System of Units: Measurement of any physical quantity depends on a standard, which is fixed and agreed upon internationally. When you go to buy sugar, you do not say that "I want to buy a sugar", you will say "I want to buy 1kg of sugar". The shopkeeper then weighs the sugar, against STANDARD weights and gives you 1 kg of sugar. Similarly, when you measure with a ruler, length of, say a pencil, the markings on the ruler are STANDARD lengths. Take another physical quantity, say time. A second, a minute and an hour on your watch has been set to a STANDARD. Now you may ask, why this is so? The answer to this question is that anywhere on the earth, your measurements should match anybody else's measurements. When you say that you have bought 10 kg of potatoes, whether you buy them in Pune, Paris or Portsmouth, 10 kg of potatoes have to be 10 kg of potatoes and nothing else. Therefore, whenever you measure any physical quantity, they are relative to or compared against some STANDARD measurements. The international community from time to time announces new, revised standards and all nations have to comply with these standards. The basic quantity of the standard is known as a unit. An actual measurement would be a fixed multiple of the unit. The multiple is called the magnitude of the unit. For example, if we decide unit length to be 1 meter, and if a length of the side of the table is 1.5 meters then magnitude of the measurement is 1.5. Thus what is a unit? The amount of a physical quantity that is used as a reference for the measurement of that quantity is called the unit of that quantity. The unit is invariable, easily reproducible and is internationally accepted. Fundamental, derived and supplementary units Fundamental units of measurements are those that are unique and cannot be derived. Their representations or prototypes are maintained in many international centres world wide, like the International Bureau of Weights and Measures at Sevres near Paris, National Institute of Standard Technology or National Physical Laboratory in the USA or Bureau of Indian Standards in New Delhi, India. Internationally everyone strictly follows a standard system of units. This system is called the S.I. units (Standard International). Calibrations used for measurement have to be standardized so that they remain constant, under normal everyday life. If this was not done, then there would be chaos in the world as everyone's measurement would be different!! Fundamental quantities are not defined or explained in terms of other physical quantities. They are to be understood by direct observation alone. Length, mass and time are three such quantities. We do not try to explain what is length. Four more quantities have been adopted at present as fundamental. They are ampere for electric current, Kelvin for thermodynamic temperature, luminous intensity and amount of substance (mole). Fundamental units are also called base units. Unit of mass : Mass is the quantity of matter present in a body. The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram (kg). The prototype is an exactly cylindrical piece of platinum–iridium alloy. Accurate copies of the standards are manufactured and maintained by countries. Although mass and weight are used in the same manner in everyday language, their meanings are very different in scientific term. Weight is the force by which a mass is attracted to earth. Weight of a body changes with its position from the centre of the earth, or it changes on the moon even though its mass remains unchanged. Unit of length : The speed of light is invariant in the universe and it is 2,99,792,458 meters/second. So this gives a convenient measure of length. Meter (m) is the standard measure of length. The meter is defined as the length of the path travelled by light in vacuum during a time interval of 1 / (299,792,458) of a second. Unit of Time : Human beings are conscious of the flow of time; past, present and future. But what is time? How can one define it? It is very difficult to define time, because our measuring standard itself may vary! Time is the epoch that elapses between repeated successive events. Second (s) is the unit of time. Internationally a standard second is measured by a Caesium atomic clock. These clocks are placed in many parts of the earth. 133Cs atom jumps from its one atomic level to another with a frequency of 9,192,631,770 Hertz. Each jump produces a photon which can be detected. Time is inverse of frequency, hence a second is defined as the inverse of the quantity 9,192,631,770. Derived units are expressed algebraically in terms of fundamental units or other derived units. The symbols for derived units are obtained by means of the mathematical operations of multiplication and division. If you want to measure the floor area of a room, you would have to measure the length of the room, and its breadth. The area would be the product of length and breadth. Similarly, to measure the speed of a vehicle, you would have to know the distance it travels and the time it takes to cover that distance. By dividing distance by time you will get speed. In these examples we see that measurement of certain physical quantities is based on the measurement of some fundamental quantities. These are, therefore, known as derived quantities. Examples of derived physical quantities are volume, density, pressure, etc. Table below gives some of the S.I. derived units There are some derived units that have special names and symbols. Any unit