Units

Unit Systems  Systems set up fundamental units  British system - foot, pound, second  Metric system - meter, kilogram, second

Time  The unit of time originally was based on the day and the year.  The second was 1/60 * 1/60 *1/24 of a day.  In the 20th century the second was measured based on the timing of atoms.  We now know that the day is getting longer and “leap seconds” are added every few years.  The SI unit of time is the second (s)

Length  The oldest standards of length were based on the human body.  The metric system defined the meter in terms of the Earth: 1/10,000,000 from the pole to the equator.  The meter is now defined in terms of the second and speed of light.  The SI unit of length is the meter (m)

Mass  Standard weights have been maintained for centuries.  Weight and mass were thought to be the same.  Now a standard 1 kilogram mass is kept in Paris.  The SI unit of mass is the kilogram (kg)

SI Prefixes  Prefixes on units are used to represent powers of ten.  Prefixes denote powers of ten from  18 to  18 in steps of three.  Example: a kilometer is 10 3 meters or 1000 meters. Most Common  micro (  )  milli (m)  kilo (k) 10 3  mega (M) 10 6  Common, but the power is not a factor of three.  centi (c )  deci (d ) 10 -1

Other Units  There are other fundamental units in SI. See NIST. NIST ampere (A)ampere (A) kelvin (K)kelvin (K) mole (mol)mole (mol) candela (cd)candela (cd)  Derived units are built from the fundamental units. area (m 2 ) volume (m 3 ) velocity (m/s) acceleration (m/s 2 ) force (kg m/s 2 ) or (N) energy (kg m 2 /s 2 ) or (J)

Matching Units  Conversion between units must be of the same type.  Length conversion: 1 in = 2.54 cm1 in = 2.54 cm  Time conversion: 1 hr = 3.6 x 10 3 s1 hr = 3.6 x 10 3 s  No conversion between different types of units. 1 in is not equivalent to some seconds1 in is not equivalent to some seconds

Conversion Factors  A value is converted by applying the ratio of the conversion factors. How many inches in 50. cm?How many inches in 50. cm? 50. cm (1 in / 2.54 cm) = (50. / 2.54) in = 20. in50. cm (1 in / 2.54 cm) = (50. / 2.54) in = 20. in  Many conversion factors use scientific notation. How many seconds in a year?How many seconds in a year? 1 yr (365 d/yr) (24 hr/d) (3.6 x 10 3 s/hr) = x 10 3 s = 3.15 x 10 7 s1 yr (365 d/yr) (24 hr/d) (3.6 x 10 3 s/hr) = x 10 3 s = 3.15 x 10 7 s

Special Units  Earth to the Sun  150,000,000 km = 1.5 x m 1 Astronomical Unit (1 AU)  (1.5 x m) / (3.0 x 10 8 m/s) / (60 s/min) = 8.3 light-minutes next