1. Mathematics and Physics
Section 1.1

2. What is Physics
Physics – a branch of science that involves the study of the physical world: energy, matter and how they are related
Motion of electrons
Motion of rockets
Energy of sound waves
Electrical circuits
And more…
Mathematics is used in physics to model and explain our theories and predictions
In physics one way to check your answers is to check if they make sense

3. SI Units There is a table of base units in your book on page 5
SI Units – an adaption of the metric system used by the worldwide scientific community
These base units were originally defined in terms of direct measurements
Derived units – units that were created by combining base units in various ways
There is a table of base units in your book on page 5

4. SI Standards
There are institutions that were established for defining and regulating the standards of measurement
The SI system is regulated by the International Bureau of Weights and Measures in Sevres, France
The National Institute of Science and Technology in Gaithersburg, MD keep the standards against which our meter-sticks, clocks and balances are calibrated

5. Prefixes Prefix Symbol Multiplier Scientific Notation Femto- f
10-15
Pico- p
10-12
Nano- n
10-9
Micro- μ
10-6
Milli- m
.001
10-3
Centi- c
.01
10-2
Deci- d .1
10-1
Kilo- k
1,000
103
Mega- M
1,000,000
106
Giga- G
1,000,000,000
109
Tera- T
1,000,000,000,000
1012

6. Dimensional Analysis
Units can be used as a way to check for correct procedure in physics problems
Confirm that the units on the answer are the expected units from the equation
Dimensional Analysis – the method of treating the units as algebraic quantities which can be cancelled

7. Significant Figures (Digits)
Significant Digits – the valid digits in a measurement
The last digit in a measurement is always the uncertain digit
Ex: If you measure a pen to be just past 14.3 cm then the measurement has two significant digits and one that you estimated

8. Scientific Notation Not all zeros are significant digits
Ex: only has 3 significant digits, the first two are strictly placeholders
Ex: 172,000 could have 2,3,4 or 5 significant digits, because of this uncertainty scientific notation is used
x 105 m has 5 significant digits

9. Significant Digits cont…
Addition and subtraction – the result is rounded to the least-precise value involved
Ex: = 6.3
Multiplication and Division – the result is rounded to the number of significant digits of the least precise value involved
Ex: / 11.4 = 35.9

10. Scientific Method
Scientific Method – a systematic method of observing, experimenting and analyzing to answer questions about the natural world
This system is used by all branches of science
These results must be reproducible
Hypothesis – an educated, testable guess about how variables are related

11. Scientific Method Cont…
Steps
State the Problem
Gather information
Form a hypothesis
Test the hypothesis
Analyze the data
Draw Conclusions
If the hypothesis was incorrect a new one must be formed and tested

12. Models, Laws and Theories
Model – used to represent scientific ideas or things not easily seen
Ex: The models of the atom in chemistry
Scientific Law – a rule of nature that sums up related observations to describe a pattern in nature
Scientific Theory – an explanation based on many observations supported by experimental results