Fundamentals and Derived Quantities and Units – SS1 Physics Lesson Note (First Term)

Fundamental quantities are the basic physical quantities that do not depend on other quantities, and derived quantities are formed by combining them.

Behavioural objectives

By the end of the lesson, students should be able to:

1. define fundamental quantities, fundamental units, derived quantities and derived units;
2. list the fundamental quantities with their S.I. units and symbols;
3. give examples of derived quantities, their derivations and their units;
4. state the differences between fundamental and derived units;
5. state the dimensions of common physical quantities in terms of M, L and T.

What are systems of units?

A system of units is a set of agreed standard units used to measure physical quantities.

• Physical quantity: anything that can be measured, such as length, mass, time or speed.
• Unit: the standard amount used to measure a quantity, such as the metre for length.
• Why units matter: a unit must be defined before any measurement can be made.

There are four systems of units: FPS, CGS, MKS and S.I.

• S.I. units: the International System of Units, now accepted all over the world.
• Two groups: physical quantities are divided into fundamental quantities and derived quantities.

What are fundamental quantities and units?

Fundamental quantities are the basic quantities that are independent of others and cannot be defined in terms of other quantities.

• Fundamental units: the units of the fundamental quantities. All other units depend on them.
• Other name: fundamental quantities are also called base quantities.
• Link to derived quantities: every derived quantity is built from the fundamental quantities.

What are the three most important fundamental quantities?

The three most important fundamental quantities in mechanics are length, mass and time.

• Length: the distance between two points. It is measured with a metre rule or tape.
• Mass: the quantity of matter in a body. It is measured with a beam balance.
• Time: the interval between two events. It is measured with a clock or stopwatch.

What are the S.I. fundamental quantities and their units?

There are seven S.I. fundamental quantities, each with its own unit and symbol.

What are derived quantities and units?

Derived quantities are quantities obtained by combining fundamental quantities, and their units are called derived units.

• Dependence: derived quantities and units depend on the fundamental quantities and units.
• Derivation: a formula showing how the derived quantity is made from other quantities.

What are examples of derived quantities?

How do you obtain the unit of a derived quantity?

You obtain a derived unit by replacing each quantity in its formula with its unit.

1. Write the formula of the derived quantity.
2. Replace each quantity with its S.I. unit.
3. Simplify using the rules of indices.

• Volume: m × m × m = m³, read as “cubic metre” or “metre cubed”.
• Density: kg/m³ = kg m^-3, read as “kilogram per metre cubed”.
• Velocity: a car covers 120 m in 10 s, so velocity = 120 m/10 s = 12 m s^-1.
• Force: kg × m s^-2 = kg m s^-2, which is called the newton (N).

What are the differences between fundamental and derived units?

A fundamental unit is the unit of a fundamental quantity, and it is defined on its own.

A derived unit is the unit of a derived quantity, and it is obtained by combining fundamental units.

What are the dimensions of physical quantities?

The dimension of a physical quantity shows how it is related to the quantities mass, length and time.

• Mass: its dimension is M.
• Length: its dimension is L.
• Time: its dimension is T.

How do you find the dimension of a quantity?

1. Write the formula of the quantity.
2. Replace each quantity with its dimension (M, L or T).
3. Simplify using the rules of indices.

• Velocity: length/time = L/T = LT^-1.
• Acceleration: velocity/time = LT^-1/T = LT^-2.
• Force: mass × acceleration = M × LT^-2 = MLT^-2.
• Pressure: force/area = MLT^-2/L² = ML^-1T^-2.

Evaluation

1. Define a fundamental quantity and give three examples with their units.
2. What is a derived quantity? Show how the unit of density is obtained.
3. Write the derivation and the unit of force.
4. State the dimensions of velocity and momentum.
5. Name three systems of units that have been used in the past.

Assignment

1. State the dimension of the following quantities:
   • (a) Acceleration
   • (b) Pressure
   • (c) Density
2. From the quantities given below, list the derived and fundamental quantities in a table: velocity, mass, weight, length, volume, density, torque, speed, acceleration, power, energy, temperature, heat capacity, electric current, relative density.