This document provides an overview of key physics concepts and mathematical tools. It covers units of measurement in the SI system, vector notation and operations like addition/subtraction, trigonometry, and dimensional analysis. Example problems demonstrate various concepts like finding components of vectors and adding multiple vectors. The document concludes with additional mathematical rules and functions important for physics problems.

1. Chapter 1 Introduction and Mathematical Concepts

3. Chapter 1: Introduction and Mathematical Concepts Section 1 – The Nature of Physics

5. Chapter 1: Introduction and Mathematical Concepts Section 2 - Units

10. Chapter 1: Introduction and Mathematical Concepts Section 3 The Role of Units in Problem Solving

17. Example DIMENSIONAL ANALYSIS [L] = length [M] = mass [T] = time Is the following equation dimensionally correct?

21. Chapter 1: Introduction and Mathematical Concepts Section 4 - Trigonometry

22. Basics you should remember…

23. Basics you should remember…

27. Chapter 1: Introduction and Mathematical Concepts Section 5 – Scalar & Vectors

31. Chapter 1: Introduction and Mathematical Concepts Section 6 Vector Addition and Subtraction

35. Chapter 1: Introduction and Mathematical Concepts Section 7 Components of a Vector

36. Vector Component

37. Scalar Components It is often easier to work with the scalar components rather than the vector components. In math, they are called i and j

42. Chapter 1: Introduction and Mathematical Concepts Section 8 Addition of Vectors by Means of Components

43. Addition using components

47. Adding Multiple Vectors Adding Vectors F 2 F 3 F 4 F 1

48. Adding Multiple Vectors F 1 F 2 F 3 F 4  1  2  3  4 F 1 = 50 N  1 = 30 o F 2 = 100 N  2 = 135 o F 3 = 30 N  3 = 250 o F 4 = 40 N  4 = 300 o 43.3 25.0  70.7 70.7  10.3  28.2 20.0  34.6  17.7 32.9

49. Adding Multiple Vectors F R = 37.4 N  R   17.7 32.9

50. Now You Try: F 1 F 2 F 3 F 4  1  2  3  4 F 1 = 90 N  1 = 45 o F 2 = 80 N  2 = 150 o F 3 = 50 N  3 = 220 o F 4 = 70 N  4 = 340 o

51. Chapter 1: Introduction and Mathematical Concepts “ Section 9” Additional Stuff You Should Know

59. END