CHAPTER TWO

MEASUREMENTS IN PHYSICS

Physics is concerned with measurement of physical quantities and classifying them into groups according to their nature. To measure is to find the value of a physical quantity using a scientific instrument with a standard scale. 

Physical Quantities 

A physical quantity is a physical property that can accurately be measured. 

Types of Physical Quantities 

There are two types of Physical Quantities namely;

 (i) Fundamental Quantities or Basic Quantities 

(ii) Derived Quantities 

FUNDAMENTAL QUANTITIES OR BASIC QUANTITIES 

These are quantities from which all other quantities are obtained. They are seven in total and these are: 

Note: In mechanics, we use only three fundamental quantities; i.e length, mass and time. 

LENGTH: 

Length is the distance between any two points. It can also be defined as the distance covered by matter. It is a measurement of the extent of something from end to end. 

The S.I unit of length is a metre (m). Other units of length include; Miles, kilometer, Hectometre, Decametre, Decimetre, Centimetre, etc. 

CONVERSIONS 

Example: 

1 Convert the following as instructed: 

(i) 16.4mm to metres 

(ii) 20m to centimetres 

(iii) 0.092km to metres 

(iv) 250cm to metres 

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. 

(iii) Vernier calipers or Slide calipers : Accurately measures length greater than 1cm but less than 12 cm:2.5cm<𝑙<12 cm. E.g Internal and External diameters of test tubes and beakers, breadth of a metre rule. etc. 

A vernier caliper gives readings in cm to 2dp. 

Engineer calipers 

The distance between the jaws is after wards measured on an ordinary scale like a metre-rule. 

How to read a vernier Caliper 

Reading of vernier calipers, 

1. Record the reading on the main scale to two places in cm. 

2. Look along the Vernier scale carefully until you see division on it which coincides with the main scale, this gives the second decimal place. 

Main scale = 2.40cm 

Vernier scale = 0.04cm 

Final reading = 2.44cm 

What readings are represented in the diagram? 

(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. 

A micrometer screw gauge gives readings in cm to 2dp. 

Precautions taken when using a micrometer screw gauge  

-The faces of the anvil and the spindle must be cleaned to remove dust so as to get accurate readings.  

-The reading must be checked. 

MASS: 

Mass is the quantity of matter in a substance. 

The S.I unit of mass is a kilogram (kg). Other units of mass include: Tonnes (1tonne = 1000kg), Hectogram (Hg), Decagram (Dg), Gram (g), Decigram (dg), Centigram (cg), Milligram (mg), etc. 

Instruments Used in measuring Mass 

(i) weighing beam balance 

(ii) Digital beam balance 

(iii) Top arm beam balance 

(iv) Lever arm beam balance 

(v) Tripple beam balance Conversions 

Conversions 

Example 

1: Convert the following as instructed: 

(i) 100grams to kilograms 

(ii) 2kg to dg 

(iii) 40mg to kg 

(iv) 20.55g to cg 

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), decade, century, and a millennium.

Instruments Used in measuring Time  

Stop clock  

stop watch  

Half life of a radioactive substance eg Carbon – 14  

Shadows  

DERIVED QUANTITIES 

These are quantities which can be expressed in terms of the fundamental quantities. Besides the seven fundamental quantities, the rest of the Physical quantities’ are derived quantities. Their S.I units are also called Derived units. 

AREA: 

Types of areas 

(i) Cross-sectional area 

(ii) Surface area 

VOLUME: 

Experiment to determine the volume of an irregular object 

The volume of an irregular object can be obtained by the Displacement method.  

• Pour water into a measuring cylinder up to a certain level. 

• Record the volume of water (V1).  

• Tie a thread on the irregular object and gently lower it into the water in the measuring cylinder. 

• Note the new volume of water in the cylinder (V2).  

• The Volume of the irregular object is then equal to the volume of displaced water; Thus V = (V2 – V1). 

OR  

• Pour water in an over flow can up to the level of the spout. 

• Place a measuring cylinder just below the spout.  

• Tie a thread around the irregular object and gently lower it into the overflow can.  

• Note the volume of water, V that collects in the measuring cylinder. It is equal to the volume of the irregular object. 

DENSITY AND RELATIVE DENSITY