Units of Measurements Conversion Factors Dimensional Analysis Unit Analysis

1. Units of MeasurementsConversion FactorsDimensional AnalysisUnit Analysis

2. The Most Basic Measurements Base Quantities • Base Quantities are physical measurements that define a standard quantity. • Often base quintiles can not be simplified into a simpler set of quantities • Seven (7) Base Measurements • 1. length (L) 5. amount of substance (mole) • 2. time (t) 6. electric current (I) • 3. mass (m) 7. luminous intensity (candela) • 4. temperature (Kelvin)

3. Derived Quantities • Derived Quantities are physical measurements using combinations of base quantities. • Examples: • Speed or velocity (v); length/time (L/t) • Area (A); length x length (L2) • Volume (V); length x length x length (L3) • Acceleration (a); Δvelocity/time (L/t/t) (L/t2 ) • Force (F); mass x acceleration (m∙ L/t2) • work & energy (joule)(J); force x distance (F∙L) • many many more

4. Standard Units of Measurement • Two widely accepted standard units of measurement 1) BRITISH system : only used by 1 major industrialized country USA) 2) METRIC system (SI system): used by the rest of the industrialized world and Physists

5. Systseme International (SI) • Systseme International (SI) is the metric system, it has its origins in the late 1700’s

6. Systseme International (SI) • Systseme International (SI) is the metric system, it has its origins in the late 1700’s • UNITS of MEASUREMENT for SI

7. Systseme International (SI) • Systseme International (SI) is the metric system, it has its origins in the late 1700’s • UNITS of MEASUREMENT for SI • Base QuantitiesStandard SI Units • length meter • time second • mass kilogram ≠ weight • electric current ampere • temperature Kelvin • amount of a substance mole • luminous intensity candela

8. Systseme International (SI) • Systseme International (SI) is the metric system, it has its origins in the late 1700’s • UNITS of MEASUREMENT for SI • Base QuantitiesStandard SI Units • length meter • time second • mass kilogram ≠ weight • These three quantities are the units most often used in the 1st semester of this course

9. Systseme International (SI) MKS • Systseme International (SI) is the metric system, it has its origins in the late 1700’s • UNITS of MEASUREMENT for SI • Base QuantitiesStandard SI Units • length meter • time second • mass kilogram ≠ weight • This is the MKS measurement system of the SI meter kilogram second are the standards for basic measurement

10. Systseme International (SI) MKS • Systseme International (SI) is the metric system, it has its origins in the late 1700’s • UNITS of MEASUREMENT for SI • Base QuantitiesStandard SI Units • length meter • time second • mass kilogram ≠ weight • This is the MKS measurement system of the SI meter kilogram second are the standards for basic measurement • We will be using the MKS measurements in this course

11. Systseme International (SI) cgs • Base QuantitiesStandard SI UnitsAbbreviation • Length centimeter cm • time second s • mass grams ≠ weight g

12. Systseme International (SI) cgs • Base QuantitiesStandard SI UnitsAbbreviation • length centimeter cm • time second s • mass grams ≠ weight g • This is the cgs measurement system of the SI Centimeter gram second are the standards for basic measurement • We will NOT be using cgs measurements in this course

13. Value of SI measurements length (meter) 1/10,000,000 distance from equator to North Pole along a meridian line running through Paris Distance traveled in 1/ 299,792,458 of a second by light in a vacuum Mass (kilogram) 1/1,000 of a cubic of pure water at 4oC mass of a particular platinum- iridium cylinder kept at the International Bureau of Weights and Measurements in Paris Time (second) 1/86,400 of a mean solar day 9,192,631,770 periods of radiation released from cesium atoms

14. Value of SI measurements Other measurements will be introduced as needed

15. Prefixes; Measurement Modifiers • In the British system different measurements of the same base quantity have different names length: feet, inches, yards, miles, etc weight: pounds, ounces, tons time: seconds, minutes, hours, days, years, etc

16. Prefixes; Measurement Modifiers • In the SI system prefixes combined with a common root are used to express different quantities length: meter, kilometer, centimeter, millimeter mass: gram, milligram, kilogram, decagram, time: second, millisecond, kilosecond, megasecond hours, minutes, years

17. standard base units in SI system

18. NOTICE THAT THE STANDARD BASE UNIT FOR MASS IN THE METRIC SYSTEM IS A KILOGRAM

19. Prefixes; Measurement Modifiers

20. Conversion Factors • Often times a measured quantity in one set of units must be converted to an equivalent quantity in another set of units • To make the conversion, a conversion factor is required. • A conversion factor is often expressed as a fraction with the numerator and denominator having the same quantity expressed in different units • The quantity to be converted is then multiplied by the conversion factor. The units to be changed must cancel leaving only the desired unit(s).

21. Examples of Conversion Factors A conversion factor must have a value of 1 (one). • 12 inches/1 foot • 1 foot/12 inches • 36 inches/ 1 yard • 1 yard/ 36 inches • 60 seconds / 1 minute • 1 minute/ 60 seconds • 3600 seconds/ 1 hour • 2.54 cm/1 inch • 1000m/kilometer 1000m/km • 1 m/1000mm In each example the quantity in the numerator equals the quantity in the denominator

22. Applicatin of Conversion Factors 1. Convert 18 inches into feet 18 inches (1 foot/12 inches) = 1.5 feet 2. Convert 1.33 hrs into seconds 1.33 hrs (3600 seconds/1 hr) = 4788 seconds sig figs 4790 seconds 3. Convert 758 mm into meters 758 mm (1 m/1000mm) = 0.758 m

23. Application of Conversion Factors Sometimes two or more conversion factors must be used. 4. Convert 26.7 m/s into kilometers/hr 26.7 m/s ( 1 km/1000m) ( 3600 s/1 hr) = 96.12 km/hr sig figs 96.1 km/hr • Convert 4580 cm3 into m3 4580 cm3 (1 m/1000cm)3 = 0.000004580 m3 = 4.58 x 10-6 m3

24. Conversion Factorsproper dimension • When using conversion factors the original measurement must have the same dimension as the final measurement • 60 km/minute (1 minute/60 sec) = 1 km/sec • velocity dimension = velocity dimension

25. Dimensional Analysis Dimensional analysis: is a procedure that determines if a mathematical equation will produce the expected dimension. If the equation is expected to produce the dimension length, each number in the equation should be a length 6m + 4m = 10 m L + L = L

26. Dimensional Analysis 6m + 6ft = ? L + L = L

27. Dimensional Analysis 6m + 6ft = ? L + L = L dimensionally correct 3m/s(5s) + 6m = 21m L + L = L dimensionally correct 35m + 15 s = 50m L + t ≠ L dimensionally incorrect

28. Dimensional Analysis To be mathematically correct an equation must be dimensionally correct An equation that is dimensionally correct may not be mathematically correct This will be demonstrated and explained further at a later time

29. Unit Analysis In an equation, measurements will involve units of time, length, mass, velocity, force etc. Unit analysis is analyzing each of these measurements to be sure that each measurement is using the same unit 5 min + 10 min = 15 min units are correct-- same time unit thru out the equation

30. Unit Analysis 5 min + 600 sec = ? Seconds can not be added to minutes Dimensionally correct Units of time are not the same Equation can not be solved in this form Requires a conversion

31. Unit Analysis 5 min + 600 sec = ? 5 min ( 60 sec/min) = 300 sec 300 sec + 600 sec = 900 sec Dimensionally correct Units of time are the same Equation can be solved in this form

32. Order of magnitude could also be considered a type of measurement