All measurements in physics, even of such things as density,
are related to the three chosen fundamental quantities of
length,mass, and time.until about the year 1800 ,workers in
various countries used different systems of units. Thus ,while the
English used inches, a continental scientist would measure
lengths in centimeters. Fortunately, this situation has now
changed by the efforts of various international committees of
scientists who have met for discussion regularly over many
When we measure something ,we are
determining its size or magnitude.
To carry out any measurement we need to
1.the quantity being measured.
2.the unit for measuring it.
In 1960 ,scientist agreed on one international
system of units to be used, International System
of Units ,shortened to SI units ,in all languages.
There are seven basic physical quantities and
units from which other quantities can be derived.
The seven basic quantities ,their symbols and SI
units are given in Table 1.1 below.
Other quantities can be formed from these
quantities for example;area ,volume
,density,acceleration and charge. These quantities
are called derived physical quantities.
Length is a measure of distance between two
points. Breadth ,width,height,radius,depth and
diameter are all lengths. THE SI unit of length is
Example : convert the following;
a)1000 km into m
b)270 Hm into dm
c)100 m into mm
d)100 mm into Hm
Measurement of Length
Length can be determined by estimation or
accurately by using a measuring instrument.
There are various instruments for measuring
length. Some instruments used to measure
length are metre rule and tape-measure.
They are graduated in centimetres and
When using a metre rule:
•Place the metre rule in contact with the object
•Place the end of the object against the zero mark on the scale.
•Position your eye perpendicularly above the scale.
Figure shows the inaccurate use of the rule. The arrangement will
not give us affair result because:
•The rule is not in contact with the object.
•The object is not aligned to the zero mark on the scale
•The position of eye is not perpendicular to the scale.
What are the readings indicated by arrows P1,
P2, and P3 on the metre rule in figure 2.3?
(Diagram not to scale)
There are several types of the tape
measures,ie:tailor`s carpenter`s and surveyor`s
types. The choice of tape measure is determined
by the nature of the distance to be measured.
Always ensure that the tape measure is taut
Measurement of Curved Length
Curved lengths such as roads and railways
lines on a map or dimensions of some containers
can be measured using a thread. For curved
surfaces such as a cylinder,a thread is closely
wrapped around the surface a number of times.
To measure the circumference of a cylinder
using a cylinder using a thread.
•Measure the length between the ink marks and call it a1 . repeat three
times, recording the readings as a2 and a3 to ensure accuracy of your measurement.
Find the average length a;
Divide the average length by 10 to find the
length of one turn. This gives the circumference
of the cylinder. Thus;
Estimation of Length
One may to wish to know which of several
objects is the largest. This could be established
by comparing the sizes of the object directly. At
times ,it is better to compare all of them with
that of a chosen basic length called a standard
The estimation of sizes of various objects such
as the height of tree,flagpost or the length of
rope possible by comparing with standard
To estimate the height of tree
The height of the tree is estimated from the relation:
Hamad found that the width of her desk was
approximately 10 palm-lengths. If his palm was
15.0 cm long ,what was the width of her desk in
Area refers to the measure of surface.It is
derived quantity of length.The SI unit of area is
the square metre,written as m2 .It can also be
measured in multiples and sub-multiples of
m2,for example ; cm2 and km2
Measurement of Area
Area of regularly-shaped objects
The area of regularly-shaped surfaces such as
rectangles,triangles and circles can be obtained
by applying the appropriate formula.
AREA=length x width
A=l x w
Area of irregularly-shaped surfaces
The area of an irregular shaped surface can be
estimated by dividing it into smaller regular
shapes for example squares whose sides are 1
cm in length.
A=no. of complete squares+1/2 (no. of
Calculate the area of the trapezium above:
Volume is the amount of space occupied by
The SI unit of volume is the cubic metre(m3).
1 m3=1m x 1m x 1m
= 100 cm x 100 cm x 100 cm
= 1000 000 cm3
Other units like litres (l) and millilitres (ml) are also
1m3=1000 000 cm3
Volume of Regularly-Shaped Solids
The volume of regularly-shaped solids can be
obtained by applying the appropriate formula.
Volume = area of cross-section x height
Volume = area of cross-section x height
=(∏ r2 ) h
= ∏ r2 h
Volume = area of cross-section x length
Homework Exercise 2.4
Measurement of Volume of
Liquids have no definite shape, but
assume the shapes of the containers in
which they are put.
One of the methods which can be used to
measure the volume of a liquid is to pour the
liquid into a container with a uniform cross-
section ,as shown in figure 2.8.
