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

2. 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

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

4. 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 /

5. 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

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

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

8. Converting Units

9. Significant Figures (s.f.)
trailing 0’s count, e.g
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.

10. Calculating with Significant Figures

11. 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

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

13. Vector Components 13 13

14. Vector Addition by Components:14 14

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

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

17. 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

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

21. 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

22. these vectors are all the same

23. Multiplication by ConstantsA -A
0.5A
-1.2A