1 Introduction Theories & Laws Math Review Measurements & Units Significant Figures Problem Solving Vectors General Properties of Vectors Hk: 1, 5, 23, 35, 53.

Theories & Laws Theories explain phenomena Laws are statements Laws usually come first. Example: Boyle’s Law; P ~ 1/V (1662) Bernoulli’s Kinetic Theory of gases (1740). 2

Math Review Percentages (Giam 01 9) Proportions (Giam 01 11+) Graphs & slopes Derivatives & Integrals (polynomial)

Measurement & Units Units describe and clarify (Giam 01 21) SI units include meter, kg, and second Combinations of these units are called Derived Units, e.g. speed = m/s, acceleration = m/s/s, force = kg·m/s/s Brackets used to indicate units of a variable, e.g. [v] = m/s /

Unit Analysis calculation and comparison of units Given: v = at, [v] = m/s, [t] = s, what are the value of [a]? [v] = [a][t] m/s = [a]s [a] = m/s/s 5 5

Dimensional Analysis units replaced by “dimensions” e.g. meter = L, seconds = T unit-independent e.g. [velocity] = L/T / 6 6

Prefixes for SI Units convenient shorthand for powers of 10 examples: m = 10-3 e.g. millimeter c = 10-2 e.g. centimeter k = 103 e.g. kilometer

Converting Units

Significant Figures (s.f.) trailing 0’s count, e.g. 1.560 leading 0’s not counted, e.g. 0.01 more s.f. implies more precision 1.56 3 s.f. 1.560 4 s.f. 1.056 12.001 5 s.f. 0.001 1 s.f. 0.0010 2 s.f.

Calculating with Significant Figures

Problem Solving write key data as you read mark unknowns with “?” double check each value use SI values, e.g. meter, kg, s draw physical situation write equations solve, consider, read question again

Vectors Magnitude & Direction Magnitude || (g4-5) Notation, Example Component Example Animated Phet Vectors 12

Vector Components 13 13

Vector Addition by Components: 14 14

Example Vector Addition R = (10cm, 0°) + (10cm, 45°): 15 15

(cont) Magnitude, Angle: (cont) Magnitude, Angle: 16 16

General Properties of Vectors size and direction define a vector location independent change size and/or direction when multiplied by a constant written: Bold or Arrow

Summary Theories explain. Laws describe. Math Review SI units & analysis Significant Figures Problem Solving Strategy Vector = magnitude + direction /

Common Metric Prefixes Prefix Symbol Power of 10 giga G 109 mega M 106 kilo k 103 centi c 10-2 milli m 10-3 micro μ 10-6 nano n 10-9

these vectors are all the same

Multiplication by Constants A -A 0.5A -1.2A