The height of the liquid,h is
measured.The volume of the liquid is then
obtained by applying the formula;
The graph of V against h is the a
straight line,indicating that height
increases with the increase of volume V.
Measuring devices which are marked off
like this are called measuring cylinders.
They are used to measure volumes of
Measuring cylinders are made of glass
or transparent plastic and graduated in
cm3 or ml.
1.The scale of the burette begins from zero at
the top and increases downwards to the
2.The reading of volume is taken with the eye
positioned in level with the bottom of the
meniscus,see figure 2.11.
Measuring the Volume of an
Volumes of irregular solids are
measured using the displacement
method.The method works with solids
that are not soluble in water, do not
absorb water, do not react with water and
sink in water.
EXP.2.5:To determine the volume of
an irregularly-shaped object
a)Using a measuring cylinder
Apparatus:Measuring cylinder,stone,thread and
Result: the volume of the stone V=V2-V1
b) Using Eureka can
A eureka or displacement can is a
container with a spout from the side.It is
used to measure volumes by
displacement method.It is also known as
an overflow can.
Result: The volume of water collected in the
measuring cylinder is the volume of the object.
EXP.2.6: To determine the volume of
an object that floats on water
using the displacement can
Apparatus : Eureka can,measuring
cylinder,floating object and a sinker(small metal
When finding the volume of an
object that floats on water,e.g.,a
cork, another object that sinks in
water is attached to it so that both
are totally submerged. This object is
known as a sinker.
The water collected in the
measuring cylinder is the volume of
sinker and cork. Call it V2.so, the
volume of the cork V=V2-V1
HOMEWORK: EXERCISE 2.5
The mass of an object is the
quantity of matter in it.Matter is
anything that occupies space.The
mass of an object depends on its
size and the number of particles it
The SI unit of mass is the
kilogram(symbol kg).The commonly used
sub-multiples and multiples of kilogram
are given table 2.6.
The mass of an object is the
same everywhere because the
number of particles in an object
Measurement of Mass
There are two common types
of balances for measuring
mass,namely,the electrical and
the mechanical types.
HOMEWORK: EXERCISE 2.6
The density of a substance is defined as its
mass per unit volume.Its symbol is rho(p) and
its SI unit is kilogram per cubic metre
(kg/m3).Another commonly used unit is gram
per cubic centimetre(g/cm3).
From definition, the density of a substance is
Measurement of Density
To measure the Density of a Solid
The density of the object is then calculated
from the formula:
Exp 2.8: To find the density of a
Apparatus : clean dry beaker, balance,
measuring cylinder, a burette or a pipette.
A density bottle is a small glass bottle fitted
with glass stopper which has a hole through
which excess liquid flows out.
Normally, the density bottle has its capacity
indicated on the side.
To find the density of a liquid
using a density bottle
Measure the mass m1 of a clean dry density
bottle with its stopper.
Fill the bottle with liquid and replace the
Dry the bottle on the outside.
Measure the mass m2 of the bottle plus the
If the capacity of be is V, then
Density of liquid= (m2-m1)/V
Exp :2.10: to measure the density
of a solid using a density bottle
This method is used for solids in form of
grains,beads or turnings.
1.Measure the mass m1 of a clean dry empty
2. Fill the bottle with lead shot and measure
the mass m2.
3. Fill up the bottle with water up to the neck
and measure its mass m3.
4. Empty the bottle and rinse it.
5. Fill it with water and replace the stopper .
Wipe the outside dry and measure the mass m4
of the bottle filled with water.
mass of water = (m4-m1) g
Volume of water =m4-m1(density of water is 1g/cm3)
Volume of bottle =(m4-m1) cm3
Mass of lead shot =(m2-m1)g
Mass of water present when bottle is filled with lead shot
and water = (m3-m2)g
Volume of water =(m3-m2)cm3
Volume of lead shot =(m4-m1)-(m3-m2)
It should be noted that this method is
unsuitable for solids which are either soluble in
water or react with it.
Densities of mixtures
A mixture is obtained by putting together two
or more substances such they do not react with
one another. It is assumed that the volume of
the mixture is equal to the sum of the volumes
of the individual constituents.
Time is a measure of duration of an event. The
SI unit of time is second(s).
Multiple and Sub-multiple units of the second
Microsecond µs 0.000001 seconds
Millisecond ms 0.001 seconds
Minute min 60 seconds
Hour hr 3600 seconds
Day day 86400 seconds
Week wk 604800 seconds
Measurement of Time
In laboratories ,intervals of time are measured
using either a stopwatch or stop-clock,depending
on the accuracy required.