Engineering Statics/Appendices/SI Units Used in Mechanics

SI Units Used in Mechanics Quantity Unit SI Symbol (Base Units) Length meter* m Mass kilogram kg Time second s (Derived Units) Acceleration, linear meter/second2 m/s2 Acceleration, angular radian/second2 rad/s2 Area meter2 m2 Density kilogram/meter3 kg/m3 Force newton N (= kg-m/s2) Frequency hertz Hz (= 1/s) Impulse, linear newton-second N-s Impulse, angular newton-meter-second N-m-s Moment of force newton-meter N-m Moment of inertia, area meter4 m4 Moment of inertia, mass kilogram-meter2 kg-m2 Momentum, linear kilogram-meter/second kg-m/s (= N-s) Moment, angular kilogram-meter2/second kg-m2/s (= N-m-s) Power watt W (= J/s = N-m/s) Pressure, stress pascal Pa (= N/m2) Product of inertia, area meter4 m4 Product of inertia, mass kilogram-meter2 kg-m2 Spring constant newton/meter N/m Velocity, linear meter/second m/s Velocity, angular radian/second rad/s Volume meter3 m3 Work, energy joule J (= N-m) (Supplementary and Other Acceptable Units) Distance (navigation) nautical mile (= 1,852 km) Mass ton (metric) t (= 1,000 kg) Plane angle degrees (decimal) ° Plane angle radian — Speed knot (1.852 km/h) Time day d Time hour h Time minute min * Also spelled metre Metric prefixes Prefix Symbol 1000m 10n Decimal Short scale Long scale SinceThe metric system was introduced in 1795 with six prefixes. The other dates relate to recognition by a resolution of the CGPM. yotta Y 10008 10241,000,000,000,000,000,000,000,000 Septillion Quadrillion 1991 zetta Z 10007 10211,000,000,000,000,000,000,000 Sextillion Trilliard 1991 exa E 10006 1018 1,000,000,000,000,000,000 Quintillion Trillion 1975 peta P 10005 1015 1,000,000,000,000,000 Quadrillion Billiard 1975 tera T 10004 1012 1,000,000,000,000 Trillion Billion 1960 giga G 10003 1091,000,000,000 Billion Milliard 1960 mega M 10002 106 1,000,000 Million 1960 kilo k 10001 103 1000 Thousand 1795 hecto h 10002/3102 100 Hundred 1795 deca da 10001/3 101 10 Ten 1795 10000 100 1 One – deci d 1000−1/3 10−1 0.1 Tenth 1795 centi c 1000−2/3 10−2 0.01 Hundredth 1795 milli m 1000−1 10−3 0.001 Thousandth 1795 micro μ 1000−2 10−6 0.000001 Millionth 1960 nano n 1000−3 10−9 0.000000001 Billionth Milliardth 1960 pico p 1000−4 10−12 {0.000000000001 Trillionth Billionth 1960 femto f 1000−5 10−15 0.000000000000001 Quadrillionth Billiardth 1964 atto a 1000−6 10−18 0.000000000000000001 Quintillionth Trillionth 1964 zepto z 1000−7 10−21 0.000000000000000000001 Sextillionth Trilliardth 1991 yocto y 1000−8 10−24 0.000000000000000000000001 Septillionth Quadrillionth 1991 Selected Rules for Writing Metric Quantities For readability, use unit prefixes such that the number is between 0.1 and 1000. The most common prefixes in engineering are giga, mega, kilo, centi, milli, and micro. Prefixes like hecto, deka, and deci make for awkward numbers. Unit combinations should only use prefixes in the numerator (write kJ/s instead of J/ms), with the exception of kg. Do not double up the prefixes, e.g. write GW not kMW. Use a dot to multiply units (write N•m not Nm) Avoid the ambiguity of multiple divisions (write N/m3 not N/m/m/m) Exponents refer to the entire unit symbol (mm2 means (mm)2) Use spaces instead of commas to make long numbers easier to read (e.g. 1 210 000 000.001 W), ignore for numbers of four digits.