1 Introduction & Math

1 Introduction & Math - Chapter 1 Introduction and...

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Chapter 1 Introduction and Mathematical Concepts 1 Chapter 1 INTRODUCTION AND MATHEMATICAL CONCEPTS PREVIEW This chapter introduces you to the basic mathematical tools for doing physics. You will study units and converting between units, the trigonometric relationships of sine , cosine , and tangent , and the manipulation of scalars and vectors . The content contained in all sections of chapter 1 of the textbook is included on the AP Physics B exam. QUICK REFERENCE Important Terms base SI (Systeme Internationale) units the fundamental units of meters for length, kilograms for mass, and seconds for time used in the metric system cosine ratio of the length of the adjacent side to an angle in a right triangle to the length of the hypotenuse derived unit any unit, such as m/s, in the metric system which is not fundamental and is a combination of meters, kilograms, and/or seconds equilibrant a vector which is equal and opposite to the resultant vector, and can cancel the effects of the individual vectors resultant the vector sum of two or more vectors scalar component the magnitude of a component of a vector scalar quantity a quantity, such as mass, which can be completely specified by its magnitude or size. sine ratio of the length of the opposite side to an angle in a right triangle to the length of the hypotenuse tangent ratio of the length of the opposite side to an angle in a right triangle to the length of the adjacent side
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Chapter 1 Introduction and Mathematical Concepts 2 vector quantity a quantity, such as displacement, which is specified by its magnitude (size) and its direction (angle) vector component the projection of a vector onto the x – or y – axis vector addition adding vectors to each other either graphically (head-to-tail) or using vector components to find the sum (resultant) of the vectors Equations and Symbols a o a o a o h h h h h h h h h r S r V r rl S l r V lwh V r C r A bh A bh A tan cos sin Triangle Right 4 and 3 4 Sphere 2 2 and Cylinder iped Parallelep 2 and Circle 2 1 Triangle Rectangle 2 2 2 2 3 2 2 2 h a h o h θ
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Chapter 1 Introduction and Mathematical Concepts 3 where A = area b = base h = height C = circumference V = volume l = length w = width S = surface area r = radius θ = angle sin = sine cos = cosine tan = tangent Ten Homework Problems Chapter 1 Problems 7, 17, 36, 40, 46, 48, 49, 54, 55, 60. DISCUSSION OF SELECTED SECTIONS 1.3 The Role of Units in Problem Solving All physical quantities have units so that we can communicate their measurement. IN the metric system, the base units are called SI units. The base SI units for the fundamental quantities of mass , length , and time are the kilogram , meter , and second , respectively. Only SI units are used on the AP Physics B exam . Any unit which is a combination of these fundamental units is called a derived unit. An example of a derived unit would be meters/second or kilometers/hour , which are both units for speed.
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1 Introduction & Math - Chapter 1 Introduction and...

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