Should Kinetics Follow Kinematics? Only In The Dictionary!

The majority of dynamics textbooks are organized with an almost identical ordering of topics. This ordering is generally particle kinematics, particle kinetics, rigid body kinematics, rigid body kinetics, 3-D kinematics and kinetics and finally vibrations. There are a few textbooks that introduce more fully the concept of kinematics, including both particle and rigid body kinematics prior to the discussion of kinetics principles, but to the authors’ knowledge no book starts with an extensive discussion of kinetics prior to kinematics. At Rose-Hulman Institute of Technology we have taken the approach of introducing the kinetics principles in the larger context of conservation principles, that is, conservation of mass, charge, linear momentum, angular momentum and energy using only very basic kinematics. Only after all of the kinetics principles are clearly understood are additional kinematics topics discussed. This approach is currently part of a sophomore curriculum where the concepts of conservation and accounting permeate a sequence of courses and assessment results indicate improved student learning. The purpose of this paper is to present a case for how and why a dynamics instructor teaching a conventional course might adopt this approach. I. Review of dynamics textbooks There are a large number of textbooks designed for use in introductory dynamics courses and the ordering of topics can be categorized in primarily two ways as shown in Table 1. The books using Ordering #1 as shown in Table 1 include those by Hibbeler, Boresi and Schmidt, Jong and Rogers, Beer and Johnston, Meriam and Kraige, Sandor, Shames, Bedford and Fowler, and Soutas-Little and Inman. Although there are some variations among these books, for example, some include a chapter on systems of particles, their ordering of the topics is essentially identical. This ordering is: particle kinematics followed by particle kinetics followed by rigid body kinematics followed by rigid body kinetics. Ordering #2 is used in the dynamics book by Riley and Sturges. In this book kinematics, including both rigid body and particle kinematics, is presented prior to the discussion of kinetics principles. The authors are unaware of any books that begin with a discussion of kinetics prior to kinematics. The closest is the book by Pytel, Gosling, and Kiusalaas. In this book the first chapter on particle dynamics integrates kinematics and kinetics. They state in the preface that “We found this arrangement superior to the traditional approach of devoting the opening chapter exclusively to kinematics. Introducing the student immediately to practical problems, where the equations of motion are derived and not given, provides a stronger motivation for learning.” The authors agree with this statement, but would take it further. All of the kinetics principles should be discussed prior to an extensive discussion of kinematics! P ge 10116.1 Proceedings of the 2005 American Society for Engineering Education Annual Conference & Exposition Copyright © 2005, American Society for Engineering Education Table 1 – Conventional ordering of topics in introductory dynamics books. Ordering #1 Ordering #2 1. Kinematics of a particle 2. Kinetics of a particle (Newton’s laws) 3. Kinetics of a particle (work and energy) 4. Kinetics of a particle (impulse and momentum) 5. Planar kinematics of a rigid body 6. Planar kinetics of a rigid body (Newton’s laws) 7. Planar kinetics of a rigid body (work and energy) 8. Planar kinetics of a rigid body (impulse and momentum) 9. Three dimensional kinematics of a rigid body 10. Three dimensional kinetics of a rigid body 11. vibrations 1. Kinematics of particles 2. Kinematics of rigid bodies 3. Kinetics of particles (Newton’s laws) 4. Kinetics of rigid bodies (Newton’s laws) 5. Kinetics of particles (work and energy) 6. Kinetics of rigid bodies (work and energy) 7. Kinetics of particles (impulse and momentum) 8. Kinetics of rigid bodies (impulse and momentum) 9. Vibrations When examining the curricula of a variety of schools, the authors discovered that most schools require Newtonian physics prior to dynamics. Therefore, students have already been exposed to the basic kinetics principles used in dynamics, that is, Direct Application of Newton’s 2 Law, Work-Energy Methods, and Impulse-Momentum Methods. It is the authors’ opinion that students could learn dynamics better by building on this material they already know rather than pretending that this is their first exposure to this material (even though they may claim this and their apparent lack of knowledge confirms this.) At Rose-Hulman Institute of Technology we have taken the approach of presenting the kinetics principles in the larger context of conservation principles, that is, conservation of mass, charge, linear momentum, angular momentum and energy. Initially only very basic kinematics are used, that is, the kinematics students have already learned in prior courses of Newtonian physics or calculus. “Conservation” in this sense is not limited to situations in which the energy or momentum of a system is constant, but is used to denote the more general definition of conservation of energy, linear momentum and angular momentum. Only after all of the kinetics principles are clearly understood are additional kinematics topics discussed. Applying the kinetics is what motivates the teaching of additional kinematics. This approach is currently part of a sophomore curriculum in which the concepts of conservation and accounting permeate a sequence of courses and assessment results indicate improved student learning. The details of P ge 10116.2 Proceedings of the 2005 American Society for Engineering Education Annual Conference & Exposition Copyright © 2005, American Society for Engineering Education how this approach is used at Rose-Hulman and how it could possibly be implemented in a single dynamics course is presented below. II. The Sophomore Engineering Curriculum (SEC) at Rose-Hulman A number of pedagogical techniques are being used to try to enhance the learning of dynamics. These include cooperative learning, simulation software such as Working Model, computer algebra systems such as Maple or MathCad, looking at a full range of motion rather than “static dynamics”, concept questions, etc. All of these have been used at Rose-Hulman, and in the authors’ opinion are beneficial for enhancing student learning. However, the only quantified improvement in student learning took place when an entirely new curriculum was implemented in 1995. Rose-Hulman, as part of the NSF sponsored Foundation Coalition, implemented a new sophomore curriculum starting in the 1995-96 academic year. The sophomore year curriculum primarily concentrates on engineering science material that is traditionally covered in courses such as Dynamics, Thermodynamics I, Fluid Mechanics and Circuits I. Even though basic principles such as conservation of energy and conservation of linear and angular momentum are encountered in these courses, the notation and methodology are often such that the principles look different in different classes. Therefore, subsequent courses do not reinforce the material taught in previous courses. At Rose-Hulman this material has been repackaged into a new sequence of courses called the Sophomore Engineering Curriculum (SEC) as shown in Figure 1. One purpose of the curriculum is to teach engineering science in a more cohesive and internally consistent manner. Figure 1 Summary of the current sophomore engineering curriculum (SEC) at RoseHulman. A sequence of three courses can be used since Rose-Hulman is on the quarter system. In the fall-quarter course Conservation and Accounting Principles (ES201), students are taught the basic principles for both open and closed systems. That is, we discuss conservation of mass, charge, linear momentum, angular momentum, and energy and the accounting of entropy. We also teach a problem solving methodology and homework format that is used in all subsequent courses. Electrical Systems (ES203) is also taught this quarter. In the winter quarter the students take two courses that build on ES201. These courses are Mechanical Systems and Fluid and Thermal Systems. In these courses the more detailed applications of the conservation principles are discussed as well as some of the additional topics required to solve problems such as Fall Winter Spring ES202 Fluid and Thermal Systems ES204 Mechanical Systems ES203 Electrical Systems ES201 Conservation and Accounting Principles ES205 Analysis and Design of Engineering Systems