Chapter 1 Measurement

We measure things (such as weight, time, length, speed, etc.) We use tools (rulers, clocks, speedometers, etc.) to measure things Measurement tools are calibrated Calibration is in units (inches, seconds, pounds, mph’s, etc.) Units require standards (conventional, habitual, customary)

Modern standards Not all quantities in nature are independent (e.g., speed is distance per time) Standards are created for independent (base) quantities: length, time, mass, + some other Modern day standards should be as invariable as possible Should be uniformly defined Should be accessible

SI (Systéme Internacional) – most accepted international system of units Adopted in 1971 Is commonly known as metric system Standard units are (there are more): 1 m (meter) for length 1 s (second) for time 1 kg (kilogram) for mass All other SI units are defined as derivatives of the base units (e.g., energy: 1 J (Joule) = 1 kg x 1 m 2 / s 2 )

Length SI unit – m (meter) Initially adopted as one ten-millionth of a distance between the North pole and the equator (standard – platinum-iridium bar) Currently - a modern standard: 1 m = the length of the path traveled by light in vacuum during a time interval of 1/ of a second

Time SI unit – s (second) Historically 1 s = 1 / 8640 day Currently - a modern standard: 1 s = the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the Cs 133 atom

Time SI unit – s (second) Historically 1 s = 1 / 8640 day Currently - a modern standard: 1 s = the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the Cs 133 atom

Mass SI unit – kg (kilogram) Historically 1 kg – mass of 1 liter of water Initially adopted in prototype of the kilogram was made of platinum-iridium and declared: “This prototype shall henceforth be considered to be the unit of mass” Currently - an alternative modern standard: 1 kg = mass of C 12 atom * / (Don’t confuse mass and weight: 1 kg is the same on the Earth and on the Moon)

Scientific notation s = = 2.37 x 10 8 s = = 2.37 E8 s m = = 6.64 x m = = 6.64 E-5 m

SI system prefixes FactorName Symbol yottaY zettaZ exaE petaP teraT 10 9 gigaG 10 6 megaM 10 3 kilok 10 2 hectoh 10 1 dekada FactorName Symbol decid centic millim microµ nanon picop femtof attoa zeptoz yoctoy Examples: 1.25E4 J = 12.5 kJ 2.34 x s = ns

Good SI web resource: National Institute of Standards and Technology (NIST)

Conversion of units Need to know a conversion factor Use chain-link conversion (Check Appendix D for SI conversion factors)

Conversion of units

Order of magnitude Order of magnitude is the power of 10 that applies Divide the number by the power of 10 Compare the remaining value to ( ) If the remainder is less than 3.162, the order of magnitude is the power of 10 in the scientific notation If the remainder is greater than 3.162, the order of magnitude is one more than the power of 10 in the scientific notation

Answers to the even-numbered problems Chapter 1 Problem 2: 2.15 × 10 4 kg/m 3

Answers to the even-numbered problems Chapter 1 Problem 10: 9.19 nm/s

Answers to the even-numbered problems Chapter 1 Problem 22: (a) 13.4 (b) 49.1

Answers to the even-numbered problems Chapter 1 Problem 60: ~ stars