IGCSE PHYSICS COURSE
Physical quantities and measurement techniques
Why is it important to have a common language in physics?
Scientists need a shared language to communicate between themselves and with the wider public.
Part of this language involves agreeing the terms for physical Quantities and the units used to specify
data.
What is a physical quantity?
A physical quantity is a property of an object that can be measured with a measuring instrument.
A physical quantity is usually expressed as “a magnitude (numerical value) and an SI unit or more”
For example, if you are told that your journey to school has a value of 5000 then you need to know
whether this is measured in metres (originally a European measure) or feet (an Old Icelandic length
measure).
The agreed set of units and rules is known as the Système Internationale d'Unités (almost always
abbreviated as SI). In this system, seven fundamental (base) units are defined and all other units are
derived from these. You are required to use the first three of the seven fundamental (basic) units; the
seventh is the unit of luminous intensity, the Candela that is not used in this physics course.
Derived Physical quantities
These as the name suggests are taken(formed) from combining the basic physical quantities. For
example density is formed by dividing the mass by volume. The SI units used are called derived SI
units.
Prefixes
In Physics, prefixes are words placed before quantities to modify their meaning. For example, when
we refer to 'sub-zero temperatures' on a snowy day, the prefix 'sub' meaning 'lower than', we are
describing temperatures lower than zero
Examples:
•1MJ means………..1 mega Joule
or
1×106J
= 1,000,000J
•1dm means………..1 decimetre
or
1×10-1m
=
•1nm means………..1 nanometre
or
1×10-9m
= 0.000,000,001m
•1GW means……….1 Gigawatt
or
1×109W
= 1,000,000,000W
0.1m
Activity 1.0
Convert the following figures with prefixes to the actual values.
a) 100cm to m
b) 200mm to m
c) 7800µm to m
d) 10km to m
e) 80ms to s
Powers of ten shorthand or standard notation
This is a neat way of writing numbers, especially if they are large or small. The example below shows how
it works
The small figures 1, 2, 3, etc., are called powers of ten. The power shows how many times the number
has to be multiplied by 10 if the power is greater than 0 or divided by 10 if the power is less than 0. Note
that 1 is written as 100.
This way of writing numbers is called standard notation.
The format is A x 10n
Where
A is a number less than 10 but greater than or equal to 1: n is a whole number
Activity 1.1
Write the following numbers in standard notation
a) 3.5 x 104
d) 975000
b) 700
e) 0.0000000756
c) 0.0095
f) 1.0
Significant figures
Every measurement of a quantity is an attempt to find its true value and is subject to errors arising from
limitations of the apparatus and the experimenter. The number of figures, called significant figures, given for
a measurement indicates how accurate we think it is and more figures should not be given than is justified.
For example, a value of 4.5 for a measurement has two significant figures; 0.0385 has three significant figures,
3 being the most significant and 5 the least, i.e. it is the one we are least sure about since it might be 4 or it
might be 6. Perhaps it had to be estimated by the experimenter because the reading was between
two marks on a scale.
When doing a calculation your answer should have the same number of significant figures as the
measurements used in the calculation. For example, if your calculator gave an answer of 3.4185062, this
would be written as 3.4 if the measurements had two significant figures. It would be written as 3.42
for three significant figures. Note that in deciding the least significant figure you look at the next figure
to the right.
If it is less than 5 you leave the least significant figure as it is (hence 3.41 becomes 3.4) but if it equals or is
greater than 5 you increase the least significant figure by 1 (hence 3.418 becomes 3.42).
If a number is expressed in standard notation, the number of significant figures is the number of
digits before the power of ten. For example, 2.73 × 10^3 has three significant figures.
Average values in measurements
To minimize the errors in a measured quantity due to systemic or random errors an average of the
measurements is used. To get an average value for example of length L two or three measurements
are carried out. Then the sum of these measurements is divided by the number of measurements.
