1.1 - Physical Quantities

Measurement, Magnitude and Units

Measurement determines the value of a physical quantity. Physical quantities comprise base quantities and derived quantities.
State a physical quantity with its magnitude and unit. In length = 100 m, length is the quantity, 100 is the magnitude and m is the unit.
Accurate measurements help in making correct decisions.
Measurement examples: Mount Kinabalu has a height of 4 095 m; a tiger has a speed of $49$ – $65 km h^{- 1}$ ; Mohamad Ridzuan Puzi recorded 11.87 s in the 100 m sprint (T36 category) at the 2018 Asian Para Games.
Frequency, impulse, power and specific heat capacity are also derived quantities.
Metric units include centimetre and kilopascal; imperial units include inch, psi (pounds per square inch), gallon, mile, foot and yard. Imperial and metric units can be converted into one another. Metric units are more commonly used today.
In 1999, inconsistent use of imperial and metric units caused measurement-data errors in the Mars Climate Orbiter mission and its crash onto Mars.

A base quantity cannot be derived from another physical quantity.
The International System of Units (S.I.) standardises measurement units. It was agreed upon at the 11th General Conference on Weights and Measures in Paris in 1960. Standard units facilitate science, sports, trade and medicine.

Base quantity and symbol	S.I. unit and symbol
Length, $l$	metre, m
Mass, $m$	kilogram, kg
Time, $t$	second, s
Thermodynamic temperature, $T$	kelvin, K
Electric current, $I$	ampere, A
Luminous intensity, $I_{v}$	candela, cd
Amount of substance, $n$	mole, mol

Amount of substance is normally used in Chemistry for the quantity of an element or compound.

A derived quantity can be expressed in terms of base quantities through a formula. Its unit follows from the same combination of base units.
Substitute base quantities into the formula, simplify, then replace them with their S.I. units.
For example, density $ρ = m / V$ . Using $V = l^{3}$ gives $ρ = m / l^{3}$ , hence the unit $kg m^{- 3}$ .
The expressions below show how the quantities are formed from base quantities; $l$ denotes length and $t$ denotes time.

Derived quantity and formula	Expression in base quantities; S.I. unit
Area, $A = l^{2}$	$l^{2}$ ; $m^{2}$
Volume, $V = l^{3}$	$l^{3}$ ; $m^{3}$
Density, $ρ = m / V$	$m / l^{3}$ ; $kg m^{- 3}$
Velocity, $v = l / t$	$l / t$ ; $m s^{- 1}$
Acceleration, $a = v / t$	$l / t^{2}$ ; $m s^{- 2}$
Force, $F = ma$	$m l / t^{2}$ ; $kg m s^{- 2}$ = newton (N)
Momentum, $p = m v$	$m l / t$ ; $kg m s^{- 1}$
Pressure, $P = F / A$	$m / (l t^{2})$ ; $kg m^{- 1} s^{- 2}$ = pascal (Pa)
Energy or work, $W = Fl$	$m l^{2} / t^{2}$ ; $kg m^{2} s^{- 2}$ = joule (J)
Charge, $Q = I t$	$I t$ ; $A s$ = coulomb (C)

Metrology studies measurements and standards. Scientists use advanced measurement technology to establish base-unit standards.
In Malaysia, SIRIM is responsible for preparing measurement standards.

Classification	Meaning and examples
Scalar quantity	Has magnitude only: distance, area, length, work, temperature, time, volume, speed, energy and density.
Vector quantity	Has magnitude and direction: displacement, velocity, force, acceleration and momentum.

A distance of 50 m specifies magnitude. Adding towards a particular tree also specifies a direction, illustrating the additional information needed for a vector.