Units of Measurement and Basic Concepts
👉 Physical Quantities
A quantity that can be measured and whose value can be expressed using a numerical value and a unit is called a physical quantity.
Examples - length, mass, time, area, volume, density, force, velocity, etc.
Physical Quantities
Scalar Quantities
Vector Quantities
🔹 Scalar Quantity - A physical quantity that has magnitude only and no specific direction is called a scalar quantity.
Examples - length, mass, time, work, area, volume, density, etc.
⭐ Scalar quantities can be added or subtracted using ordinary algebraic rules.
🔹 Vector Quantity - A physical quantity that has both magnitude and direction is called a vector quantity.
Examples - displacement, velocity, acceleration, force, etc.
⭐ Vector quantities cannot always be added or subtracted using ordinary algebraic rules. The rules of vector addition must be used.
⭐ The product of two vectors is not always a scalar. A scalar product or dot product gives a scalar quantity, while a vector product or cross product gives a vector quantity.
| Feature | Scalar Quantity | Vector Quantity |
|---|---|---|
| Information required | Magnitude only | Magnitude and direction |
| Addition and subtraction | Using ordinary algebraic rules | Using vector addition rules |
| Examples | Mass, time, area | Displacement, velocity, force |
👉 What is a Unit?
To measure a physical quantity, we compare it with a fixed, convenient and accepted standard amount of the same quantity. This standard amount is called the unit of that physical quantity.
Examples - the unit of length is metre (m), the unit of mass is kilogram (kg), and the unit of time is second (s).
🔹 Numerical Value - The value of a quantity is determined by comparing it with its unit. The number that tells how many times the unit is contained in the measured quantity is called its numerical value.
🔹 Measurement of a quantity = numerical value × unit
Example - In 5 m, 5 is the numerical value and m is the unit.
🔹 Standard Value of a Unit - The accurately defined and preserved value of a unit is its standard value. It ensures that the same unit represents the same quantity everywhere.
🔹 Dimensionless Quantity - A quantity obtained as the ratio of two quantities of the same kind has no unit. Such a quantity is called a dimensionless quantity.
Examples - relative density, refractive index, strain, etc.
Units
Fundamental Units
Derived Units
👉 Fundamental or Base Units
Units that are defined independently without the help of other units and are used to form many other units are called fundamental units or base units.
For example - length (L), mass (M), time (T).
The SI system has seven fundamental physical quantities and seven corresponding base units.
| Fundamental Quantity | SI Unit | Symbol |
|---|---|---|
| Length | metre | m |
| Mass | kilogram | kg |
| Time | second | s |
| Electric current | ampere | A |
| Thermodynamic temperature | kelvin | K |
| Amount of substance | mole | mol |
| Luminous intensity | candela | cd |
👉 Systems of Units
Different systems of units may be used to measure physical quantities. At school level, the CGS system and the SI system are commonly discussed.
Systems of Units
CGS System
SI System
| Quantity | CGS System | SI System |
|---|---|---|
| Length | centimetre (cm) | metre (m) |
| Mass | gram (g) | kilogram (kg) |
| Time | second (s) | second (s) |
👉 Derived Units
A unit formed by combining one or more fundamental units is called a derived unit.
Examples - units of area, volume, speed, acceleration, density, etc.
Area: The amount of surface enclosed within the boundary of a two-dimensional figure is called its area.
🔹 For a rectangle
| ∵ Area = | length × breadth |
| ∴ Unit of area = | unit of length × unit of length |
| = | (unit of length)² |
🔹 Units of area -
⭐ CGS system - cm² or square centimetre
⭐ SI system - m² or square metre
🔹 Area is a scalar quantity, and its unit is a derived unit.
Volume: The amount of three-dimensional space occupied by an object is called its volume.
🔹 For a cuboid
| ∵ Volume = | length × breadth × height |
| ∴ Unit of volume = | unit of length × unit of length × unit of length |
| = | (unit of length)³ |
🔹 Units of volume -
⭐ CGS system - cm³ or cubic centimetre
⭐ SI system - m³ or cubic metre
🔹 Volume is a scalar quantity, and its unit is a derived unit.
Density: The mass per unit volume of a substance is called its density.
🔹 Units of density -
⭐ CGS system - g/cm³ or gram per cubic centimetre
⭐ SI system - kg/m³ or kilogram per cubic metre
🔹 Density is a scalar quantity, and its unit is a derived unit.
Quick Revision
| Concept | Key Idea | Example |
|---|---|---|
| Physical quantity | A quantity that can be measured | Length, mass, time |
| Scalar quantity | Has magnitude only | Mass, time, area |
| Vector quantity | Has magnitude and direction | Displacement, velocity, force |
| Fundamental unit | Defined independently | m, kg, s |
| Derived unit | Formed from fundamental units | m², m³, kg/m³ |
Common Mistakes
| Incorrect Idea | Correct Idea |
|---|---|
| Any number alone is a measurement | A measurement generally requires both a numerical value and a unit. |
| Scalars and vectors are added in the same way | Scalars are added algebraically, but vector addition must take direction into account. |
| The product of two vectors is always a scalar | A dot product is scalar, but a cross product is a vector. |
| gm is the official symbol for gram | The official SI symbol for gram is g. |
| A dimensionless quantity has no value | A dimensionless quantity has a numerical value but no unit. |
