Physical Quantities and Measurements

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A physical quantity is a measurable property that can be expressed using a numerical value and a standard unit. Length, mass, time, temperature, volume and density are physical quantities because instruments can measure them. A non-physical quantity cannot be measured directly with scientific instruments or expressed using a standard unit. Love, affection, fear, wisdom and beauty are non-physical quantities because their description depends mainly on human perception or interpretation. Physics is based on physical quantities because scientific laws require measurable and reproducible data.

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Base physical quantities are independently selected fundamental quantities that are not defined in terms of other quantities. Their corresponding units are called base units. The seven SI base quantities are length, mass, time, temperature, electric current, luminous intensity and amount of substance. Derived physical quantities are obtained by combining base quantities mathematically. Their units are derived from base units. For example, area is length multiplied by breadth and has unit m², while speed is distance divided by time and has unit m s^-1.

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Measurement is the comparison of an unknown physical quantity with an accepted standard quantity of the same kind. A measurement has two essential parts: a numerical value and a unit. In the past, people used hand spans, feet, arms and steps, but these produced different results because body sizes vary. Standard units were introduced so that measurements made by different people and countries would have the same meaning. Standardization supports accurate trade, scientific communication, experimentation and comparison of results.

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The International System of Units, abbreviated SI, is an internationally accepted system recommended for uniform measurement. It allows scientists around the world to record and compare results without confusion. Its seven base quantities and units are: length - metre (m), mass - kilogram (kg), time - second (s), temperature - kelvin (K), electric current - ampere (A), luminous intensity - candela (cd), and amount of substance - mole (mol). Derived units such as newton, pascal and coulomb are expressed using these base units.

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Derived units are units expressed in terms of SI base units. Area is calculated as length multiplied by breadth. Since both quantities are measured in metres, the unit of area is m x m = m². Speed is calculated as distance divided by time. Distance is measured in metres and time in seconds, so the unit of speed is m/s or m s^-1. This shows that derived units are formed by mathematical combinations of base units.

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SI prefixes are names or symbols placed before SI units to represent powers of ten. They make very large and very small measurements convenient to write and understand. Multiples include kilo (10³), mega (10⁶) and giga (10⁹). Submultiples include milli (10^-3), micro (10^-6) and nano (10^-9). For example, 5000 m is written as 5 km, 0.002 s as 2 ms, and the thickness of a thin wire may be written in millimetres. Prefix symbols must be written directly before unit symbols without spaces.

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Scientific notation expresses a number as a value from 1 to less than 10 multiplied by an integer power of ten. For a large number, move the decimal point left until one non-zero digit remains before it; the number of places moved becomes a positive exponent. Thus 138000000 becomes 1.38 x 10⁸. For a small number, move the decimal point right until one non-zero digit remains before it; the number of places moved becomes a negative exponent. Thus 0.0000052 becomes 5.2 x 10^-6. Scientific notation saves space and simplifies calculations.

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For addition and subtraction, first express all quantities with the same power of ten. Then add or subtract their numerical coefficients and normalize the final result. For multiplication, multiply the coefficients and add the exponents. For example, (2 x 10³)(4 x 10²) = 8 x 10⁵. For division, divide the coefficients and subtract the exponent of the denominator from that of the numerator. For example, (8 x 10⁶)/(2 x 10²) = 4 x 10⁴. The final coefficient should normally lie between 1 and 10.

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An SI unit is represented by a symbol, not an abbreviation. For example, second is written s, not sec. Symbols do not take plural forms, so 10 kg and 5 s are correct. Unit names normally begin with lowercase letters, while symbols of units named after scientists begin with capitals, such as N for newton and Pa for pascal. Prefixes are written immediately before unit symbols, such as mm and mN. Compound prefixes are not allowed. Units multiplied together should be written with suitable spacing or notation.

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A metre rule is commonly used in laboratories to measure lengths up to one metre. Its smallest division is 1 mm, so its least count is 1 mm. The zero mark should coincide with one edge of the object and the position of the other edge gives the length. The eye must be directly above the reading to prevent parallax error. A measuring tape also has a least count of about 1 mm but can measure lengths from millimetres to several metres. It is suitable for longer, curved or large objects.