that can be obtained by the combination of fundamental units is known as derived unit. The SI system has various derived units, used for measuring force, energy, power, frequency and so on. They can be expressed in terms of the base unit. In the class of supplementary units, there are only two items : radian which is the unit for measuring plane angle (angles in two dimensions) and steradian which is a unit for measuring solid angles (angles in three dimensions). Both radian and steradian are dimensionless quantities. In SI units, decimal prefixes are also standardized. If a quantity is too low or too large, standard allowed prefixes are used. A prefix attaches directly to the name of a unit, and a prefix symbol attaches directly to the symbol for a unit. For example, one kilometer, symbol 1 km, is equal to one thousand meters, symbol 1000 m or 103 m. When prefixes are attached to SI units, the units so formed are called "multiples and sub–multiples of SI units". Alternative definitions of the SI, prefixes and their symbols are not permitted. Units used in computers such as bytes, kilobytes are not accepted in the system of standard units. System of Units Since the development of measuring processes, a number of systems of unit have been put forward. Here are a few: F P S System (Foot–Pound–System): In this system of unit, length is measured in foot; mass in pound; and time in second. This is also known as British system of measurement. C G S system (Centimeter–gram–second) :In this system of unit, length is measured in centimeter; mass in gram; and time in second. M K S system (Meter–kilogram–second) or metric system : Here, length is measured in meter; mass in kilogram; and time in second MKS units and the SI system of units are nearly similar. Thus in most measurements, standard units or MKS units are used these days. Rules for Writing Units When writing a complete unit, all the letters in the word must be in small letters. For example, the length of a pencil is 10 centimetres. The force on a ball is 0.5 newton (and not 0.5 Newton). (Plural of complete unit is acceptable.) When writing in the abbreviated form, if the unit is named after a scientist, the first letter should be in capitals, otherwise it should be written in small letters. Examples: the mass of a book is 200 g (where g stands for gram); or, period of oscillation is 5 s (s stands for second); or, the temperature of a body is 100 K (where K stands for Kelvin, named after a scientist). If more than a single letter of the word are used in the abbreviation, then the other letters must also be written in small script. The length of a chain, for instance, is 7 cm (where cm stands for centimeter). The frequency of a tuning fork is 256 Hz (where Hz stands for Hertz, named after the scientist Hertz). In the abbreviated unit plural form is not written. For instance, it is wrong to write 'the train covered 100 kms. in 2 hrs'. Instead, one must write '100 km in 2 hr'. The abbreviated form of a unit is not followed by the punctuation mark (.) to show that it is an abbreviation. Writing 'the point is at 10 cm. from the wall' is wrong. Instead, one should write 'the point is at 10 cm from the wall'. Multiplication of units is shown by leaving a space or a raised dot. For example, unit of work is newton meter; which is the correct way to write it or write it as N m or N.m. Avoid writing compound prefixes. For example, the capacity of a capacitor is 10 pF; it should not be written as 10 mmF. Leave space between the number and the unit. For example, 7 kg, not 7kg. Division of units is indicated by the / sign or negative power. For example, the unit for power is written as J/s or J s–1. Unit of thermal conductivity may be written as W/m K or W m–1K–1 but never W/m/K. Put a hyphen between the number and the unit when the number together with the unit is used as an adjective. For example, 35–mm film. The thickness of a metal sheet, on the other hand, would be written as 35 mm. Dimension of a Physical Quantity All physical quantities can be derived from the fundamental physical quantities. The relation between a physical quantity and the fundamental quantities can be expressed in symbols representing the fundamental quantities, which are called dimensions. In other words dimension of a physical quantity is the total of all units attached to it. For example, speed is given as distance x time. In the MKS system the dimension of speed is expressed as meters/second (m/s), in CGS system it will be centimeters/second (cm/s). In the FPS system it is feet/second (ft/s). In whichever system we are measuring, the dimension of measurement is same. Thus, dimension of measurement of speed is L / T = L T–1 Dimension of speed is given as [M0 L1 T–1] One of the most important concepts in Physics is that dimensions have to be balanced exactly in a given equation. This is similar to a chemical reaction where the number of atoms in a reaction has to be balanced exactly. Dimensional validity of an equation only tells us that the equation may be correct; the actual correctness of the equation must be ascertained separately. The method of dimensional analysis can thus be used for : checking the validity of physical equations and obtaining the powers of different physical quantities in a physical relation if the physical quantities involved are identified by some intelligent guess. Table below gives dimensions of some quantities in use most often. Dimensional Formulae of physical Quantities and their SI units