Average Length = Sum of measured values / number of measurements
Average length = (L1 + L2 + L3) / 3
Example
Calculate the average of the following values.
890, 900, 910, 875, 888, 925, 900, 889, 898
Activity 1.2
Calculate the average values for the following measurements:
a) Time:
t1 = 0.70s, t2 = 0.68s,
b) Mass:
m1 = 67.45kg,
c) Voltage:
v1 = 1.45v,
t3 = 0.71s,
m2 = 67.59kg,
v2 = 1.36v,
t4 = 0.695s
m3 = 66.99kg,
v3 = 1.52v
m4 = 67.98kg
Length
The unit of length is the metre (m) and is the distance travelled by light in a vacuum during a
specific time interval. At one time it was the distance between two marks on a certain metal bar.
Many length measurements are made with rulers; the correct way to read one is shown in the
diagram below. The reading is 76 mm or 7.6 cm. Your eye must be directly over the mark on the
scale or the thickness of the ruler causes a parallax error.
Using the Vernier Calipers & Micrometer Screw Gauge
The vernier calipers
The vernier calipers found in the laboratory incorporates a main scale and a sliding vernier scale
which allows readings to the nearest 0.01mm, 0.02 mm or 0.5mm depending on the type. This
instrument may be used to measure outer
dimensions of objects (using the main jaws), inside dimensions (using the smaller jaws at the top),
and
depths (using the stem).
Follow the link to the Vernier caliper
https://www.stefanelli.eng.br/en/virtual-vernier-caliper-simulator-05millimeter/#swiffycontainer_2
Micrometer Screw Gauge
A micrometer screw gauge is used to measure small lengths ranging between
0.10 mm and 25.00 mm.
This instrument can be used to measure diameters of wires and thicknesses of
steel plates to an accuracy of 0.01 mm.
The micrometer scale comprises a main scale marked on the sleeve and a scale marked on
the thimble called the thimble scale. The difference between one division on the upper
scale and one division on the lower scale is 0.5 mm.
The thimble scale is subdivided into 50 equal divisions. When the thimble is rotated
through one complete turn, i.e. 360, the gap between the anvil and the spindle
increases by 0.50 mm. This means that one division on the thimble scale is
0.01 mm.
When taking a reading, the thimble is turned until the object is gripped very gently
between the anvil and the spindle.
=
The ratchet knob is then turned until a `click' sound is heard. The ratchet knob is used
to prevent the user from exerting undue pressure.
Readings on the micrometer are taken as follows.
(a) The last graduation showing on the main scale indicates position between 2.0 mm
and 2.5 mm. Thus the reading on the main scale is read as 2.0 mm.
Readings on the micrometer are taken as follows.
(b) The reading of the micrometer screw gauge is the sun of the main scale reading and the
thimble scale reading which is:
 2.0 + 0.22 =2.22 mm
Readings on the micrometer are taken as follows.
(b) The reading on the thimble scale is the point where the horizontal reference line of the
main scale is in line with the graduation mark on the thimble scale Figure 1.15(b)
shows this to be the 22nd mark on the thimble scale, thus giving a reading of 22 x
0.01 mm = 0.22 mm.
The Simple Pendulum
A simple pendulum consists of a bob suspended at the end of a thread that is so light as to
be considered massless. The period of such a device can be made longer by increasing its
length, as measured from the point of suspension to the middle of the bob. A change in the
mass of the bob, however, does not affect the period, provided the length is not thereby
affected.
Terms used:
• An Oscillation is the movement of the bob from B to C to B to A and back to B.
• The Period of a pendulum is the time taken for it to make one complete oscillation.
• Frequency of a pendulum, is the number of oscillations made per second. It is measured in Hertz(Hz)
To get an accurate value of the period a number of oscillations are made and the total time is recorded. Then
the equation below is used
Period = total time taken / number of oscillations
T=t/n
Frequency = 1 / period
f=1/T