumptions about the distributions being compared. Instead the data labels (“without tutorial” and “with tutorial” in this case) are exchanged and the respective means of the two categories under all possible combinations (or a sufficiently large subset) are examined. The proportion of combinations in which the average of the “with tutorial” category is greater (or less) than the actual value, is p. We also performed t-tests in those cases in which there were data from several sections with and without the tutorial, and found p-values smaller than those obtained through the permutation tests. However, even for those questions given after instruction to several classes, the data are only marginally sufficient for establishing that the distributions are normal, and therefore we believe the model-independent permutation test to be more appropriate.
© 2013 American Association of Physics Teachers.
2013
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