FUNDAMENTAL AND DERIVED QUANTITIES AND UNITS

Subject: 

PHYSICS

Term:

FIRST TERM

Week:

WEEK 2

Class:

SS 1

Topic:

FUNDAMENTAL AND DERIVED QUANTITIES AND UNITS

Previous lesson: 

The pupils have previous knowledge of

 INTRODUCTION TO PHYSICS

that was taught as a topic in the previous lesson

Behavioural objectives:

At the end of the lesson, the learners will be able to

• say the meaning of FUNDAMENTAL AND DERIVED QUANTITIES AND UNITS
• give examples of various FUNDAMENTAL AND DERIVED QUANTITIES AND UNITS
• explain the importance of FUNDAMENTAL AND DERIVED QUANTITIES AND UNITS
• point out the need TO UNDERSTAND THE FUNDAMENTAL AND DERIVED QUANTITIES AND UNITS

Instructional Materials:

• Wall charts
• Pictures
• Related Online Video
• Flash Cards

Methods of Teaching:

• Class Discussion
• Group Discussion
• Asking Questions
• Explanation
• Role Modelling
• Role Delegation

Reference Materials:

• Scheme of Work
• Online Information
• Textbooks
• Basic Education Curriculum
• Workbooks

Content:

Definition: A fundamental quantity is a physical quantity that cannot be expressed in terms of other quantities

Derived quantities are those physical quantities which can be expressed in terms of fundamental quantities

Units are used to express the magnitudes or values of corresponding quantities

The SI unit (International System of Units) is the modern form of the metric system and is the most widely used system of measurement

Examples

1) Length is a fundamental quantity while area is a derived quantity

2) The SI unit for length is the meter while the SI unit for area is the square meter

3) Mass is a fundamental quantity while density is a derived quantity

4) The SI unit for mass is the kilogram while the SI unit for density is the kilogram per cubic meter

5) Time is a fundamental quantity while velocity is a derived quantity

6) The SI unit for time is the second while the SI unit for velocity is the meter per second.

EVALUATION

1) What is a fundamental quantity?

A) A physical quantity that cannot be expressed in terms of other quantities

B) A physical quantity that can be expressed in terms of other quantities

C) A unit of measurement

D) The SI unit

2) What is a derived quantity?

A) A physical quantity that cannot be expressed in terms of other quantities

B) A physical quantity that can be expressed in terms of other quantities

C) A unit of measurement

D) The SI unit

3) What is a unit?

A) A physical quantity that cannot be expressed in terms of other quantities

B) A physical quantity that can be expressed in terms of other quantities

C) A way to measure a physical quantity

D) The SI unit

4) What is the SI unit?

A) The modern form of the metric system

B) The most widely used system of measurement

C) A physical quantity that cannot be expressed in terms of other quantities

D) A physical quantity that can be expressed in terms of other quantities

5) What is the SI unit for length?

A) The meter

B) The square meter

C) The kilogram

D) The second

Other Fundamental Quantities

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 =forcearea

∴ 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.

Derived quantities are those physical quantities which can be expressed in terms of the seven basic units. Examples of such derived quantities are Area, Volume, Density, Speed, Acceleration, Force, Energy, Power,Work etc. The SI unit of each physical quantity is also mentioned in the table

The SI unit of work and energy is the Joule (J), of momentum and impulse is the Newton-second (Ns), of volume is the metre cube (m3), of area is the metre square(m2), of pressure is the Pascal (Pa) which is equal to one newton per metre square, of power is the watt (W) which is equal to one joule per second, of density is the kilogramme per metre cube (kg/m3), of moment is the newton-metre (Nm) and of angular momentum is the kilogramme metre square second (kgm2s). The SI unit of angular velocity is the radian per second (rad/s) or degree per second (°/s).

The SI unit of each physical quantity is also mentioned in the table

The table lists the various dimensions and S.I units of some derived physical quantities. The first column shows the various quantities, the second column lists their corresponding dimensions while the third column provides the S.I units in which they are expressed. As can be seen, work and energy are represented in terms of the Joule, momentum and impulse by the Newton-second, volume is given in terms of the metre cube, area in terms of the metre square, pressure as the Pascal which is equal to one newton per metre square, power in watts and so on.

Evaluation

1. What is the SI unit of work and energy?

2. What is the SI unit of momentum and impulse?

3. What is the SI unit of volume?

4. What is the SI unit of area?

5. What is the SI unit of pressure?

Presentation

The topic is presented step by step

Step 1:

The subject teacher revises the previous topics

Step 2.

He introduces the new topic

Step 3:

The subject teacher allows the pupils to give their own examples and he corrects them when the needs arise

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

Conclusion

The class teacher wraps up or concludes the lesson by giving out short notes to summarize the topic that he or she has just taught.

The class teacher also goes round to make sure that the notes are well copied or well written by the pupils.

He or she does the necessary corrections when and where the needs arise.

Assignment 

Read about      DIMENSIONS AND MEASUREMENT OF PHYSICAL QUANTITIES

in preparation for the next lesson