AP PHYSICS 1 BIG IDEAS AND LEARNING OBJECTIVES KINEMATICS (original) (raw)

Module 9: Analysis of Physics Concepts

Processes of Thought at DigitalCommons@University of Nebraska -Lincoln. It has been accepted for inclusion in Workshop Materials: Physics Teaching and the Development of Reasoning by an authorized administrator of DigitalCommons@University of Nebraska -Lincoln. concrete version of the same physical quantity).

Orbital Mechanics for Engineering Students

This textbook evolved from a formal set of notes developed over nearly ten years of teaching an introductory course in orbital mechanics for aerospace engineering students. These undergraduate students had no prior formal experience in the subject, but had completed courses in physics, dynamics and mathematics through differential equations and applied linear algebra. That is the background I have presumed for readers of this book. This is by no means a grand, descriptive survey of the entire subject of astronautics. It is a foundations text, a springboard to advanced study of the subject. I focus on the physical phenomena and analytical procedures required to understand and predict, to first order, the behavior of orbiting spacecraft. I have tried to make the book readable for undergraduates, and in so doing I do not shy away from rigor where it is needed for understanding. Spacecraft operations that take place in earth orbit are considered as are interplanetary missions. The important topic of spacecraft control systems is omitted. However, the material in this book and a course in control theory provide the basis for the study of spacecraft attitude control. A brief perusal of the Contents shows that there are more than enough topics to cover in a single semester or term. Chapter 1 is a review of vector kinematics in three dimensions and of Newton's laws of motion and gravitation. It also focuses on the issue of relative motion, crucial to the topics of rendezvous and satellite attitude dynamics. Chapter 2 presents the vector-based solution of the classical two-body problem, coming up with a host of practical formulas for orbit and trajectory analysis. The restricted three-body problem is covered in order to introduce the notion of Lagrange points. Chapter 3 derives Kepler's equations, which relate position to time for the different kinds of orbits. The concept of 'universal variables' is introduced. Chapter 4 is devoted to describing orbits in three dimensions and accounting for the major effects of the earth's oblate, non-spherical shape. Chapter 5 is an introduction to preliminary orbit determination, including Gibbs' and Gauss's methods and the solution of Lambert's problem. Auxiliary topics include topocentric coordinate systems, Julian day numbering and sidereal time. Chapter 6 presents the common means of transferring from one orbit to another by impulsive delta-v maneuvers, including Hohmann transfers, phasing orbits and plane changes. Chapter 7 derives and employs the equations of relative motion required to understand and design two-impulse rendezvous maneuvers. Chapter 8 explores the basics of interplanetary mission analysis. Chapter 9 presents those elements of rigid-body dynamics required to characterize the attitude of an orbiting satellite. Chapter 10 describes the methods of controlling, changing and stabilizing the attitude of spacecraft by means of thrusters, gyros and other devices. Finally, Chapter 11 is a brief introduction to the characteristics and design of multi-stage launch vehicles. Chapters 1 through 4 form the core of a first orbital mechanics course. The time devoted to Chapter 1 depends on the background of the student. It might be surveyed xi xii Preface briefly and used thereafter simply as a reference. What follows Chapter 4 depends on the objectives of the course. Chapters 5 through 8 carry on with the subject of orbital mechanics. Chapter 6 on orbital maneuvers should be included in any case. Coverage of Chapters 5, 7 and 8 is optional. However, if all of Chapter 8 on interplanetary missions is to form a part of the course, then the solution of Lambert's problem (Section 5.3) must be studied beforehand. Chapters 9 and 10 must be covered if the course objectives include an introduction to satellite dynamics. In that case Chapters 5, 7 and 8 would probably not be studied in depth. Chapter 11 is optional if the engineering curriculum requires a separate course in propulsion, including rocket dynamics. To understand the material and to solve problems requires using a lot of undergraduate mathematics. Mathematics, of course, is the language of engineering. Students must not forget that Sir Isaac Newton had to invent calculus so he could solve orbital mechanics problems precisely. Newton (1642-1727) was an English physicist and mathematician, whose 1687 publication Mathematical Principles of Natural Philosophy ('the Principia') is one of the most influential scientific works of all time. It must be noted that the German mathematician Gottfried Wilhelm von Leibniz (1646-1716) is credited with inventing infinitesimal calculus independently of Newton in the 1670s. In addition to honing their math skills, students are urged to take advantage of computers (which, incidentally, use the binary numeral system developed by Leibniz). There are many commercially available mathematics software packages for personal computers. Wherever possible they should be used to relieve the burden of repetitive and tedious calculations. Computer programming skills can and should be put to good use in the study of orbital mechanics. Elementary MATLAB® programs (M-files) appear at the end of this book to illustrate how some of the procedures developed in the text can be implemented in software. All of the scripts were developed using MATLAB version 5.0 and were successfully tested using version 6.5 (release 13). Information about MATLAB, which is a registered trademark of The MathWorks, Inc.

