Science

AP Physics C

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Overview

The enrichment suggestions for this course focus on two fundamental knowledge/skill domains:

• Vectors
• Calculus concepts

This overview helps you understand content that will be useful in the course next school year. There will be no direct or isolated assessment on this material; however, practice will help you master these skills.

Academic enrichment suggestions are intended to help you prepare for the first semester of AP Physics C – the study of Newtonian Mechanics, chiefly kinematics and dynamics, comprising:

• describing the behavior of objects in terms of time and space;
• quantitative models that predict this behavior;
• properties of interactions between/among objects;
• and conserved quantities that are present in and transferred between/among systems.

In Newtonian Mechanics we use vector quantities that change with time to describe motion; primarily position, velocity, and acceleration, but including several other quantities. Newton’s theory of dynamics asserts a general relationship between the rate of change of the velocity (vector) of an object and the interactions between the object and other objects in its environment. Using Newton’s theory (a.k.a. Newton’s Laws), we discover three conserved quantities:

1. Energy (a scalar quantity)
2. Linear Momentum (a vector quantity)
3. Angular Momentum (a vector quantity)

(Vector quantities are used even more extensively in the second semester in the study of Electricity and Magnetism.)

Fundamentally, it is helpful to have knowledge to encode and manipulate essentially geometric constructs in vector form and to describe the rates of change and accumulated changes overtime of a variety of scalar and vector quantities. We understand that it takes time and practice to get good at this kind of analysis. This review is designed to warm you up to these underlying mathematical constructs: vectors and the calculus of changing quantities, their accumulated changes over time, and rates of change.

The vector review recapitulates ideas that you have previously studied in math classes. It is most helpful if you have knowledge to apply the basic geometric context of vectors that point from place to place in space. (In physics we call these relative position vectors.) We also suggest you have the knowledge to translate quickly between/among three representations of vectors: arrows on a scale diagram; linear combinations of the orthogonal unit vectors and; and magnitude and direction/angle (polar representation).

Further, it is helpful to have the knowledge to employ the ideas of vector addition, multiplication by positive and negative scalars, projection and resolution into components, vector equations, scalar (dot) products, and vector (cross) products: each with high accuracy and relative ease. The relevant vector concepts are covered in the vector review part of this assignment. Feel free to read other resources and practice as needed to attain confidence using vectors at the level of the problems provided in the AP_Vector_WorkSheet.

Feel free to familiarize yourself with the two main constructs of Calculus – derivatives and integrals – as well as the relationship between them, known as the Fundamental Theorem of Calculus. While there is abundant information regarding the technical development of these concepts, for the purpose preparing for AP Physics C, it is relevant to understand these ideas in the context of the kind of problem scenario described in the Calculus_Application_Scenario document.

Finally – be aware that notation is important and is not to be dismissed as a trivial technicality. We will introduce you to the notation that we will use in the course when we write these things down as mathematical expressions. The vector and scalar notation that we insist upon throughout the course is likely not the same as that which is employed in your math classes. While the purely mathematical notation is convenient for calculations, ‘physics notation’ carries maximum information regarding physical quantities and is critical to their explicit, unambiguous representation.

We are especially cognizant that quantitative solutions to physics problems be expressed in this notation, and full credit on assignments and assessments requires its proper application. Please pay close attention to the vector notation indicated in the AP_Vector_Worksheet.

Vector Review

We assume that you already have some experience with vectors in your math classes. Here we refer to some online resources to help you refresh your memory. Please review the following link on vector properties: AP_Vector_Tutorial (MIT). This is, in large part, a repeat of the MIT review; however, it also contains some practice problems at the end.

We also recommend this video.

The first part covers the same basics of vectors and notation previously mentioned. The video goes on to show you some of the applications of vectors that we will take up during our course. The physical applications to Mechanics discussed in the video offer a good peek at how we will be using vectors to describe basic motion.