Round and round in circles—shifting relevance structures as students discuss acceleration and forces during circular motion in a vertical plane

Abstract

Working out the relations between the forces involved in circular motion in a vertical plane can be challenging for first-year students, as illustrated in this analysis of a 30 minute group discussion of a textbook problem where a remote-control model car moves with constant speed inside a cylinder. The analysis includes timelines of semiotic resources used, as well as of topics brought up by individual students.
Questions from the students include: What is that force you drew on the paper? Does it act on the car or on the wall? What keeps the car from falling down? The normal force and the “centripetal force” both point to the center – does it mean they are the same? Is it only a gravitational force at the top? Does the normal force at the bottom just cancel gravity or does it need to be larger? What is “normal” about the normal force? Arriving at the correct numerical result is insufficient evidence for student understanding of forces in circular motion!

Can students with fragmentary understanding bring their pieces together to solve the puzzle? From the timelines, we can identify a few critical moments where the discussion changes focus. This happens when one of the students in the group introduces a new dimension of variation, e.g. a reminder about the force of gravity, a freebody diagram drawn, as well as diagrams drawn in other parts of the circle than
the top or bottom, where the centripetal and normal forces are no longer in the same direction. Embodied experiences are invoked, but only at a very late stage in the discussion. For teachers, an awareness of the different ways students use terms and think about the forces can be a guide to offering a larger variation in the interventions, as well as in problems assigned.