Physics

1:1:1:1. LENGTH:
PHYSICS Length is the distance between any two points.
Physics is a branch of science that deals with the study of It can also be defined as the distance covered by matter. It is
matter, energy and their interactions. a measurement of the extent of something from end to end.

Branches of Physics The S.I unit of length is a metre (m).
1. Mechanics: Motion and properties of matter. Other units of length include; Miles, kilometer, Hectometre,
2. Heat: A form of energy that causes rise in Decametre, Decimetre, Centimetre, etc.
temperature.
3. Optics: Light and waves. CONVERSIONS
4. Electricity and Magnetism. Example: 1
5. Modern Physics: Atomic and Nuclear Physics. Convert the following as instructed:
(i) 16.4mm to metres
Why we study Physics (ii) 20m to centimetres
 To help students develop an experimental attitude by (iii) 0.092km to metres
performing experiments and acquire skills such as (iv) 250cm to metres
observation, measuring, drawing logical conclusions.
 To understand scientific theories, principles and Solution
concepts (i) 16.4mm to metres
 To prepare students for further studies in Physics. km Hm Dm M dm cm mm
 To understand the applicability of Physics in other 1 0 0 0
disciplines like security, medicine, engineering, e.t.c 1m = 1000mm
and improve the world’s technology.
x = 16.4mm
1000𝑥 = 16.4 × 1𝑚
1 MECHANICS AND PROPERTIES 1000𝑥 = 16.4
OF MATTER 1000𝑥 16.4
=
1000 1000
𝑥 = 0.0164𝑚
1:1. MEASUREMENTS: Thus 16.4mm = 0.0164 m

Physics is concerned with measurement of physical (ii) 20m to centimetres
quantities and classifying them into groups according to Solution
their nature. 20m to centimetres
To measure is to find the value of a physical quantity using Km Hm Dm M dm Cm Mm
a scientific instrument with a standard scale. 1 0 0
1m = 100cm
Physical Quantities 20m = X
A physical quantity is a physical property that can
accurately be measured. 1 × 𝑥 = 20 × 100𝑐𝑚
𝑥 = 2000 𝑐𝑚
Types of Physical Quantities Thus 20m = 2000 cm
There are two types of Physical Quantities namely;
(i) Fundamental Quantities or Basic Quantities (iii) 0.092km to metres
(ii) Derived Quantities Solution
0.092km to metres
1:1:1. FUNDAMENTAL QUANTITIES OR BASIC Km Hm Dm M dm cm Mm
QUANTITIES 1 0 0 0
These are quantities from which all other quantities are 1km = 1000m
obtained. They are seven in total and these are: 0.092km = X

Fundamental Quantities S.I unit Symbol 𝑥 = 0.092 × 1000𝑚
1. 𝐋𝐞𝐧𝐠𝐭𝐡 Metre M 𝑥 = 92 𝑚
𝑥 = 92 𝑚
2. 𝐌𝐚𝐬𝐬 Kilogrm Kg
Thus 0.092km = 92 m
3. 𝐓𝐢𝐦𝐞 Second S
4. Thermodynamic TemperatureKelvin K
(iv) 250cm to metres
5. Electric current Ampere A
Solution
6. Amount of a substance Mole Mol. 250cm to metres
7. Luminous Intensity Candela Cd Km Hm Dm m Dm cm mm
1 0 0
Note: In mechanics, we use only three fundamental 1m = 100cm
quantities; i.e length, mass and time.
x = 250cm

,100 × 𝑥 = 250 × 1𝑚 Reading of vernier calipers,
100𝑥 250 1. Record the reading on the main scale to two places in cm.
= 2. Look along the Vernier scale carefully until you see
100 100
𝑥 = 2.5𝑐𝑚 division on it which coincides with the main scale, this gives
Thus 250cm = 2.5m the second decimal place.

Examples:
Instruments Used in measuring length
(i) Tape-measure: (Accurately measures length greater
than 1metre:𝑙 > 1𝑚). E g length of a foot ball field,
length of a plot of land etc.

