DIMENSIONS AND MEASUREMENT OF PHYSICAL QUANTITIES
SS 1 PHYSICS FIRST TERM ELEARNING NOTE
Subject:
PHYSICS
Term:
FIRST TERM
Week:
WEEK 3
Class:
SS 1
Topic:
DIMENSIONS AND MEASUREMENT OF PHYSICAL QUANTITIES
Previous lesson:
The pupils have previous knowledge of
FUNDAMENTAL AND DERIVED QUANTITIES AND UNITS
that was taught as a topic in the previous lesson
Behavioural objectives:
At the end of the lesson, the learners will be able to
 say the meaning of DIMENSIONS AND MEASUREMENT OF PHYSICAL QUANTITIES
 give examples of various DIMENSIONS AND MEASUREMENT OF PHYSICAL QUANTITIES
 explain the importance of DIMENSIONS AND MEASUREMENT OF PHYSICAL QUANTITIES
Instructional Materials:
 Wall charts
 Pictures
 Related Online Video
 Flash Cards
Methods of Teaching:
 Class Discussion
 Group Discussion
 Asking Questions
 Explanation
 Role Modelling
 Role Delegation
Reference Materials:
 Scheme of Work
 Online Information
 Textbooks
 Basic Education Curriculum
 Workbooks
Content:
DIMENSIONS AND MEASUREMENT OF PHYSICAL QUANTITIES
CONTENT
 Measurement of Length/Distance
 Measurement of Mass/Weight
 Measurement of Volume
 Measurement of Area
 Measurement of Time
 Units of Measurement in Industries
Measurement of Length/Distance
Length is measured using the following instruments.
(a) Metre Rule: A metre rule is a measuring device calibrated in centimetres (cm) with a range of 0 – 100cm. In using the metre rule, the eye must be fixed vertically on the calibration to avoid parallax errors.The smallest reading that can be obtained on a metre rule is 0.1cm (0.01cm).
(b) Callipers: These are used in conjunction with metre rule for measuring diameter of tubes, thickness of sheet, etc. The callipers are of two types –
(i) The external calliper and
(ii) The internal calliper.
The external calliper is used to measure the external diameters of solid objects; while the internal calliper is used to measure the internal diameters of solid objects.
(c) Vernier calliper
The vernier calliper can be used for measuring small linear length and diameters of objects within the range of 012cm at least. It is calibrated in centimetres (cm). It has a reading accuracy of 0.1mm (0.01cm)
(d) The micrometer screw gauge: It is used to measure the thickness of a round objects E.g, the diameter of a wire. The micrometer screw guage gives a more accurate reading than the vernier calliper. It is calibrated in millimetre (mm). It has a reading accuracy of 0.01mm (0.001cm)
Other instruments for measuring length include: measuring tape, ruler, etc. The S.I. unit of length is metre (m).
EVALUATION
 Mention any three instrument used in measuring length.
 Which of the above instrument could give the highest degree of accuracy?
Three common instruments used to measure length are rulers, tape measures, and calibrated scales. Among these three, calibrated scales can give the highest degree of accuracy. This is because they are able to measure length to the nearest fraction of an inch or millimeter. Ruler and tape measures can only measure length to the nearest inch or centimeter, which is not as precise. Calibrated scales are typically used in settings where precision is important, such as in manufacturing or scientific research.
Measurement of Mass/Weight
Mass is defined as the quantity of matter a body contains; while Weight is the amount of gravitational force acting on a body or the force with which a body is attracted towards the centre of the earth. The weight of a substance varies from place to place due to variation in acceleration due to gravity,‘g’ over places but mass remains constant from place to place.
Mass and weight of objects are measured using instrument such as spring balance, beam balance, chemical balance, scale balance, etc.
However, the differences between mass and weight are shown below.
S/N  MASS  WEIGHT  
1  Mass is a scalar quantity.  Weight is a vector quantity.  
2  Mass is the amount of stuff or quantity of matter contained in a body. 
Weight is the amount of gravitational force acting on a body. 

3  Mass is measured using a beam balance, chemical balance 
Weight is measured using spring balance. 

4  The S.I. unit of mass is kilogramme (kg)  The S.I. unit of weight is Newton (N).  
EVALUATION
 State three instruments used in measuring mass and weight.
 Differentiate between mass and weight in four ways.
 Why is weight a vector quantity?
Three common instruments used to measure mass and weight are balances, bathroom scales, and truck scales. There are four main ways in which mass and weight differ:
1. Mass is a measure of the amount of matter in an object, whereas weight is a measure of the force exerted by gravity on an object.
