Measurement and Physical Quantities
Definition of Physical Quantity
Physical quantities are quantities that can be measured and in terms of which laws of physics are described. Examples include length, mass, time, force, and energy. These quantities are fundamental to understanding and describing the physical world.
Types of Physical Quantities
Physical quantities are classified into two main types:
- Fundamental Quantities: These are quantities that cannot be expressed in terms of any other physical quantities. Examples include length, mass, time, electric current, temperature, luminous intensity, and the amount of substance.
- Derived Quantities: These are quantities that can be expressed in terms of fundamental quantities. Examples include area, volume, velocity, acceleration, and force.
Examples of Fundamental and Derived Quantities
| Quantity Type | Examples |
|---|---|
| Fundamental | Length, Mass, Time |
| Derived | Area, Volume, Velocity, Force |
Systems of Measurement
Measurement systems provide a standard for comparing physical quantities. The common systems used in mechanics include:
- FPS System: The British Engineering system uses foot, pound, and second as the basic units for measuring length, mass, and time, respectively.
- CGS System: The Gaussian system uses centimeter, gram, and second as the basic units for measuring length, mass, and time, respectively.
- MKS System: This system uses meter, kilogram, and second as the basic units for measuring length, mass, and time, respectively.
- SI Units: The International System of Units (SI) is a globally accepted system that uses a standard scheme of symbols, units, and abbreviations. It includes seven fundamental units as shown below:
SI Base Quantities and Units
| Base Quantity | SI Units | Unit Symbol | Definition |
|---|---|---|---|
| Length | meter | m | One meter is the length of the path traveled by light in vacuum in \( \frac{1}{299,792,458} \) of a second (1983). |
| Mass | kilogram | kg | One kilogram is the mass of the prototype cylinder of platinum-iridium alloy, preserved at the International Bureau of Weights and Measures, Paris (1901). |
| Time | second | s | One second is the duration of 9,192,631,770 periods of radiation corresponding to the transition between the two hyperfine levels of the ground state of Cesium-133 atom (1967). |
| Electric Current | ampere | A | One ampere is the constant current which, when maintained in each of two straight parallel conductors of infinite length and negligible cross-section, held one meter apart in vacuum, produces a force per unit length of \(2 \times 10^{-7} \) N/m between them (1948). |
| Temperature | kelvin | K | One kelvin is the fraction of \( \frac{1}{273.16} \) of the thermodynamic temperature of the triple point of water (1967). |
| Amount of Substance | mole | mol | One mole is the amount of substance containing as many elementary entities as there are atoms in 0.012 kg of pure carbon-12 (1971). |
| Luminous Intensity | candela | cd | One candela is the luminous intensity in a given direction of a source that emits monochromatic radiation of frequency \( 5.4 \times 10^{14} \) Hz and has a radiant intensity of \( \frac{1}{683} \) watt/steradian in that direction (1979). |
Derived Quantities and their Units
| Physical Quantity | Expression | Unit |
|---|---|---|
| Area | length × breadth | \( \text{m}^2 \) |
| Volume | area × height | \( \text{m}^3 \) |
| Velocity | displacement / time | \( \text{m/s} \) |
| Acceleration | velocity / time | \( \text{m/s}^2 \) |
| Force | mass × acceleration | \( \text{N} \) ( \( \text{kg m/s}^2 \)) |
| Pressure | force / area | \( \text{Pa} \) ( \( \text{N/m}^2 \)) |
| Energy (work) | force × distance | \( \text{J} \) ( \( \text{N m} \)) |
| Power | work / time | \( \text{W} \) ( \( \text{J/s} \)) |
Importance of Measurement
The process of measurement is fundamental to all scientific studies and experiments. Measurement allows for the comparison of quantities and provides a basis for verifying scientific theories and laws.
Definition of Unit and its Types
A unit is an arbitrarily chosen standard of measurement of a quantity, which is accepted internationally. The units in which the fundamental quantities are measured are called fundamental or base units, and the units of measurement for all other physical quantities are called derived units.
Types of Measurement Systems
The measurement systems include:
- FPS System (Foot, Pound, Second)
- CGS System (Centimeter, Gram, Second)
- MKS System (Meter, Kilogram, Second)
- SI Units (International System of Units)
π radian = 180°
1 radian = \( \frac{180}{π} \) ≈ 57.27°
Also, 1° (degree of arc) = 60′ (minute of arc) and 1′ (minute of arc) = 60” (seconds of arc)
1° = \( \frac{π}{180} \) rad = \( 1.745 \times 10^{-2} \) rad
1′ = \( \frac{1}{60} \)° = \( \frac{1.745 \times 10^{-2}}{60} \approx 2.908 \times 10^{-4} \) rad
1′′ = \( \frac{1}{3600} \)° = \( \frac{1.745 \times 10^{-2}}{3600} \approx 4.85 \times 10^{-6} \) rad
Frequently Asked Questions (FAQs)
1. What is a fundamental physical quantity?
Answer: Fundamental physical quantities are those that cannot be expressed in terms of any other physical quantities. Examples include length, mass, and time.
2. What are derived physical quantities?
Answer: Derived physical quantities are those that can be expressed in terms of fundamental quantities. Examples include area, volume, and velocity.
3. What is the FPS system?
Answer: The FPS system is the British Engineering system of units, which uses foot, pound, and second as the basic units for measuring length, mass, and time, respectively.
4. What is the CGS system?
Answer: The CGS system is the Gaussian system of units, which uses centimeter, gram, and second as the basic units for measuring length, mass, and time, respectively.
5. What is the MKS system?
Answer: The MKS system uses meter, kilogram, and second as the basic units for measuring length, mass, and time, respectively.
6. What are SI units?
Answer: SI units, or the International System of Units, are a globally accepted system that includes seven fundamental units: meter, kilogram, second, ampere, kelvin, mole, and candela.
7. How are derived quantities formed?
Answer: Derived quantities are formed by combining fundamental quantities according to specific physical laws, such as area (length × breadth) and velocity (displacement/time).
8. Why is measurement important in physics?
Answer: Measurement is crucial in physics because it allows for the comparison of quantities, the verification of scientific theories and laws, and the development of technology.
9. What is the unit of force in SI?
Answer: The unit of force in the SI system is the Newton (N), which is defined as kg · m/s².
10. What is the relationship between energy and work?
Answer: In physics, energy and work are related concepts. Work is done when a force moves an object over a distance, and this work is a transfer of energy. The unit of energy (work) is the Joule (J), which is defined as N · m.