(ii) Metre-rule :( Accurately measures length greater than
12 centimetres but less than 1metre:12𝑐𝑚 < 𝑙 < 1𝑚).
Eg length of a desk, breadth of a window, etc.
A metre rule gives readings in cm to 1dp. Main scale = 2.40cm
Vernier scale = 0.04cm
(iii) Vernier calipers or Slide calipers : Final reading = 2.44cm
Accurately measures length greater than 1cm but less than
12 cm:2.5cm < 𝑙 < 12 cm. E.g Internal and External What readings are represented in the diagram?
diameters of test tubes and beakers, breadth of a metre rule.
etc.
A vernier caliper gives readings in cm to 2dp.


Main scale

(iv) Micrometer screw gauge: (Accurately measures
length less than 1centimetre: 1𝑚𝑚 < 𝑙 < 25𝑚𝑚). Eg
Diameter of wires, Diameter of ball beairings and
pendulum bob, etc.
Vernier scale A micrometer screw gauge gives readings in cm to 2dp.




Engineer calipers




For each turn the spindle moves through 0.5mm.The
fraction of each turn is indicated on the thimble. This has a
1
scale of 50 divisions on the thimble and represents of half
50
1
a millimeter i.e. × 0.5 mm = 0.01mm.
The distance between the jaws is after wards measured on 10
The sleeve-reading gives units to the 1st two decimal places
an ordinary scale like a metre-rule. and the thimble gives 2nd decimal place.

Example I:
How to read a vernier Caliper




Sleeve scale reading = 14.50mm
Thimble scale reading = 0.44mm
= 14.94mm
 The main scale is in centimeters, 1cm has 10 divisions
1 Example II:
each division is cm = 0.1cm.
10
1
 Vernier scale, each division is cm = 0.01cm.
100

, 2kg = X
1 × 𝑥 = 2 × 10000𝑑𝑔
𝑥 = 20,000𝑑𝑔
Thus 2 kilograms = 20000dg

(iii) 40mg to kg
Solution
40mg to kg
Sleeve scale reading = 9.5 00mm
Thimble scale reading = 0.29mm Kg Hg Dg G dg Cg mg
= 9.79mm 1 0 0 0 0 0 0
1kg = 1000000mg
Precautions taken when using a micrometer screw gauge x = 40mg
 The faces of the anvil and the spindle must be cleaned
to remove dust so as to get accurate readings. 1000000 × 𝑥 = 40 × 1𝑘𝑔
1000000𝑥 40
 The reading must be checked. =
1000000 1000000
𝑥 = 0.00004𝑘𝑔
1:1:1:2: MASS: Thus 40miligrams = 0.0000kg
Mass is the quantity of matter in a substance.
The S.I unit of mass is a kilogram (kg). (iv) 20.55g to cg
Other units of mass include: Tonnes (1tonne = 1000kg), Solution
Hectogram (Hg), Decagram (Dg), Gram (g), Decigram (dg), 20.55g to cg
Centigram (cg), Milligram (mg), etc. Kg Hg Dg g dg Cg mg
1 0 0
Instruments Used in measuring Mass 1g = 100cg
(i) weighing beam balance (iv) Lever arm beam balance 20.55g = X
(ii) Digital beam balance (v) Tripple beam balance
(iii) Top arm beam balance 1 × 𝑥 = 20.55 × 100𝑐𝑔
𝑥 = 2055𝑐𝑔
Thus 20.55grams = 2055cg

1:1:1:3: TIME:
Time is the interval between two events.
The S.I unit of time is a second (s).
Other units of time include Minute (1min = 60s), Hour
(1hr=60min), Day (1day=24hrs), Week (7 days), fortnight
(2weeks), Month (1month=30days), Year (1yr=12months),
Conversions
decade, century, and a millennium.
Example 1:
Convert the following as instructed:
Instruments Used in measuring Time
(i) 100grams to kilograms
(ii) 2kg to dg  Stop clock
(iii) 40mg to kg  stop watch
(iv) 20.55g to cg  Half life of a radioactive substance eg Carbon – 14
 Shadows
Solution
(i) 100grams to kilograms 1:1:2. DERIVED QUANTITIES
Kg Hg Dg G Dg Cg Mg These are quantities which can be expressed in terms of the
1 0 0 0 fundamental quantities. Besides the seven fundamental
1kg = 1000g quantities, the rest of the Physical quantities’ are derived
quantities. Their S.I units are also called Derived units.
x = 100g
1000 × 𝑥 = 100 × 1𝑘𝑔 Examples of Derived Physical quantities include:
1000𝑥 100 Derived Quantities S.I unit Symbol
= 1. Area squaremetre m2
1000 1000
𝑥 = 0.1𝑘𝑔 2. Volume cubicmetres m3
Thus 100grams = 0.1kg 3. Density kilogram per kgm−3
cubicmetre
(ii) 2kg to dg 4. Speed and Velocity metres per second ms −1
Solution 5. Pressure newton per square Nm−2
2kg to dg metre (or pascal) (or Pa)
Kg Hg Dg G dg Cg mg 6. Force and weight Newton N
1 0 0 0 0 E. t. c
1kg = 10,000dg

