Fundamental and Derived Quantities and Units

Fundamental Quantities

The Concept of Fundamental Quantities

Fundamental quantities are physical quantities whose dimensions and units are not usually derived from other physical quantities. Basically, there are three fundamental quantities in mechanics. They include:

(i) Mass

(ii) Length and

(iii) Time

(i) Mass: This is a fundamental quantity with dimension ‘M’, usually written in capital letter. The S.I. unit of mass is kilogramme (kg). Mass can also be measured in gramme (g), tonne (t), etc.

(ii) Length: This is another fundamental quantity with dimension ‘L’, written in capital letter. The S.I. unit of length is metre (m). Length can also be measured in kilometre (km), centimetre (cm), inches (inch), feet (ft), etc.

(iii) Time: Time is a fundamental quantity with dimension ‘T’, also written in capital letter. The S.I. unit of time is second (s). Time can also be measured in minutes and hours.

The below table summarized the dimensions and units of the basic fundamental quantities.

	S/N	Quantity	Dimension	S.I. Unit
	1	Mass	M	Kilogramme (kg)
	2	Length	L	Metre (m)
	3	Time	T	Second (s)

EVALUATION

1. List the three basic fundamental quantities.
2. What are their dimensions and SI units?

Other Fundamental Quantities

	S/N	Quantity	S.I. Unit
	1	Temperature	Kelvin (K)
	2	Current	Ampere (A)
	3	Amount of substance	Mole (mol)
	4	Luminous intensity	Candela (cd)

NB: The educator should carry out activities on simple measurement of current and temperature with the students.

ACTIVITY: PRACTICAL

1. Measuring the temperature of boiled water in a specific interval of time say, 2mins as it cools down.
2. Measuring the current value in a simple electric circuit.

EVALUATION

1. Mention the three other fundamental quantities and their SI units.
2. How many fundamental quantities are there altogether?
3. Enumerate all the fundamental quantities with their SI units.
4. Write down the dimension of the three basic fundamental quantities.
5. Why are the above quantities called fundamental quantities?

Derived Quantities

The Concept of Derived Quantities

Derived quantities are physical quantities whose dimensions and units are usually derived from the fundamental quantities. E.g, force,speed, etc.

Other physical quantities apart from the fundamental quantities are derived quantities. This is because their dimensions and units are usually derived from the fundamental ones.

Derived quantities include:

1. Work
2. Energy
3. Momentum
4. Impulse
5. Volume
6. Area
7. Pressure
8. Power
9. Density
10. Moment
11. Torque, etc.

 EVALUATION

1. What are derived quantities?
2. Mention five examples of derived quantities.

Dimensions and Units of Derived Quantities

1. Derive the dimensions and the S.I. units of (i) speed (ii) acceleration (iii) Force.

SOLUTION

(i) Speed =distancetime=lengthtime=LT=LT−1

∴ The dimension for speed is LT−1

The S.I. unit of length is ‘m’ and that of time is ‘s’

∴ The S.I. unit of speed is msorms−1

NB: Speed and velocity have the same dimension and S.I.unit.

Also, velocity =displacementtime

(ii) Acceleration =velocitytime=LT−1T=LT2=LT−2

∴ The S.I. unit of acceleration = =ms−1s=ms2=ms−2orms2

(iii) Force =mass×acceleration=m×LT2=MLT2=MLT−2

∴ The unit of force is kgms2

But the S.I. unit of force is Newton (N). This is the unit used in all calculations

2. Show that the dimension of pressure is ML−1T−2. Hence, derive the S.I. unit.

SOLUTION

Now, pressure =force x area

∴ pressure =MLT−2L2=MT−2L=ML−1T−2

The S.I. unit of force is Newton, N; while that of area is metresquare, m2

Hence, the S.I. unit of pressure =Nm2orNm−2

3. Derive the dimension for work. What is the S.I. unit of work?

SOLUTION

Work =force×distance

∴ work =MLT−2×L=ML2T−2

Unit of work =Nm

But the S.I. unit of work is Joule (J). This is the unit used in all calculations.

In summary, the table below shows the dimensions and S.I. units of some derived quantities.

	S/N	Quantity	Dimension	S.I. Unit
	1	Work & Energy	ML2T−2	Joule (J)
	2	Momentum & Impulse	MLT−1	Newton-Second (Ns)
	3	Volume	L3	metre cube (m3)
	4	Area	L2	Metre square (m2)
	5	Pressure	ML−1T−2	Newton per metre square or Pascal metre cube (Nm2)
	6	Power	ML2T−3	Watt (W)
	7	Density	ML−3	Kilogramme per metre cube (kgm3)
	8	Moment	ML2T−2	Newton-metre (Nm)

EVALUATION

1. Derive the dimensions and the units of the following quantities:

(i) Volume   (ii) Power  (iii) Density.

2. Differentiate between fundamental and derived quantities.
3. List ten examples of derived quantities and explain why they are called derived quantities.
4. Write down the SI unit of (i) acceleration (ii) force (iii) momentum (iv) density