2. Mass is constant, regardless of the object’s location, whereas weight varies depending on the object’s location (because gravity is weaker at higher altitudes).
3. Mass can be measured in kilograms or pounds, whereas weight is typically measured in Newtons.
4. Mass is an intrinsic property of an object, whereas weight is a force that acts on an object.
Weight is a vector quantity because it has both magnitude and direction. The magnitude of weight is the amount of force exerted by gravity on an object, while the direction is always downward (toward the center of the Earth).
Measurement of Volume
Volume of liquid objects is measured using instruments such as cylinder, burette, pipette, eureka can, etc. For regular solid objects, their volume could be determined using their mathematical formula.
S/N  Solid Object  Formula for Volume  
1  Cube  l×l×l  
2  Cuboid  l×b×h  
3  Cylinder  πr2h  
4  Cone  13πr2h  
5  Sphere  43πr2  
The S.I. unit of volume is metre cube m3
Measurement of Area
The area of a solid object could be determined using mathematical formulae after determining the two dimensions of the object.
S/N  Solid Object  Formula for Area  
1  Triangle  12bh  
2  Rectangle  lb  
3  Square  l2  
4  Parallelogram  bh  
5  Trapezium  12(a+b)h  
The S.I. unit of volume is metre square m2
WORKED EXAMPLES
 Find the volume of a cylinder of diameter 12cm and height 15cm.
SOLUTION
d =12cm
∴ r =12cm2=6cm
h =15cm,π=227
Now, v =πr2h
∴ v =227×62×15
∴ v =22×36×157=118807
∴ v =1697.14cm3
 What is the area of a triangular card board of base 6cm and height 4cm?
SOLUTION
b =6cm and h =4cm
Now, A =12bh
∴ A =6×42=242
∴ A =12cm2
EVALUATION
 Calculate the volume of a rectangular prism of dimension 7cm by 3.5cm by 1.5cm.
 A cube has an edge of 0.8cm. Find its volume.
The volume of a rectangular prism is calculated by multiplying the length times the width times the height. Therefore, the volume of the prism in the first example would be 7cm x 3.5cm x 1.5cm, or 63.75 cm3. The volume of a cube is calculated by taking the cube of the edge length. Therefore, the volume of the cube in the second example would be (0.8cm)3, or 0.512 cm3.
Measurement of Time
The Concept of Time
You must have heard the following statements made about time:
 “Time and tide waits for no man”
 “Time is business”
 “There is time for everything: time to sow and time to reap, time to laugh and time to cry, time to go to bed and time to wake up” and so on
Time is very important in our daily activities. Many people have failed in one area or the other because of mismanagement of time. In Physics time is very important. Wrong timing can lead to wrong observations, results and wrong conclusions.
What then is time? Time may be considered as the interval between two successive events. It is a fundamental quantity. Its S.I unit is seconds.
Ways of Measuring Time
Time as mentioned earlier is very important. That is why early men developed various means of measuring time. They used the sun to tell time. Even today people still use the position of the sun to determine time. Other devices they developed and used are:
 The water clock or hourglass
 The sand clock
 The primitive Sundials
Today, we have better timemeasuring devices that measure time more accurately than the above mentioned devices. Some of them are:
 The stop watch which is the standard instrument for measuring time in the laboratory
 The wrist watch
 The modern pendulum clock
 The wall clock
It is worthy of note that:
 60 seconds makes one minute
 60 minutes makes one hour
 24 hours makes one day
 365 ¼days makes one year
 10 years makes a decade
 100 years makes a century/centenary
 1000 years makes a millennium
Calculations on Time
Example 1: How many seconds are there in 2 hours 15 minutes?
Since 60 seconds makes 1 minute and 60 minutes makes 1 hour, 1 hour will have 60 x 60 seconds. 2 hours will have 60 x 60 x 2 seconds = 7200 seconds.
15 minutes will have 60 x 15 seconds = 900 seconds
Therefore 2 hours 15 minutes will have (7200 + 900) seconds = 8100 seconds
Example 2: If it takes a pendulum bob 32 seconds to complete 20 oscillations, what is the period of oscillation of the bob?
Period ( T ) is time ( t ) taken for the bob to complete an oscillation.
i.e. T =timenumber of oscillations
=3220=1.6seconds
EVALUATION
 What are the standard instruments for measuring time in the laboratory?
 Mention 2 examples each of modern and olden days timemeasuring devices you know.
Units of Measurement in Industries
Measurement of Length
Length was considered earlier as a fundamental quantity whose S.I unit is metre. We also learnt that other units of length are centimeter, millimitre,, and kilometer.
