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Basic Physical Quantities in measurement
They cannot be obtained from any other
physical quantities.
We've seven basics quantities according to the International system of Units (SI units).
Basic physical quantities and their SI unit together with Symbol of units;
Length
SI unit is metre (m).
Mass
SI unit is kilogram (kg).
Time
SI unit is second (s).
Electric current
SI unit is ampere (A).
Thermodynamic temperature
The SI unit is Kelvin (K).
Luminous intensity
The SI unit is candela (K).
Amount of substance
The SI unit is mole (mol).
The table below shows basic physical quantities , symbols and SI unit.
Basic physical quantities
SI unit
SI symbol
1
Length
metre
m
2
Mass
kilogram
kg
3
Time
second
s
4
Electric current
ampere
a
5
Thermodynamic temperature
Kelvin
K
6
Luminous intensity
candela
k
7
Amount of substance
mole
mol
Other quantities that can be derived from basic physical quantities are ; Density, volume, Area, Work,momentum, power etc.
LENGTH
It is the distance between two points. Examples
of length are:
Breadth or width,Diameter,Height,depth , radius etc.
Unit,Symbols and equivalence in metres.
Kilometre (km) equivalent to 1000 m
Hectometre (Hm) equivalent to 100 m.
Dekametre (Dm) equivalent to 10m.
Decimetre (dm) equivalent to 0.1 m.
Centimetre (cm) equivalent to 0.01 m.
Millimetre (mm) equivalent to 0.001 m.
Micrometre (m) equivalent to 0.000001 m.
The table below shows length unit, symbol, and equivalent to metre.
Unit
Symbol
Equivalence to metre
1
Kilometre
km
1000
2
Hectometre
Hm
100
3
Dekametre
Dm
10
4
Decimetre
dm
0.1
5
Methods of measuring length;
Estimation method.
Measuring using accurate instruments.
Examples of measuring instruments.
Tape measure used to measure relatively long measurements like that of soccer ⚽ fields, tables ,desks, lockers etc.
Metre rule .
Half metre rule.
Micrometre screw gauge used to measure very small measurements like diameter of wire.
Callipers .
The following precautions should be taken to avoid errors When Using a Metre Rule;
Ensure metre rule is in contact with the object.
Ensure the end of the object is aligned with the zero mark of the metre rule.
Ensure the position of the eye is perpendicularly to the scale.
NB: Take care to avoid the damage of the metre rule.
Factors to consider when choosing measurement instruments
Accuracy of the measurements required.
Size of the object to be measured.
Shape of the object to be measured.
How to measure the diameter of a curved surface.
Requirements
Curved object like beaker.
Thin thread .
Mark pen (ink).
Procedure
Closely wrap a thin thread 10 times around a beaker.
Mark with mark pen the beginning and end of the turns.
Remove our thin thread after marking the beginning and the end of the turns.
measure the length between the ink marks and call it 1a.
Repeat this three times recording the readings as 2a and 3a to ensure your measurements are accurate.
Find the average length
a =(1a+2a+3a)/3.
Dividing by 10 we get the circumference of the beaker.
Diameter= circumference / ฯ.
AREA
It refers to the measure of the surface covered by an object.
Its SI unit is square metre (m^2).
Area of regular shape
Examples 1
Area of Circle ⭕ =1/2ฯr^2,where r stand for radius .
Example 2.
Area of triangle=1/2×base×height.
Example 3.
Area of rectangle= base×height.
Area of Irregularly−Shaped Surfaces (irregular polygon)
Can be calculated by estimating sub-division of the surface into small equal squares.
Example 1.
Find the area of the square with side 8m.
Solution
Area of square = side × side =8m×8m=64m^2.
Example 2.
Find the area of a triangle with base 8m and height 10m.
Solution
Area of a triangle=½ base ×height =½ ×8m ×10m=40m^2.
Volume
Is the amount of space occupied by matter.
It is a derivative quantity of length.
The SI unit of volume is the cubic metre (m^3).
Volume of regular solids
Cuboid ,
Triangular prism
Volume = cross
-section area x height
Volume= length × width × height
Volume= cross section area x height
Volume= ฯr^2h
Cylinder cylinder = base × width × height.
Mass
Is the quantity of matter in an object. Matter is anything that occupies space.
Mass =density × volume.
The SI unit of mass is the kilogram (kg).
Mass of an object depends the following;
Cross-section area of an object.
Volume of an object.
Density of an object.
The number of particles an object contains.
NB: The mass of an object remains constant because the number of particles will also remain constant on both earth ๐ and on moon ๐.
Instruments used to measure mass
Lever balance which is mechanical type.
Beam balance which is mechanical type.
Top pan balance which is electrical type.
Density
It is defined as the mass per unit volume of a substance.
It is defined as the mass of an object divided by volume of that object.
It is denoted by rho ๐ , which is a 17Th Greek letter .
SI unit of density is the kg/m3 or kgm-3
(kilogram per cubic metre).
symbol(kg/m3 or kgm-3)
Density=(mass)/(volume)
๐=m/v,
v= ๐× m,
๐ ; m= ๐ × V.
Time
It refers to the measure of duration taken.
Its SI unit is the second (s).
Multiples and submultiples of time and their symbols.
Microsecond ( ยตs) equivalent to 0.000001 s.
Millisecond ( ms) equivalent to 0.001 s.
Minute (min) equivalent to 60 s.
Hour (hr) equivalent to 3600 s.
Day (day) equivalent to 86400 s.
Week (wk) equivalent to 604800 s.
The table below shows Multiple and submultiples in second.
Time
Symbol
Equivalent to seconds
1
Microsecond
ยตs
0.000001
2
Millisecond
ms
0.001
3
Minute
min
60
4
Hour
hr
3600
5
Day
Day
86400
6
Week
wk
604800
Questions of length,area, volume and density.
1.Find the area of a circle with radius 7cm.(use ฯ=22/7).
Solution.
Area of a circle ⭕
=ฯr^2=22/7×(7cm)^2
=154cm^2.
2.Find the volume of a cylinder with radius 14 cm and height 10cm.(use ฯ=22/7)
Solution.
Volume of a cylinder=cross-section area×height=ฯr^2h,where r is radius and h is the height of the cylinder.
Volume of a cylinder=22/7×(14cm)^2×10cm
=6160cm^3.
3.Find the density of a liquid y with mass 20g and volume 20cm^3.
Solution.
Density=(mass)/(volume).
Density of liquid y =(20g)/(20cm^3)=1g/cm^3 or 1 g cm^-3.
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