Measurements and units

This is the foundation of physics, without knowing the physical quantities and thier units, you will find Physics difficult.

We are going to be looking at physical quantities and thier units used in Physics. In physics generally, the three basic physical quantities are: mass (kg), length (m) and time (s).

Physical quantities can be divided into two, they are Fundamental quantities and Derived quantities.

Fundamental Quantities

These are quantities that are independent of others i.e they are on thier own. Let's take a look at them.

Mass ---- kilogram (kg)
Length ---- metre (m)
Time ------. Seconds. (s)
Temperature ------kelvin (K)
Electric current------Ampere (I)
Amount of substance---- mole (mol)
Luminous Intensity ----Candela (Cd)

Derived Quantities

Theses are quantities that are formed by the combination of two or more fundamental quantities. They are dependent on fundamental quantities.

Let's take a look at them and see how their units are derived.

Area=length* breadth---m²
Volume=length* breadth * height---m³
Velocity= displacement/ Time--- ms⁻¹
Acceleration= velocity/Time--- ms⁻²
Force= mass*acceleration---Newton(N), kgms⁻².
Density= mass/volume --- kgm⁻³
Pressure= Force/Area---Nm⁻², kgm⁻¹s⁻².
Workdone, Energy= Force*distance---Joules(J), Nm, Kgm²s⁻²
Power=workdone/Time --- watts, Js⁻¹, kgm²s⁻³.
Impulse=Force*Time---Ns, kgms⁻¹
Momentum= mass*velocity---kgms⁻¹
Surface tension=force/length--N/m, kgs⁻²
Specific heat capacity----Jkg⁻¹K⁻¹
Heat capacity--- Jkg⁻¹
Energy density----Kgm⁻¹s⁻²
Gravitational constant --Kg⁻¹m³s⁻²

We are going to be looking at their dimension. If you know the unit of any quantity, then the dimension can be known.

Any quantity that has kilogram as its unit will have the dimension M. Any quantity that has metre as its unit will have the dimension L. Any quantity that has seconds as its unit will have the dimension T.

Area = L²
Volume = L³
Velocity= LT⁻¹
Acceleration= LT⁻²
Force= MLT⁻².
Density= ML⁻³
Pressure= ML⁻¹T⁻².
Workdone, Energy= ML²T⁻²
Power=ML²T⁻³.
Impulse=MLT⁻¹
Momentum=MLT⁻¹
Surface tension=MT⁻²
Energy density----ML⁻¹T⁻²
Gravitational constant --M⁻¹L³T⁻²
Electromotive force - ML²T⁻³I⁻¹

Vector and scalar quantities

Vector quantities :These are quantities that magnitude and direction. Examples are Weight, thrust, force( frictional force, gravitational force, frictional force, drag force), displacement, torque, velocity, Field, momentum, acceleration, impulse, upthrust etc
Scalar quantities: These are quantities that have magnitude but no direction. Examples are pressure, distance, work, energy, power, mass, length, temperature, electric potential, density, speed etc

Mass and weight

These two quantities are often used in place of the other, but in actual sense, they are different. Let's take a look at thier meaning.

Mass is the quantity of matter contained in a body while weight is the earth gravitational force on a body.
Mass is measured in kilogram while weight is measured in Newton
Mass is constant while weight varies
Mass is measured with beam balance while weight is measured with spring balance.
Mass is a scalar quantity while weight is a vector quantity
Mass is a fundamental quantity while weight is a derived quantity

Length

Length is a physical quantity which can be measured with different instruments like metre rule, steel tape, vernier caliper and micrometer screw guage. We are going to be looking at them one after the other.

Metre rule: This is a device use to measure distance between two points on the ground or on paper. It measures shorter distances. Metre rule is calibrated in centimeters and millimeters. The accuracy of a metre rule is 0.1cm or 1mm which is also the lowest division, as a result, the least possible error encountered when taking measurement with a metre is half of its lowest division which is 0.1cm/2 = 0.05cm or 0.5mm.
Steel tape: It is used for measuring a large area like a piece of land, a field etc
Vernier caliper: This is a device use to measure diameter( internal and external) of a tube, diameter of a rod, thickness of a plate. The lowest division a vernier caliper can measure is 0.01cm or 0.1mm, which means that the accuracy of a vernier caliper is 0.01cm or 0.1mm. It has two scales: the main scale and the vernier scale. The main scale is the upper part while the vernier scale is the lower part. The diagram below shows the measurement of an object by a vernier caliper.

Lets us calculate the measurements of the above diagram.

First, we need to get the main scale.

Main scale = 3.1cm, next is the vernier scale. If you look at the vernier scale, you will see a line that merge with the main scale( the fourth line). Multiply it by 0.01

Vernier scale = 0.04cm

Total scale = 3.1 + 0.04 = 3.14cm

Main scale= 6.2cm

Vernier scale= 0.06cm

Total scale = 6.2 + 0.06 = 6.26cm

Main scale = 5.4cm

Vernier scale = 0.03cm

Total scale = 5.4 + 0.03 = 5.43cm

Micrometer screw guage: This is an instrument used to measure tiny object like the thickness of a piece of paper, the diameter of a wire etc. The lowest division a micrometer screw guage can measure is 0.01mm or 0.001cm, which means its accuracy is 0.01mm or 0.001cm. It has two scales: the main scale and the circular scale.

The diagram below shows the measurement of an object by a micrometer screw guage

Let's calculate the reading for the main scale.

First, we need to know what each line represent. Follow my steps. From 5 to 6, we have four(4) lines. The difference between 6 and 5 is 1. Divide 1 by 4 = 0.25.

So it means that each line on the main scale is 0.25

Main scale : 6.25mm

Circular scale: Count from 10 upward, stop at the line that merge with the main scale( which is 14). Multiply it by 0.01, it gives 0.14mm

Total scale = 6.25 + 0.14 = 6.39mm

We are going apply the same principle

For the main scale, from 0 to 5, we have 10 lines( both up and down). The difference between 5 and 0 is 5. Divide it by 10. It gives 0.5. So it means that each line on the main scale is 0.5

Main scale =5.5mm

Vernier scale = 0.42mm

Total scale = 5.92mm

Exercises

Calculate the reading of the following