Instructors_Guide_Ch13

# Instructors_Guide_Ch13 - 13 Rotation of a Rigid Body...

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13 Rotation of a Rigid Body Recommended class days: 3 minimum, 4 preferred Background Information Chapter 13 is a large chapter with a high density of information. To experienced physicists, rotational motion is analogous to linear motion and presents only a few new ideas. Students don’t see it that way. I don’t know of any published papers, but researchers have given AAPT talks on student difficulties with rotational motion. Misconceptions that were successfully dealt with in linear dynamics suddenly reappear in the context of rotational dynamics. Students may have learned to work with kinematic graphs of position, velocity, and acceleration, but that skill does not transfer to an ability to relate graphs of angular position, angular velocity, and angular acceleration. Most of your students may have overcome the common misconceptions that force is proportional to velocity or that there’s a “force of motion,” but many will now think that a torque is needed to maintain a constant angular velocity. One interesting finding, discovered during research into students’ under- standing of Archimedes’ principle (Loverude et al., 2003), is concerned with an equilibrium situation. Students were shown an Atwood’s machine in which two identical blocks were held at different heights. Asked to predict what would happen when the blocks were released, about one third of students incorrectly predicted the pulley would rotate until the blocks were at equal heights. Many students explicitly noted their belief that the system would not be in equilibrium until the blocks reached the same level. Thus a hurried presentation of this chapter that assumes students can readily transfer their linear motion knowledge to rotational motion is almost certain to fail for a large fraction of the students. On the other hand, a careful presentation allows you multiple opportunities to spiral back to earlier topics, thus reinforcing student understanding of those at the same time you’re extending the ideas into a larger domain. The vector cross product is new to essentially all students. They will need focused practice computing cross products before they are comfortable using this idea to compute torque or angular momentum. In the spirit of introducing no more math than needed to accomplish the task, this text always calculates the cross product to be a vector of magnitude AB sin θ in a direction given by the right-hand rule. Determinants are not used to calculate cross products. 13-1

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13-2 Instructor’s Guide Student Learning Objectives To extend the particle model to the rigid-body model. To understand the equilibrium of an extended object. To understand rotation about a fixed axis. To understand rolling motion.
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