1. Measurement

2. Physical Quantities
Measurable characteristics that describe object’s size, position, speed, energy, etc
All measured quantities have a dimension (length, time, mass, etc)
Units used must be expressed with the measurement
Quantities are of two types: scalars, with no directional component, and vectors, which must include a direction

3. Units of Measurement
Metric system used for all scientific measurements
MKS based on meter, kilogram, second; also called SI system
CGS based on centimeter, gram, second sometimes used for smaller quantities
We will use the MKS system excluslively

4. MKS Fundamental Units

5. Standard Units
Original standard meter was made of platinum, stored in Paris
Now, meter is based on wavelength of a certain light emission
Second, once based on part of a day, now based on atomic vibrations
Only the kilogram is based on physical standard, stored in Paris

6. Derived Units Volume (liter) is derived from the meter
Other units are combinations of fundamental units
Newton, volt, joule, meters per second all derived units

7. Metric Prefixes
Very large and very small numbers are common in physics, often expressed as powers of ten using scientific notation
Multiples or fractional parts of any unit can be expressed using metric prefixes combined with a base unit

8. Metric Prefixes giga- G x 109 mega- M x 106 kilo- k x 103
centi- c x 10-2
milli- m x 10-3
micro- m x 10-6
nano- n x 10-9
pico- p x 10-12

9. Scientific Notation
Used to simplify operations involving very large or very small numbers
Use with numbers larger than 9,999 or smaller than 0.001
Consists of a coefficient multiplied by ten raised to an exponent

10. Scientific Notation
All significant digits and only significant digits are placed in coefficient, with one digit to left of decimal
Exponent of 10 is found by how many places decimal must be moved from original number
Movement to left is positive, to right is negative

11. Significant Figures
Number of significant figures that can be reported depends on precision of measuring instrument
When calculations are made, significance of answer depends on least significant measurement
Counting numbers and fundamental constants are not considered in sig. figs., only measured numbers

12. Rules for Significant Figures
Non-zero numbers are always significant
Zeros between other nonzero digits are significant
Zeros in front of nonzero digits are not significant
Zeros at the end of a decimal number are significant
Zeros at the end of a whole number are not significant unless they have been measured and are indicated by a line over the zero

13. Calculations With Significant Figures
Multiplication and division: answer must be rounded off to the same number of digits as the least significant measurement used to obtain the answer
Addition and subtraction: answer must be rounded off to the same number of decimal places as the measurement with the smallest number of decimal places

14. Rules for Rounding
When the digit(s) following the last significant figure is <5, round down
When the digit(s) following the last significant figure is >5, round up
When the digit(s) following the last significant figure is exactly = 5, round down if the last sig fig is even, round up if the last sig fig is odd

15. Accuracy
Accuracy: how close a measurement is to the actual or accepted value
Absolute error is the difference between a measurement and the accepted value
Percent error is the absolute error divided by the accepted value (times 100)

16. Precision The degree of exactness of a measurement
A measure of how many digits can be read from an instrument
How well a series of measurements agrees with each other
Precision is often estimated as one-half of the smallest division of the instrument

17. Types of Error Experimental error is not a mistake
Error is a measure of uncertainty of the measurement
Systematic or systemic error: instruments not properly calibrated or adjusted or used incorrectly; example: parallax
Random error: unknown or unpredictable variation in experimental conditions

18. Graphing Data Helps show relationships between measured quantities
Independent variable: controlled by experimenter, usually plotted on horizontal axis
Dependent variable: depends on what is done to independent variable, usually plotted on vertical axis
If time is one of the variables, it is often plotted on the horizontal axis

19. Important Graph Types
Direct proportion or direct relationship between variables, linear graph; y=mx+b
Inverse proportion or relationship: if one variable increases, other must decrease, hyperbola graph; xy=k
Quadratic or squared relationship, parabola graph; y = ax2 + bx + c

20. Reading the Graph
Graph is often used to estimate value not measured in experiment
Interpolation: estimation between measured points
Extrapolation: estimation beyond range of measured values

21. Elements of a Good Graph
Graph must be large enough to be easily read and neat—use a straightedge for all lines
Decide which variable goes on each axis
Examine data to find the range; set up scales on axes that are consistent and easy to read
Decide if the origin is a valid data point—if so, include it in the data set.

22. Elements of a Good Graph
Axes must be labeled with units
Plot the points—make them easily visible
Determine the relationship shown by the data
Draw best fit line or curve—don’t connect the points
Graph must have descriptive title

23. Physics Equations
Equations are used to write relationships between variables shown by experimental data and graphs
Letters and often Greek letters are used to represent quantities
Don’t confuse the symbol used in the equations with the abbreviation for the unit

24. Dimensional Analysis Dimensions can be treated as algebraic quantities
Quantities can be added or subtracted only if they have the same units
When multiplying or dividing quantities, units must work out to be the proper unit of the answer
A good way to check your work

25. Orders of Magnitude
Round a number to the nearest power of 10 to find its order of magnitude
Useful in estimating quantities or checking answers for reasonableness

26. Problem Solving
Read problem carefully, write down given information and what is asked for with proper symbols. Draw a sketch
Find an equation that relates given quantities and unknown. May be a 2 step problem needing 2 equations
Solve basic equation for the unknown in terms of given quantities

27. Problem Solving
Substitute numbers into equation including units and significant digits
Check dimensions (units) to make sure they match the desired answer
Do the math, rounding to correct sig figs
Check to see if answer is reasonable

28. Vocabulary accuracy precision fundamental units derived units
significant digits
absolute error
percent error
scalar
interpolation
extrapolation
direct proportion
inverse proportion
hyperbola
independent variable
dependent variable
vector

29. Vocabulary
personal error
systematic error
random error
parallax