# Comparative Critical Review Essays Examples

## Advancing Maths for AQA: Mechanics 1

and

## Physics I: Classical Mechanics I: 8.012 MIT Open Courseware

Burgasser, A. (2008) 8.012 Physics I: Classical Mechanics Massachusetts Institute of Technology: MIT OpenCourseWare [online] Available from http://ocw.mit.edu/courses/physics/8-012-physics-i-classical-mechanics-fall-2008/syllabus/ License: Creative Commons BY-NC-SA. [24 April 2015]

Graham, T. Boardman, S., Pearson, D. and Williamson, R. (Eds.) (2004) Advancing Maths for AQA: Mechanics 1 (M1) (Advancing Maths for AQA). 2nd Ed. Oxford: Heinemann Educational Publishers.

Mechanics I and other Maths level exams are significant exams because students are allowed or prevented from progressing with their studies on the topic depending upon the outcomes of their exams. The amount of studying needed to prepare for exams is not trivial. The concepts and theories learned in Physics and Mechanics need to be carefully reviewed. Students need exercises similar to the problems that will be on the exams so they can practice calculating the solutions, and then they need the solutions to check their answers. The purpose of the review is to take a critical look at both of the sources; they are compared based upon their capability for enhancing students’ knowledge of Mechanics, in particular before exams.

Classical Mechanics I, a field of physics, is the subject of the two reviewed items. The editors Ted Graham, Sam Boardman, David Pearson, and Roger Williamson are the experts who prepared and organized Advancing Maths for AQA: Mechanics 1 (M1) (Advancing Maths for AQA (Graham et al. 2004) . Heinemann advertises its Advancing Maths series as being written by Senior Examiners who have experience giving AS and A-Level examinations. The book, published in 2004, is specifically targeted to students who are moving from GCSE to AS and then all the way to A level. Mechanics 1 is the subject of the book; the contents are updated from the first edition to allow students a resource to prepare for new exams.

The second review item is an online course 8.012 Physics I: Classical Mechanics taught by Adam Buragasser in 2008. The online course is part of the Massachusetts Institute of Technology (MIT) OpenCourseWare (OCW) that is available openly and free for anyone in the world to use under the Creative Commons BY-NC-SA license. MIT OCW was created so that anyone can use the materials and most of the courses offered at MIT are available. Both formats, the paperback book and the webpage, recommend that students with a strong mathematical background and a basic knowledge of physics are best-suited to use the sources. Although the content is similar, the two formats are presented in very different ways.

Advancing Maths for AQA (Graham et al. 2004) contains eight short well-organized and easy to understand chapters, while the online course Physics I: Classical Mechanics(Burgassser 2008) is a full-fledged course that offers the same advantages of a classroom setting, but offers them online so independent study is encourage. The book is contains 14 pages of exercises that students should be able to solve on their own or with the help of their tutor. Seventeen pages at the end of the book are dedicated to the solutions of the exercises. Physics 8.012 (Burgasser 2008) online offers practice exams from previous years and their solutions are available to download from 2005, 2006, and 2007. The number of pages with example problems equals sixty four pages available to download from Burgasser’s (2008) class; the solutions are downloaded separately on the same web page.

Advancing Maths for AQA: Mechanics I (Graham et al. 2004) contains 176 pages; the paperback book is handy to carry around in order to study anywhere without needing an Internet connection as is needed for Burgasser’s (2008) course. Physics I: Classical Mechanics (Burgassser 2008) requires a textbook; An Introduction to Mechanics by Kleppner and Kolenkow published in 1973. The textbook is 600 pages and a classic textbook for freshmen. The Kleppner and Kolenkow book describes theory in great detail and the exercises are not designed as a review for the new exams; they are presented as learning tools. The Introduction to Mechanics is a good reference on Mechanics 1 and the related theories in physics. Anyone who will be continuing to take advanced classes on the topics can use the book and should keep it handy on the bookshelf. For example, all the necessary conversions and equations are available.

The online class Physics I: Classical Mechanics (Burgassser 2008) and Advancing Maths for AQA: Mechanics 1(Graham et al., 2004) cover the necessary, basic topics for mechanics, but. the paperback book covers less information. Advancing Maths for AQA: Mechanics 1(Graham et al., 2004) offers chapters on mathematical modelling in mechanics, kinematics in one and two dimensions, forces from physics, Newton’s laws of motion, connected particles and projectile momentum. Both references offer chapters on vectors, momentum, rigid bodies and particle physics. Burgasser (2008) also lectures on planetary motion, reference frames and relativity as well as energy conversation, moment of inertia tensor, gyroscopic motion (I and II), Euler’s equations (accelerated reference frames) and the Cavendish experiment.