PHYSICS LESSON NOTES FOR SENIOR SECONDARY SCHOOL1 SECOND TERM SCHEME OF WORK

Behavioral objectives: By the end of the lesson, students should be able to: i. Explain work, energy and power and give examples of each. ii. Calculate the work done, given a force and displacement it produces in its direction. Entry Behaviour: students can tell the meaning of Energy Instructional Resources: Chart showing the displacement of a box by a force acting horizontally at an angle. Chart showing a girl running with a box on her head. REFRENCE:Salihu J.E (2003) Classic Dictionary of physics for secondary schools. Akure classic Educational Publishers. (2) Prep 50 physics (2019). Onitsha. Deacons Digital Solutions Ltd (3) Okolosi L. (2019) Hidden facts in SSCE physics Ughelli. Otumudia publishers Ltd.

University Student Conceptual Resources for Understanding Forces

2017 Physics Education Research Conference Proceedings, 2018

We present preliminary results from our investigation of introductory physics students' conceptual resources for understanding forces. We analyzed a total of 1057 student responses to conceptual questions about forces and identified three common, prevalent resources that students used in justifying their answers, including the ideas that forces change the motion of objects, objects that have motion keep that motion, and motion is due to an imbalance of forces. We illustrate some of the ways in which these resources manifested in student responses and discuss how these ideas are continuous with physics understandings. We situate our work in the literature on student thinking about forces and instructor pedagogical content knowledge (PCK).

A NEW PHYSICS CURRICULUM William Flannery Berkeley Science Books

Classical physics is based on the analysis of differential equation models of physical processes. Computers have given physicists and engineers a new way to analyze differential equations that has revolutionized science and engineering outside the university. Unlike Newton's analytic calculus, computational calculus, i.e the computational methods used to calculate solutions to differential equations, is simple, intuitive, and easy to learn. Euler's method, the basis of computational calculus, can be taught to high school science students in a single one-hour lecture. The analysis of real physical systems, e.g. central force motion, can begin in the next lecture. Incorporating computational methods into the courses in classical physics will lead to a complete transformation of the physics and engineering curriculums. This paper shows how the process of incorporation can begin, and includes analyses of physical systems spanning the range of classical physics that demonstrate the simplicity, ease of use, and the extraordinary power of computational methods.

Module 5: Analysis of Physics Problems and Test Questions

You may be wondering how to apply the concept of developmental stages in your physics teaching, To help you with this, we have prepared modules 5-11 dealing with differing aspects of instruction. Module 5 concentrates on the analysis and writing of physics problems and test questions. As you read the examples we have selected, keep in mind the characterisrtics of concrete and formal thought described in Module 2. A matter that we find difficult to resolve concerns how to give all students, regardless of the reasoning patterns they use initially, practice in problem solving. Furthermore, evaluation through tests should give all students an opportunity to show what they have learned in physics and with respect to formal reasoning patterns.

On the Concept of Force: How Understanding its History can Improve Physics Teaching

Science & Education, 2010

Some physicists have pointed out that we do not know what force is. The most common definition of force in textbooks has been criticized for more than two centuries. Many studies have shown that the concept of force is a problem for teaching. How to conceive force on the basis of the concepts and criticism of force in the works of Newton, Euler, d'Alembert, Lagrange, Lazare Carnot, Saint-Venant, Reech, Kirchhoff, Mach, Hertz and Poincaré is the question of the present article. This part of the article is followed by an overview of definitions of force in contemporary textbooks. In the next part, an answer to the question is given: how to understand force within the framework of the laws of motion and in applications. Finally, some educational implications are considered.