Chapter 1 Physical Quantities and Measurement Physics Notes | Complete Guide with Formulas & Derivations
1.1 Introduction to Physics
1.2 Physical Quantities
Introduction
Physics deals with many properties of objects and physical phenomena. To study these properties scientifically, they must be expressed in a measurable form. A measurable property of a physical system is called a physical quantity.
Examples of physical quantities include length, mass, time, temperature, area, volume, speed, acceleration, force, energy, pressure, electric current, and voltage.
Physical quantities provide a quantitative way of describing the physical world. Instead of simply saying that an object is “long” or “heavy,” Physics allows us to express these properties numerically, together with appropriate units.
📖 Definition
A physical quantity is a measurable property of a physical object or phenomenon that can be expressed by a numerical value and a unit.
Components of a Physical Quantity
A physical measurement consists of two essential components:
- Numerical value
- Unit
For example:
Length = 5 m
Here:
- 5 is the numerical value.
- m is the unit.
- Length is the physical quantity being measured.
Therefore, a numerical value without a unit is generally incomplete when describing a physical measurement.
📦 Important Relationship
Physical Quantity = Numerical Value × Unit
For example:
Distance = 20 km
The value 20 tells us how many units are present, while kilometre tells us the size of the unit being used.
🖼️ Figure 1.5: Components of a Physical Quantity
Types of Physical Quantities
Physical quantities can be classified into two major categories:
- Fundamental quantities
- Derived quantities
This classification is based on whether a quantity can be expressed independently or is obtained from other physical quantities.
🖼️ Figure 1.6: Classification of Physical Quantities
Fundamental Quantities
Fundamental quantities are physical quantities that are considered independent and cannot be expressed in terms of other physical quantities.
In the International System of Units (SI), there are seven fundamental physical quantities.
| 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 |
These seven quantities form the foundation of the SI system. Many other physical quantities can be expressed in terms of them.
🔑 Key Concepts
- There are seven SI base quantities.
- Base quantities are independent of one another.
- Each base quantity has a corresponding SI base unit.
- Derived quantities are formed from combinations of base quantities.
Derived Quantities
Derived quantities are physical quantities that are obtained by combining two or more fundamental quantities mathematically.
Examples include:
- Area
- Volume
- Speed
- Acceleration
- Force
- Pressure
- Work
- Energy
- Power
- Density
Example: Area
Area is obtained from length multiplied by length:
Area = Length × Length
Therefore:
Area = m × m = m2
Example: Speed
Speed is defined as distance travelled per unit time:
Speed = Distance / Time
Therefore its SI unit is:
m/s
Example: Density
Density is mass per unit volume:
Density = Mass / Volume
Therefore:
Unit of density = kg/m3
🖼️ Figure 1.7: Fundamental and Derived Quantities
Examples of Derived Quantities
| Derived Quantity | Relationship | SI Unit |
|---|---|---|
| Area | Length × Length | m2 |
| Volume | Length × Length × Length | m3 |
| Speed | Distance / Time | m s−1 |
| Acceleration | Velocity / Time | m s−2 |
| Force | Mass × Acceleration | N |
| Pressure | Force / Area | Pa |
| Density | Mass / Volume | kg m−3 |
Scalar and Vector Quantities
Physical quantities can also be classified according to whether they require direction for their complete description.
They are divided into:
- Scalar quantities
- Vector quantities
Scalar Quantities
A scalar quantity has magnitude only and does not require a direction for its complete description.
Examples include:
- Mass
- Time
- Temperature
- Distance
- Speed
- Energy
- Volume
For example, saying that the temperature is 30 °C gives a complete description of the temperature measurement.
Vector Quantities
A vector quantity has both magnitude and direction.
Examples include:
- Displacement
- Velocity
- Acceleration
- Force
- Momentum
For example, a velocity of 20 m/s east includes both magnitude and direction.
🖼️ Figure 1.8: Scalar and Vector Quantities
Measurable and Non-Measurable Properties
Not every property of an object is a physical quantity.
A physical quantity must be measurable and expressible numerically with a suitable unit.
For example:
- Length is measurable and is therefore a physical quantity.
- Mass is measurable and is therefore a physical quantity.
- Temperature is measurable and is therefore a physical quantity.
