Physical Quantities
A physical quantity is any quantity that can be measured and expressed using a number and a unit.
Examples:
- Length
- Mass
- Time
- Velocity
- Force
Every physical quantity consists of:
- Numerical value
- Unit
🔹 Units
A unit is a standard quantity used to measure a physical quantity.
Example:
- Length → metre (m)
- Mass → kilogram (kg)
- Time → second (s)
🔹 Types of Units
1️⃣ Fundamental Units
These are independent units and cannot be derived from other units.
| Physical Quantity | SI Unit | Symbol |
|---|---|---|
| Length | metre | m |
| Mass | kilogram | kg |
| Time | second | s |
| Electric current | ampere | A |
| Temperature | kelvin | K |
| Amount of substance | mole | mol |
| Luminous intensity | candela | cd |
2️⃣ Derived Units
These units are obtained from fundamental units.
| Quantity | Unit | Symbol |
|---|---|---|
| Velocity | metre/second | m/s |
| Acceleration | m/s² | m/s² |
| Force | newton | N |
| Energy | joule | J |
🔹 SI System of Units
The International System of Units (SI) is the most widely used system in science.
Advantages of SI system:
- Internationally accepted
- Simple and logical
- Decimal-based system
- Easy conversion
🔹 Measurement of Length
Common methods:
- Metre scale – everyday measurements
- Vernier calipers – small lengths
- Screw gauge – very small thickness
- Spherometer – radius of curvature
🔹 Measurement of Mass
- Beam balance
- Electronic balance
- Standard unit: kilogram (kg)
🔹 Measurement of Time
- Atomic clocks
- Cesium atomic clock is the most accurate
- SI unit: second (s)
🔹 Accuracy and Precision
- Accuracy: How close a value is to the true value
- Precision: How close repeated measurements are to each other
High precision does not always mean high accuracy.
🔹 Errors in Measurement
An error is the difference between the measured value and the true value.
Types of Errors:
1️⃣ Systematic Errors
- Instrumental errors
- Observational errors
- Environmental errors
2️⃣ Random Errors
- Occur due to unknown causes
- Reduced by taking multiple readings
🔹 Absolute, Mean and Relative Error
- Absolute Error
Difference between measured value and true value - Mean Absolute Error
Average of absolute errors - Relative Error
Ratio of mean absolute error to mean value
🔹 Significant Figures
Significant figures show the precision of a measurement.
Rules:
- All non-zero digits are significant
- Zeros between non-zero digits are significant
- Leading zeros are not significant
- Trailing zeros are significant only if decimal is present
Example:
- 0.0025 → 2 significant figures
- 2.50 → 3 significant figures
🔹 Dimensions of Physical Quantities
Dimensions show the nature of a physical quantity.
Example:
- Velocity → [LT⁻¹]
- Force → [MLT⁻²]
- Energy → [ML²T⁻²]
🔹 Dimensional Formula
It represents a physical quantity in terms of fundamental quantities.
Uses of Dimensional Analysis:
- To check correctness of equations
- To convert units
- To derive relationships between quantities
🔹 Limitations of Dimensional Analysis
- Cannot determine numerical constants
- Cannot derive complex equations
- Not applicable to trigonometric and exponential functions