IMAT Physics · Free notes

Measurement and Units: SI, Dimensions and Vectors

Measurement and Units has 5 past questions since 2011, and the ministry papers from 2023 on have asked none of them.The skills still matter, because every physics calculation on the paper hides a unit conversion or a power of ten. The older papers asked which expressions share a unit, which quantity is a vector, and how to order sizes written with different prefixes. The difficulty sits in breaking a derived unit into kilograms, metres and seconds, and in squaring or cubing a prefix correctly.

The handout has every subtopic, worked example, formula and trap with answers shown. The formula sheet is the chapter’s formulas and traps alone, on one page.

IMAT home All formulas on one page

Subtopic notes

Formula & revision sheet

3 formulas · 2 reference tables · 8 gotchas across all subtopics — the exam-eve cheat-sheet

SI Units, Prefixes and Significant Figures

Formulas (1)

Prefixes, powers of ten and scientific notation · Changing a prefix $1\ \text{nm} = 10^{-9}\ \text{m} = 10^{-3}\ \mu\text{m} = 10^{3}\ \text{pm}$

Reference tables (1)

SI base units and the common derived units14 rows

Quantity	Unit	Symbol	In SI base units
Length	metre	m	base unit
Mass	kilogram	kg	base unit
Time	second	s	base unit
Electric current	ampere	A	base unit
Temperature	kelvin	K	base unit
Amount of substance	mole	mol	base unit
Force	newton	N	$\text{kg m s}^{-2}$
Energy, work	joule	J = N m	$\text{kg m}^2\text{ s}^{-2}$
Power	watt	W = J/s	$\text{kg m}^2\text{ s}^{-3}$
Pressure	pascal	Pa = N/m²	$\text{kg m}^{-1}\text{ s}^{-2}$
Charge	coulomb	C = A s	$\text{A s}$
Potential difference	volt	V = J/C	$\text{kg m}^2\text{ s}^{-3}\text{ A}^{-1}$
Resistance	ohm	Ω = V/A	$\text{kg m}^2\text{ s}^{-3}\text{ A}^{-2}$
Frequency	hertz	Hz	$\text{s}^{-1}$

The last column is what you reach when you break a derived unit all the way down.

Watch out for (4)

The base unit of mass is the kilogram
→ SI base units and the common derived units
A prefix on a squared or cubed unit is raised to that power
→ Prefixes, powers of ten and scientific notation
Milli and micro are a thousand apart
→ Prefixes, powers of ten and scientific notation
Leading zeros are not significant
→ Significant figures and rounding a result

Dimensional Analysis, Scalars and Vectors

Formulas (2)

Dimensional analysis: checking units in an equation · Working a unit down to base units $\text{J} = \text{N m} = (\text{kg m s}^{-2})(\text{m}) = \text{kg m}^2\,\text{s}^{-2}$
Adding vectors and splitting them into components · Components and the resultant $F_x = F\cos\theta, \quad F_y = F\sin\theta, \quad R = \sqrt{F_x^2 + F_y^2}$

Reference tables (1)

Scalars and vectors: which quantities have a direction14 rows

Quantity	Scalar or vector	Note
Distance	scalar	length of the path travelled
Displacement	vector	straight-line change of position
Speed	scalar	distance per unit time
Velocity	vector	displacement per unit time
Acceleration	vector	change of velocity per unit time
Mass	scalar	amount of matter
Weight, any force	vector	weight points towards the centre of the Earth
Momentum	vector	same direction as the velocity
Energy, work, power	scalar	no direction, even though forces cause them
Pressure	scalar	the force it makes on a surface is a vector
Temperature	scalar	a minus sign is not a direction
Electric charge	scalar	positive or negative, never a direction
Electric field	vector	direction of the force on a positive charge
Electric current	scalar	currents at a junction add as numbers

Watch out for (4)

Consistent units do not prove an equation is right
→ Dimensional analysis: checking units in an equation
A resistance and its reciprocal cannot be added
→ Dimensional analysis: checking units in an equation
Mass is a scalar, weight is a vector
→ Scalars and vectors: which quantities have a direction
Vector sizes add only when the vectors are parallel
→ Adding vectors and splitting them into components

PYQ weightage by concept

6 concepts · 0 PYQs — where the marks actually sit, so you know what to drill first

SI Units, Prefixes and Significant Figures0 PYQs · 0%

Concept	PYQs	Share
SI base units and the common derived unitsfoundation	—	—
Prefixes, powers of ten and scientific notationfoundation	—	—
Significant figures and rounding a resultfoundation	—	—

Dimensional Analysis, Scalars and Vectors0 PYQs · 0%

Concept	PYQs	Share
Dimensional analysis: checking units in an equationfoundation	—	—
Scalars and vectors: which quantities have a directionfoundation	—	—
Adding vectors and splitting them into componentsfoundation	—	—