On the other hand, properties such as beauty or intelligence are not normally treated as physical quantities in elementary Physics because they cannot be expressed by a universally defined physical unit in the same way as length, mass, or time.
Magnitude of a Physical Quantity
The magnitude of a physical quantity refers to its numerical size expressed in a particular unit.
For example:
Length = 4 m
The magnitude is 4 when the chosen unit is the metre.
If the same length is expressed in centimetres:
4 m = 400 cm
The numerical value changes when the unit changes, but the physical quantity itself remains unchanged.
💡 Important Idea
Changing the unit changes the numerical value of a measurement, but it does not change the physical quantity being measured.
🌍 Real-Life Applications
Physical quantities are used throughout everyday life.
- Distance is measured when travelling.
- Mass is measured when buying food.
- Time is measured using clocks and watches.
- Temperature is measured using thermometers.
- Speed is measured by vehicle speedometers.
- Electric current and voltage are measured in electrical systems.
- Energy consumption is measured using electricity meters.
- Pressure is measured in vehicle tyres and medical equipment.
📦 Knowledge Box
Physical quantities form the language of quantitative Physics. Once a physical property can be measured and expressed numerically with an appropriate unit, it can be compared, calculated, analysed, and used in scientific laws.
Physical Phenomenon → Measurement → Numerical Value + Unit → Scientific Analysis
💡 Did You Know?
The seven SI base quantities are sufficient to define the units of a very large number of other physical quantities. This makes the SI system a powerful and consistent system for scientific measurement throughout the world.
⭐ Important Board Points
- A physical quantity is a measurable property of a physical object or phenomenon.
- A physical measurement consists of a numerical value and a unit.
- Physical quantities are classified as fundamental and derived quantities.
- There are seven SI base quantities.
- Derived quantities are formed from combinations of fundamental quantities.
- Scalar quantities have magnitude only.
- Vector quantities have both magnitude and direction.
- Changing the unit changes the numerical value but not the physical quantity.
⚠️ Common Mistakes
❌ Thinking that a numerical value alone is a complete measurement.
✔ A physical measurement normally requires both a numerical value and an appropriate unit.
❌ Thinking that all physical quantities are fundamental quantities.
✔ Physical quantities are classified into fundamental and derived quantities.
❌ Confusing speed with velocity.
✔ Speed is a scalar quantity, whereas velocity is a vector quantity.
❌ Thinking that changing units changes the physical quantity.
✔ Changing units changes only the numerical representation of the same physical quantity.
❌ Considering area and volume as fundamental quantities.
✔ Area and volume are derived quantities obtained from length.
🔢 Solved Numerical
Example
A student measures the length of a table as 2.5 m. Express this length in centimetres.
Solution
Given:
L = 2.5 m
We know:
1 m = 100 cm
Therefore:
2.5 m = 2.5 × 100 cm
2.5 m = 250 cm
Therefore:
Answer: 250 cm
📝 Expected Board Questions
Short Questions
- Define a physical quantity.
- What are the two components of a physical quantity?
- What is a fundamental quantity?
- What is a derived quantity?
- Name the seven SI base quantities.
- Give three examples of derived quantities.
- What is a scalar quantity?
- What is a vector quantity?
- Give two examples each of scalar and vector quantities.
- Why is area considered a derived quantity?
Long Questions
- Define physical quantities and explain their classification.
- Describe the seven fundamental physical quantities and their SI units.
- Explain the difference between fundamental and derived quantities with examples.
- Differentiate between scalar and vector quantities with suitable examples.
⚡ Quick Revision
- Physical quantity: A measurable property expressed by a numerical value and a unit.
- Components: Numerical value + unit.
- Fundamental quantities: Independent physical quantities.
- Seven SI base quantities: Length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity.
- Derived quantities: Obtained by mathematical combinations of fundamental quantities.
- Scalar: Magnitude only.
- Vector: Magnitude and direction.
- Key relationship: Physical Quantity = Numerical Value × Unit.
🗺️ Mind Map
PHYSICAL QUANTITIES
↓
Numerical Value
Unit
Fundamental
Derived
Scalar
Vector
Length
Mass
Time
Force
Energy
Measurement → Numerical Value + Unit → Scientific Description
Topic 1.2 — Physical Quantities establishes the foundation for quantitative measurement in Physics by introducing physical quantities, their components, fundamental and derived quantities, scalar and vector quantities, and their practical significance.
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