Module No. 4
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This document discusses systems of units and the International System of Units (SI). It describes the three fundamental SI units - the meter (length), kilogram (mass), and second (time) - and how other units are derived from these. It provides details on how the definitions and standards for the meter, kilogram, and second have changed over time to become more precise and based on fundamental physical constants. The document also lists the seven base units in SI and the two supplementary units of plane angle and solid angle. It introduces prefixes used to denote multiples and submultiples of units.
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because platinum-iridium is an unusually stable alloy. The same
standard has been adopted for SI units.
Time
Second is the basic unit of time in all systems of units. Before
1960, the standard of time was defined in terms of the mean solar
day. Thus second was originally defined as [1/60] [1/60] [1/24], of
a mean solar day. In 1967, the SI unit of time, the second was
redefined by 13th General Conference on Weights and Measures
using the characteristic frequency of cesium-133 atom. According
to this standard:
1 second = duration of 9,192,631,770 vibrations of cesium-133
atom.
SI Units
In 1960, the eleventh General Conference on weights and
measures introduced a system known as International System or
SI (the abbreviation for the French equivalent, Systeme
International). The units included in this system are known as SI
units. The SI units are now used all over the world.
The SI units, unlike the three basic units of the F.P.S., the C.G.S
and the M.K.S. systems, comprise the seven basic units. These
are:](https://image.slidesharecdn.com/moduleno-200324155004/85/Module-No-4-3-320.jpg)
Module No. 4
- 1. 1 Module # 04 Units & Systems of Units Systems of Units Different systems of units have been in use in science at different times. The commonly used systems were: 1. The F.P.S. i.e., the foot pound second system. 2. The C.G.S. i.e., the centimeter, gram and second system. 3. The M.K.S. i.e. the meter, kilogram and second system. Fundamental Units All physical quantities are expressed in terms of the following three fundamental quantities. (1) Length (L) (2) Mass (M) (3) Time (T) In System International (SI) meter is the unit of length, Kilogram is the unit of mass and second is the unit of time. Length, mass and time are fundamental quantities and their units are called fundamental units. All other units are derived from fundamental units and are called derived units.
- 2. 2 Length In scientific laboratories all over the world, the length is measured in meters. In I960, in accordance with an international agreement, the meter was redefined in terms of the wavelength of the orange light emitted by Krypton-86 atoms in an electrical discharge. The meter was defined as 1,650763.73 wavelengths of orange light emitted from a Krypton 86 lamp. By 1983, the demand for high precision had reached such a point that even the Krypton-86 standard could not meet them and the meter was redefined as "the distance travelled by a light wave in vacuum during a time of 1/299792458 seconds". This definition of meter was adopted as standard by the 17th General Conference on Weights and Measures. All precise measurements are now made with light waves. Mass The unit of mass is known as kilogram. It is defined as the mass of a platinum (90%) and iridium (10%) alloy cylinder, 3.9 cm in diameter and 3.9 cm in height, kept at the International Bureau of Weights and Measures in France. This mass standard was established in 1901 and there has been no change since that time
- 3. 3 because platinum-iridium is an unusually stable alloy. The same standard has been adopted for SI units. Time Second is the basic unit of time in all systems of units. Before 1960, the standard of time was defined in terms of the mean solar day. Thus second was originally defined as [1/60] [1/60] [1/24], of a mean solar day. In 1967, the SI unit of time, the second was redefined by 13th General Conference on Weights and Measures using the characteristic frequency of cesium-133 atom. According to this standard: 1 second = duration of 9,192,631,770 vibrations of cesium-133 atom. SI Units In 1960, the eleventh General Conference on weights and measures introduced a system known as International System or SI (the abbreviation for the French equivalent, Systeme International). The units included in this system are known as SI units. The SI units are now used all over the world. The SI units, unlike the three basic units of the F.P.S., the C.G.S and the M.K.S. systems, comprise the seven basic units. These are:
- 4. 4 Quantity Unit Name Unit Symbol Length meter m Mass kilogram kg Time second s Electric current ampere A Temperature kelvin K Amount of substance mole mol Luminous intensity candela cd In addition to these seven fundamental units (listed above), the SI units also include two supplementary units. These supplementary units are those of plane angle and solid angle. Their units are radian and steradian respectively. Candela The SI unit of luminous intensity is candela. It is defined as the luminous intensity in the perpendicular direction of a surface of 1/600000 square meter of a black body radiator at the solidification temperature of platinum under standard atmospheric pressure. This definition was adopted by the 13th General Conference of Weights and Measures in 1967.
- 5. 5 Steradian It is used for the measurement of solid angles i.e. unit of solid angle. Derived Units Some units are expressed in terms of other units, which are derived from fundamental units, are known as derived units e.g., the unit of velocity, acceleration, pressure, Area, volume, density, force, power, work done etc. Thus, the nine physical quantities, as mentioned in SI Units, are regarded as the fundamental quantities and their units are called the fundamental units. Other physical quantities which can be defined in terms of these fundamental quantities are, therefore, called derived quantities and their units are, thus, called derived units. Examples (1) Speed is defined as distance travelled in unit time. In SI units, the distance is measured in meters and time in seconds. So, the units for speed would be meter per second. (2) Acceleration is defined as the time rate of change of velocity. As the unit of velocity is same as that of speed, therefore, the SI unit of acceleration is meter per second per second.
- 6. 6 (3) Force is defined as mass times (multiplication) acceleration. The SI unit of mass is kilogram and that of acceleration is meter per second per second. Thus, the SI unit of force is kg ms-2 and is known as Newton. Conversion Factors Sometimes, it becomes necessary to convert units from one system to another. Conversion factor between the S.I. and conventional units of lengths are as follows: 1 mile = 1609 m = 1.609 km 1 ft. = 0.3048 m = 30.48cm 1 m = 39.37 inches = 3.281ft 1 inch = 0.0254 m = 2.54 cm 1 gallon = 4.5461 liters 1 tola = 11.636 grams 1 pound = 0.4536 kg 1 ft. = 0.3048 m = 30.48cm 1 m = 39.37 inches = 3.281ft 1 inch = 0.0254 m = 2.54 cm 1 newton = 105 dyne
- 7. 7 Prefix In physics, sometimes, we deal with very large numbers and sometimes with very small numbers. Prefixes are used to express these large or small numbers as multiple of ten. For example, (in case of large number) 1 light year = 9460000000000000 m = 946 x 1013 m = 9.46xl015m. Similarly, (in case of small number) Radius of Proton = 0.0000000000000012m = 12x 10-16 m = 1.2x10-15 m Other Use of Prefix Sometimes, we use prefix to express appropriate units. For example, centi means 1/100, therefore, centimeter means 1/100 meter, or; 1/100 m = 1 centimeter Similarly, 1000 m = 103 meter = 1 kilometer 1/1000m = 10-3m = 1 millimeter Hence, centi, kilo, milli are called prefixes. The commonly used prefixes are given below in the table.
- 8. 8 Prefix Symbol Multiple tera T 1012 giga G 109 mega M 106 kilo k 103 hecto h 102 deca da 101 deci d 10-1 centi c 10-2 milli m 10-3 micro 10-6 nano n 10-9 pico P 10-12 femto f 10-15 atto a 10-18