, 1:1:2:1. AREA: Types of areas
Area is ameasure of the size of a surface. (i) Cross-sectional area
The S.I unit is a squaremetre (m2). (ii) Surface area
Other units of area include:
𝑐𝑚2 , 𝑚𝑚2 , 𝑘𝑚2 𝑒. 𝑡. 𝑐 Figure Name Formula for
Area
Example 1: 1. Rectangle 𝐴 = 𝑙𝑤
Convert the following as instructed w
(i) 15 mm2 to cm2
l
(ii) 20 m2 to mm2
(iii) 16.4 mm2 to m2 2. Square 𝐴 = 𝑆2
Solution s (All sides
(i) 15 𝑚𝑚2 𝑡𝑜 𝑐𝑚2 are equal)
Km Hm Dm M dm Cm Mm 3. Triangle 1
𝐴= 𝑏ℎ
1 0 2
1cm = 10mm h
(1cm)2 = (10mm)2 b
2 2
1cm = 100mm 4. Circle 𝐴 = 𝜋𝑟 2
2
x = 15 mm r
2
100 × 𝑥 = 15 × 1𝑐𝑚
𝑥 = 0.15𝑐𝑚2
Thus 15 𝑚𝑚2 =0.15𝑐𝑚2 1
5. Trapezium
b (2 parallel 𝐴 = ℎ(𝑎 + 𝑏)
2
(ii) 20 𝑚2 𝑡𝑜 𝑚𝑚2 un equal
km Hm Dm M dm Cm Mm h sides)
1 0 0 0
1m = 1000mm a
(1m)2 = (1000mm)2 6. Sphere 𝑆. 𝐴 = 4𝜋𝑟 2
1m2 = 1000000mm2
20 m2 = X
7. Cuboid 𝑆. 𝐴
1 × x = 20 × 1000000mm2 h = 2(𝑙𝑤)
x = 20,000,000mm2 + 2(𝑤ℎ)
Thus 20 m2 =20,000,000mm2 or 𝟐. 𝟎 × 𝟏𝟎𝟕 𝐦𝐦𝟐 w + 2(𝑙ℎ)
l
Solution 8. Cube 𝑆. 𝐴 = 6𝑆 2
(All faces
(iii) 16.4 𝑚𝑚2 𝑡𝑜 𝑚2
are equal)
Km Hm Dm M dm Cm Mm
1 0 0 0
1m = 1000mm 1:1:2:2. VOLUME:
(1m)2 = (1000mm)2 Volume is the space occupied by matter.
The S.I unit of volume is cubic metre (m3).
1m2 = 1000000mm2 Other units of volume include:
x = 16.4 mm 2 𝑐𝑚3 , 𝑚𝑚3 , 𝑘𝑚3 , 𝑚𝑖𝑙𝑙𝑖𝑙𝑖𝑡𝑟𝑒(𝑚𝑙), 𝑙𝑖𝑡𝑟𝑒(𝑙). 𝑒. 𝑡. 𝑐
1000000 × x = 16.4 × 1m2 Instruments for measuring Volume include:
1000000x 16.4
=  Measuring cylinder
1000000 1000000  Volumetric flask
x = 0.0000164m2
 Burette
Thus 20 m = 0.0000164m2 or 𝟏. 𝟔𝟒 × 𝟏𝟎−𝟓 𝐦𝟐
2
 Pipette