Mathematics and Physics Section 1.1

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

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

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

Prefixes Prefix Symbol Multiplier Scientific Notation Femto- f .000000000000001 10-15 Pico- p .000000000001 10-12 Nano- n .000000001 10-9 Micro- μ .000001 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

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

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

Scientific Notation Not all zeros are significant digits Ex: 0.0860 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 1.7200 x 105 m has 5 significant digits

Significant Digits cont… Addition and subtraction – the result is rounded to the least-precise value involved Ex: 3.86 + 2.4 = 6.3 Multiplication and Division – the result is rounded to the number of significant digits of the least precise value involved Ex: 409.2 / 11.4 = 35.9

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

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

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