A physical quantity is any quantity that can be measured, and every measurement has two parts: a numerical magnitude telling you how much, and a unit telling you of what. This topic covers the six SI base units, prefixes and standard form, choosing and reading measuring instruments, timing a pendulum, and the difference between scalars and vectors.
It underpins every calculation in the course, from speed in Kinematics to power in Current of Electricity. Examiners penalise missing or wrong units in every topic, so the habits built here earn or lose marks all year.
What these notes cover
- •Physical quantities and SI base units
- •Derived units
- •Prefixes from nano to tera
- •Standard form and prefix conversion
- •Converting area and volume units
- •Orders of magnitude and estimation
- •Choosing instruments: range and precision
- •Zero error on digital instruments
- •Human reaction time and timing a pendulum
- •Scalars and vectors
- •Adding vectors by scale drawing
- •Common mistakes and exam technique
Key definitions
- Physical quantity
- Any quantity that can be measured. It consists of a numerical magnitude and a unit.
- Order of magnitude
- The value of a quantity rounded to the nearest power of ten, e.g. a person of height 1.7 m has height of order 10⁰ m.
- Precision of an instrument
- The smallest division the instrument can read, e.g. 0.1 cm for a metre rule and 0.001 mm for a digital micrometer.
- Period of a pendulum
- The time for one complete oscillation — one full swing there and back.
- Vector quantity
- A quantity with both magnitude and direction, such as displacement, velocity, acceleration, force and weight. A scalar quantity has magnitude only.
Key formulas
Physical quantity
quantity = numerical magnitude × unit
The number gives the size of the measurement; the unit states what it is counted in. A final answer without its unit is usually awarded zero for that answer mark.
Standard form
a × 10ⁿ, where 1 ≤ a < 10 and n is an integer
Large numbers get positive powers and small numbers get negative powers, e.g. 52 000 = 5.2 × 10⁴ and 0.0047 = 4.7 × 10⁻³.
Area and volume conversions
1 cm² = (10⁻² m)² = 10⁻⁴ m²; 1 m² = 10⁴ cm²; 1 m³ = 10⁶ cm³
The prefix is squared (or cubed) along with the unit: divide cm² by 10⁴ to get m², and cm³ by 10⁶ to get m³.
Zero-error correction
actual value = measured reading − zero error
Read the zero error by closing the jaws fully with nothing between them. Subtracting a negative zero error makes the answer bigger.
Period from repeated timing
T = t ÷ N
T is the period, t is the total time measured for N complete oscillations (at least 20).
Resultant of perpendicular vectors
R = √(F₁² + F₂²)
A checking tool for a scale drawing, valid only when the two vectors are at right angles. The angle to F₁ is tan⁻¹(F₂ ÷ F₁).
Worked example
Two forces act on a ring: 5.0 N horizontally to the right and 12.0 N vertically downward. Find the resultant force by scale drawing, and check your answer by calculation.
- 1Choose and state the scale: 1 cm represents 2 N.
- 2Draw a horizontal arrow 2.5 cm long to the right to represent 5.0 N.
- 3From the tip of that arrow, draw a vertical arrow 6.0 cm long downward to represent 12.0 N.
- 4Join the tail of the first arrow to the tip of the second; this resultant measures 6.5 cm, and the protractor gives 67° between the resultant and the horizontal.
- 5Convert using the scale: R = 6.5 × 2 = 13.0 N.
- 6Check by calculation, valid because the forces are perpendicular: R = √(5.0² + 12.0²) = √(25 + 144) = √169 = 13.0 N.
- 7Check the angle: θ = tan⁻¹(12.0 ÷ 5.0) = 67.4°.
- 8Answer: the resultant force is 13.0 N, directed at 67° below the horizontal, to the right.
Watch out: Drawing the resultant the wrong way round, from the tip of the second arrow back to the start, gives a vector in exactly the opposite direction. A force is a vector, so both magnitude and direction must be stated.
Common mistakes
Taking the gram as the SI base unit of mass
Wrong: Mass is measured in grams, so the gram is the base unit.
Right: The SI base unit of mass is the kilogram (kg), the only base unit whose name already carries a prefix. Convert grams to kg before substituting into any formula.
Not squaring the conversion factor for areas
Wrong: 1 m = 100 cm, so 1 m² = 100 cm².
Right: Area is length × length, so 1 m² = 100 × 100 = 10⁴ cm². For volume the factor appears three times: 1 m³ = 10⁶ cm³.
Timing a single oscillation
Wrong: Starting and stopping the stopwatch for one swing of a pendulum.
Right: Human reaction time of about 0.2 s to 0.3 s can make a single timing wrong by 20% or more. Time many oscillations (typically 20), divide the total time by the number of oscillations, then repeat and average.
Questions students ask
What are the six SI base quantities and their units?
Mass in kilograms (kg), length in metres (m), time in seconds (s), electric current in amperes (A), thermodynamic temperature in kelvin (K) and amount of substance in moles (mol). The base unit of mass is the kilogram, not the gram, and kelvin is written without a degree sign.
How do you convert cm² to m²?
Square the prefix along with the unit: 1 cm² = (10⁻² m)² = 10⁻⁴ m², so divide an area in cm² by 10⁴ to get m². For volumes, divide cm³ by 10⁶ to get m³. Dividing by 100 is the common slip that loses marks in density and pressure calculations.
Why do you time 20 oscillations of a pendulum instead of one?
Starting and stopping the stopwatch introduces human reaction time, which is a random error of roughly fixed size. Timing 20 oscillations and dividing by 20 spreads that error over many oscillations, reducing its effect on the calculated period. Repeating the timing and averaging reduces the random error further.
What is the difference between mass and weight?
Mass is the amount of matter in a body, measured in kg; it is a scalar and is the same everywhere. Weight is the gravitational force acting on that mass, W = mg, measured in N; it is a vector pointing downward and changes when g changes.
In the full PDF
- •The full prefix ladder from nano to tera, with a memory hook for each prefix
- •The instruments table covering precision and reading tips, from the metre rule to the voltmeter
- •Diagrams: the order-of-magnitude ladder, one complete pendulum oscillation with a fiducial marker, and tip-to-tail vector additions
- •Further worked examples on prefix conversion, area conversion, zero error and pendulum timing
- •The remaining five common mistakes, including capital K vs small k, centi vs milli and the heavier-bob myth
- •Exam technique checklist, a full-mark model answer on timing, and the end-of-topic summary