Advancing Maths for AQA: Mechanics 1(Graham et al., 2004) (Graham 2004) explains the major concepts of mechanics in eight straight-to-the point; the chapters are focused on one topic each and the subcategories of the main topic. For each chapter, a sample exercise is worked out step-by-step with careful explanations integrating the chapter’s lesson. The lessons are very practical, but do not explain theory in great detail; instead the equations are the main focus. The length of the chapters depends on how many subtopics are linked with the main topic; the book is only contains176 pages. On the other hand, the online class is far more complex; the exercises and solutions appropriate for pre-exam studying were not before time was spent in trial and error attempts. Once the exams and their solutions were found on the website though, the can be downloaded for easy access on one’s computer or tablet.

The first chapter in Advancing Maths forAQA: Mechanics 1(Graham et al., 2004) reviews how to use mathematical models in mechanics to solve real world problems. Solving problems one faces in the everyday world is often more attractive to students, because they see a practical use for the maths. Understanding how to set up a mathematical model properly and choose the proper equations is essential for solving problems correctly. The book offers students an opportunity to test their own skills at problem solving. At the end of each chapter is a ‘Test Yourself’ section and more problems to solve are located in the back of the book in the section ‘Exam-style practice exercises.’ The answers are available in the pages before the index and after the practice exercises; the majority of pages contain examples for students to work out and then compare their answers to the worked out solutions.

The home page of Physics I: Classical Mechanics (Burgassser 2008) includes a description from Wikimedia Commons, “Classical mechanics provides an elegant means of describing the motion of a seemingly unwieldy system, like this physical pendulum.” A drawing of a symmetrical pendulum with angle θ and the vectors with sin θ is pictured above the description of classical mechanics. Elegant is also an apt description for the solutions offered by Burgasser (2008) on the web site (described in more detail below). The web links for the syllabus, class calendar, the assigned readings from The Introduction to Mechanics, and the project rules with project topic choices are listed on the left side of the monitor. The other web links lead to pdf’s to download for assignments, exams, and ‘related resources.’ The related resource web page includes a link to a video of the Cavendish Experiment and some relevant lectures from MIT Tech TV. The last link in the list is the most important link for exam review purposes, the link leads to a button to download the course materials.

The exercises and solutions available on the ‘related resources’ web page for Physics I: Classical Mechanics (Burgassser 2008) are presented in a very good, well-organized layout that enhances the understanding of the problems’ solutions. The exercises are presented with figures that are well drawn and labeled. An example of one of the exams is the pdf for the exam from Midterm Exam 1 from 2007. The first problems section includes ‘quick multiple choice questions’ and then typical problems are presented for the students to solve. The last part of the exam lists the useful equations to help solve the problems. The solutions are available by clicking the button next to the ‘exam’ button. The solutions are elegantly solved, especially compared to the Advancing Maths for AQA: Mechanics 1 (Graham et al., 2004). The exercises and solutions provided in the book seem to be written down hurriedly and, in fact, in the reviews of the book on Amazon.com, some complained that the solutions were incorrect.

The solutions from Physics I: Classical Mechanics (Burgassser 2008) are presented in a well-organized way and include all the necessary information for understanding and working out solutions to the problems. The first part of each solution is a figure that lays out the geometry of the problem presented and any helpful diagrams. The solution uses text and formulas to provide a step-by-step explanation of the solution to the problem. Assumptions are explained where applicable, and when special circumstances are presented, they are highlighted with asterisks so

the student cannot miss seeing the explanation. Boxes are put around derived equations in the problem to separate the final derivation from the other equations. The solution with the relevant equation is also placed in a box.

Perhaps the best way to study for level exams is to use the two references to complement each other, in that way students can enhance their exam studies using both Advancing Maths for AQA: Mechanics 1 (Graham et al., 2004) and Physics I: Classical Mechanics online class (Burgassser 2008). The most helpful component for the purpose of studying to prepare for exams is the ‘related resources’ link, because the pdfs available for downloading can be used for practice exams. Even more importantly, the solutions are presented in a well-organized, detailed and easy to understand layout and can be accessed on the same web page. Difficult concepts and theory can be better understood by studying the solutions from Burgasser (2009). On the other hand, Advancing Maths for AQA: Mechanics 1 (Graham et al., 2004) is a great resource for practicing calculations before exams, once students have gained confidence in their background knowledge.

## References

Burgasser, A. (2008) 8.012 Physics I: Classical Mechanics Massachusetts Institute of Technology: MIT OpenCourseWare [online] Available from http://ocw.mit.edu/courses/physics/8-012-physics-i-classical-mechanics-fall-2008/syllabus/ License: Creative Commons BY-NC-SA. [24 April 2015]

Graham, T. Boardman, S., Pearson, D. and Williamson, R. (Eds.) (2004) Advancing Maths for AQA: Mechanics 1 (M1) (Advancing Maths for AQA). 2nd Ed. Oxford: Heinemann Educational Publishers.

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