Tutorial details

A major focus of this tutorial is on helping students learn how the variables mass and mass distribution affect balancing. In the first section of the tutorial, students are guided to make the proper observations about the motion of a rigid body pivoted at its center of mass and to relate these observations to the conditions of equilibrium. The students are asked to make a prediction about the motion of an irregularly shaped board that is placed on a frictionless pivot at its center of mass. After they have observed the demonstration, the students are guided through a set of experiments in which they hang the object from a point other than its center of mass and balance with a piece of clay. Through these exercises, students generalize how mass on either side of the pivot influences balancing.

Later in the tutorial, students are asked to compare the amount of mass on the left to that on the right of the vertical line through the center of mass of the board alone. Students are asked to check to see if their prediction is consistent with their generalizations about mass. This question is meant to help students recognize that the amount of mass of the two pieces of the board could differ and the board could still balance as they previously observed.

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Students should already have been introduced to the topics of center of mass (of both continuous uniform mass distributions and of systems of single particles) and the conditions of equilibrium.

Equipment

List

• white board or large sheet of paper with markers
• clay
• T-shaped board with axis and stand

Discussion