Physical Quantities

Base Quantity

Physical Quantities	SI Unit	Symbol	Derived Quantity		derived SI units
length	metre	m	m	area	$\text{m}^2$
mass	kilogram	kg	kg	volume	$\text{m}^3$
time	seconds	s	s	speed	$\text{m/s}$
current	ampere	A	A	force	$\text{N}$
temperature	kelvin	K	K	pressure	$\text{N/m}^2$
luminous intensity	candela	cd	cd	power	$\text{W}$
amount of substance	mole	mol	mol	density	$\text{kg/m}^3$

Submultiples	<	<	Multiples	<	<
Factor	Prefix	Symbol	Factor	Prefix	Symbol
$10^{-1}$	deci-	d	$10^1$	deca-	da
$10^{-2}$	centi-	c	$10^2$	hecto-	h
$10^{-3}$	milli-	m	$10^3$	kilo-	k
$10^{-6}$	micro-	$\mu$	$10^6$	mega-	M
$10^{-9}$	nano-	n	$10^9$	giga-	G
$10^{-12}$	pico-	p	$10^{12}$	tera-	T
$10^{-15}$	femto-	f	$10^{15}$	peta-	P
$10^{-18}$	atto-	a	$10^{18}$	exa-	E

systematic	random
mistakes in experimental design	unavoidable but can me minimised
zero error / constant parallax error	larger sample size / take average of readings

zero error of the vernier calipers / micrometer used
end error of metre rule
parallax error in the measurement if observer consistently reads from the same wrong position
human reaction time if the observer consistently stops 1 s before pendulum reaches fiducial line

random errors are inherent in the measurement.

varying human reaction time which affects the measurement of timing for the determination of the period
energy transferred to the environment which affects the measurement of temp. of water
parallax error in determining the alignment of pins which affects the measurement of the angle of refraction

measuring tape / metre rule

parallax error
- position eyes vertically above the reading of the scale ⇒ line of sight is perpendicular to the rule
- place the rule such that its scale at the edge is touching / as close to the object to be measured
- use a thin ruler so that the scale at the edge is touching the object.
end error
- do not use the ends of the rule for any measurements. ⇒ avoid end errors (can occur due to wear and tear of the rule) digital caliper + micrometer
application of excessive measuring force → jaws tilt
thermal expansion ← temperature difference between caliper + object
abbe error (caliper only) — axis of the instrument and the axis along which the object is measured is not aligned

the line of best fit has an equal number of readings on both sides
⇒ cancelling out the errors which cause over– and underestimation of the true value
⇒ reducing the effect of the errors on trends

Sf indicate the precision of a measurement. The more significant figures a number has, the more precise the measurement is.

Rule	Example	Number of s.f.
Non-zero digits are always significant.	2.3	2
Zeros after a decimal point (trailing zeros) are always significant.	0.500	3
Zeros between 2 s.f. (sandwiched zeros) are always significant.	7.06	3
Zeros before a non-zero digit (leading zeros) are not significant.	0.003	1

Multiplication/Division
- Round final answer to the lowest number of significant figures found in any of the original numbers used in the calculation $4.56 (\text{3 s.f.}) × 1.4 (\text{2 s.f.}) = 6.4(\text{to 2 s.f.})$
Addition/subtration
- Round final answer to the lowest number of decimal places found in the original numbers $12.11 (\text{2 d.p.}) + 18.0 (\text{1 d.p.}) + 1.013 \text{(3 d.p.)} = 31.1\text{(to 3d.p.)}$
Intermediate working is always to +1 sf/dp