Instructors_Guide_Ch07 - 7 Dynamics III, Motion in a Circle...

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7 Dynamics III, Motion in a Circle Recommended class days: 3 Background Information Circular motion requires a shift in thinking from the emphasis until now on linear motion and motion that can be decomposed into independent linear motions along two axes. Not surprisingly, this evokes new difficulties for students. Arons (1990) cites an experiment in which a marble is rolled around the inside of an incomplete circular hoop lying flat on a table. Students are asked to predict the marble’s trajectory after passing point B. Some predict it will continue with perfect circular motion, reentering the hoop at A. Others predict a circular tendency that “runs down,” so the marble curves to the left but gradually straightens out. Either way, students seem to be thinking that the marble is subject to a “force of motion” that has a memory of previous motions. Few predict the correct linear trajectory from B. The “Physics Education Research” chapter cited the Van Heuvelen (1991a) study in which students at the end of instruction were asked about the forces on a ball swinging in a vertical circle on the end of a string. At the lowest point, 60% identified a “force of motion” tangent to the circle. Further, if you look only at their vertical forces, 64% showed the tension force and the weight as being of equal magnitude while only 36% recognized that the tension force would need to be larger than the weight force. Although students may have learned the term centripetal force in high school, few have any sense of what it means. This is demonstrated by rolling a heavy ball (such as a bowling ball) across the floor and asking students to create a circular motion about a specified point by tapping on the ball with a rubber mallet. Most attempt to apply tangential forces, rather than centripetal forces— another example of thinking that force needs to be in the direction of motion. In fact, merely the term “centripetal force” causes difficulty for some students. They consider it to be a new kind of force, like the gravitational force or the normal force, and they will dutifully add a force vector labeled “centripetal force” to their free-body diagrams. Student Learning Objectives • To understand the kinematics of uniform circular motion. • To understand the dynamics of uniform circular motion. • To learn the basic ideas of orbital motion. • To answer “How does the water stay in the bucket?” and related questions. 7-1
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7-2 Instructor’s Guide Pedagogical Approach The focus of this chapter, within the context of single-particle dynamics, is to understand how circular motion occurs as a consequence of center-directed forces. This is a very non-intuitive idea, one that students need to see in a variety of contexts. There have been many suggestions in recent years, especially in
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This note was uploaded on 01/14/2011 for the course CD 254 taught by Professor Kant during the Spring '10 term at Central Oregon Community College.

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Instructors_Guide_Ch07 - 7 Dynamics III, Motion in a Circle...

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