Units of Length
Multiples of other units  Other units  Conversion to S.I unit  
_______  1 inch  = 2.54cm = 0.0254m  
12 inches make  1 foot  = 0.3048m  
3 feet make  1 yard  = 0.9144m  
22 yards make  1 chain  = 20.12m  
10 chains make  1 furlong  = 201.2m  
8 furlongs make  1 mile  = 1.609 km  
Class Activity
 Mention the unit for measuring the following quantitiesby the following person
 Classify these units under S.I units and other units.
S/N  Persons  Physical quantity  Unit  
1  Bricklayers  Distance  ___________  
2  Tailors  Length  ___________  
3  Science teachers  Length  ___________  
4  Petroleum engineers  Volume  ___________  
5  Butcher  Mass of meat  ___________  
6  Electrical engineers  Electrical energy  ___________  
Example 1
 Convert 3550km to miles
 The length of an iron rod is given as 66 inches. What is its length in metres?
Solution
 1 mile = 1.609km
Hence, 3550km = (3550 x 1.609) miles = 5,712 miles
 1 inch = 2.54cm
Therefore 66 inches = (66 x 2.54) cm = 167.64cm.
But 100cm = 1m,
Thus 167.64cm = =167.64100m = 1.6764m
Therefore the length of the iron rod in metres is 1.676.4m
EVALUATION
 The height of a girl is 7.5 feet. Estimate her height in metres
 Convert 30km to miles
Measurement of Volume
Volume is a measure of the space contained in an object. A barrel of oil is equivalent to 158.987 litres.
Example 2
The table below is a statistics of oil exportation to the United States for three years by NNPC
Year  Price per barrel ( ₦ )  Volume exported (barrels)  
1993  140  1.05 million  
1994  135  1.5 million  
1995  162  0.9 million  
(i) What volume of oil in litres was exported in 1994?
(ii) What is the highest amount gotten and in what year was it gotten?
Solution
(i) In 1994, 1.5 million barrels of oil was exported.
Since 1 barrel = 158.987 litres
1.05 million barrels = (1.5million x 158.987) litres = 238.4805million litres
(ii) In 1993, volume of oil exported = 1.05 million barrels. Price per barrel = N140
Amount realized = 1.05million × 140 = N147,000000
In 1994, volume of oil exported = 1.5million, price per barrel = N135
Amount realized = 1.5million × N135 = N202.5 million
In 1995, volume of oil exported = 0.9 million barrels. Price per barrel = N162
Amount realized = 0.9 million × N162 = N145.8 million
Therefore, the highest amount of money gotten is N202.5 million and it was gotten in 1994
Measurement of Temperature
The S.I unit of temperature is Kelvin. Other units for temperature include degree Celsius and degree Fahrenheit. In the U.S.A, degree Fahrenheit is still in use. On the Celsius scale, the freezing point and the boiling point of water are measured as 00C and 1000C respectively. But on the Fahrenhiet scale, the freezing point and the boiling point of water are measured as 320F and 2120F respectively.
The Celsius Scale is related to the Fahrenheit scale by the equation:
F is temperature in Fahrenheit scale, C is temperature in Celsius scale
F–329=C100orC5=F–329
Example: (a) Convert 77 degrees Fahrenheit to Celsius scale (b) Convert 105 degrees Celsius to degrees Fahrenheit
Solution
(a) Considering the equation:
C5=F–329C=5(F–32)9=5(77–32)9=5×459=25
(b) C5=F–329F=9C5+32=9×1055+32=9×21+32=189+32=221oF
EVALUATION
 Discuss the significance of time to the study of science.
 Highlight the various instrument for measuring time.
 State four differences between mass and weight.
 Draw the following measuring instruments: (i) Beam balance (ii) Spring balance
Presentation
The topic is presented step by step
Step 1:
The subject teacher revises the previous topics
Step 2.
He introduces the new topic
Step 3:
The subject teacher allows the pupils to give their own examples and he corrects them when the needs arise
EVALUATION
 Derive the dimensions and the units of the following quantities:
. (i) Volume (ii) Power (iii) Density.
 Differentiate between fundamental and derived quantities.
 List ten examples of derived quantities and explain why they are called derived quantities.
 Write down the SI unit of (i) acceleration (ii) force (iii) momentum (iv) density
Conclusion
The class teacher wraps up or concludes the lesson by giving out short notes to summarize the topic that he or she has just taught.
The class teacher also goes round to make sure that the notes are well copied or well written by the pupils.
He or she does the necessary corrections when and where the needs arise.