Chapter 1: Physical Quantities
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1.1 What is a Physical Quantity?
Physics is the branch of science that studies matter, energy, and the interaction between them, and it does so by measurement. Any property of a body, substance, or phenomenon that can be measured and expressed in the form of a number accompanied by a unit is called a physical quantity. Length, mass, time, temperature, electric current, force, energy, and velocity are all physical quantities because each of them can be measured with a suitable instrument and expressed as a numerical value multiplied by a chosen unit. For example, when we say the length of a table is 2 metres, the number "2" is called the magnitude and "metre" is the unit. A physical quantity is therefore always expressed as: Physical Quantity = Magnitude × Unit. Qualities that cannot be measured numerically, such as beauty, honesty, or intelligence, are not physical quantities because there is no standard, universally agreed unit or instrument to measure them.
Physical quantities are broadly classified in two useful ways for exam purposes. The first classification is based on whether a quantity has direction associated with it: scalar quantities (such as mass, distance, speed, work, and energy) are completely described by a magnitude and a unit alone, whereas vector quantities (such as displacement, velocity, acceleration, force, and momentum) require both magnitude and direction to be completely specified. The second, and more important classification for this chapter, is based on whether the quantity is independent of other quantities or is derived from other quantities — this gives us fundamental (base) quantities and derived quantities.
1.2 Fundamental (Base) Quantities
A fundamental or base physical quantity is one that is independent of all other physical quantities — it cannot be expressed in terms of any other quantity, and it is not defined in terms of any other quantity. Historically, different sets of fundamental quantities were used by different systems of measurement, but the internationally accepted modern system — the SI (Système International d'Unités, or International System of Units) — recognises exactly seven fundamental (base) quantities. These are: length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity. Every other physical quantity used in science and engineering can be expressed as a combination (product, quotient, or power) of these seven base quantities. In addition to the seven base quantities, SI also recognises two supplementary (dimensionless) quantities: plane angle (measured in radian) and solid angle (measured in steradian), which are used to describe angular measurements without introducing a new independent dimension.
1.3 Derived Quantities
A derived physical quantity is one that is obtained by combining two or more fundamental quantities through multiplication, division, or the use of powers, according to a definite physical relationship. For example, speed is defined as the distance travelled per unit time, so its unit (metre per second) is derived by dividing the unit of length by the unit of time. Similarly, force, according to Newton's second law, equals mass multiplied by acceleration, and acceleration itself is velocity divided by time; hence force is a derived quantity built up from the base quantities mass, length, and time. The vast majority of physical quantities encountered in mechanics, heat, electricity, magnetism, optics, and modern physics — including area, volume, density, velocity, acceleration, momentum, force, work, energy, power, pressure, electric charge, potential difference, resistance, and magnetic flux — are derived quantities. Only the seven base quantities of SI are fundamental; every other named physical quantity, no matter how important, is derived from them.
Quick comparison: Fundamental vs Derived Quantities
Feature | Fundamental (Base) Quantity | Derived Quantity |
|---|---|---|
Definition | Independent; not defined using other quantities | Obtained by combining base quantities |
Number in SI | Exactly 7 (plus 2 supplementary) | Unlimited — as many as physical relations exist |
Examples | Length, mass, time, current, temperature, amount of substance, luminous intensity | Speed, force, work, power, pressure, density, charge |
Units | Base units (metre, kilogram, second, ampere, kelvin, mole, candela) | Derived units (formed from base units, e.g. newton, joule) |
A useful exam tip: whenever a question asks you to identify whether a quantity is fundamental or derived, check whether it appears in the list of the seven SI base quantities (length, mass, time, electric current, temperature, amount of substance, luminous intensity). If it does not appear in that list, it is derived, however basic it might feel — for instance, area, volume, and even angle are derived (or supplementary), not fundamental, even though they seem elementary.