Basic Physical Units and SI System

Study Notes

Basic Physical Units

Physical quantities are properties that can be measured. Examples include length, mass, time, temperature, and electric current.
These quantities are often represented by symbols, like 'l' for length, 'm' for mass, 't' for time.
Fundamental or base units are the units in which basic physical quantities are measured.
Derived units are formed by combining fundamental units.

SI Units (International System of Units)

The SI system is a widely used system of measurement based on seven fundamental units.
The SI system is the modern form of the metric system.
These fundamental SI units are:
- Length: meter (m)
- Mass: kilogram (kg)
- Time: second (s)
- Electric current: ampere (A)
- Thermodynamic temperature: kelvin (K)
- Amount of substance: mole (mol)
- Luminous intensity: candela (cd)
Units for other quantities are derived from these base units.
Examples of derived units include:
- Area (m²)
- Volume (m³)
- Speed (m/s)
- Acceleration (m/s²)
- Force (kg⋅m/s²) (also known as Newton, N)
- Energy (kg⋅m²/s²) (also known as Joule, J)

Dimensional Analysis

Dimensional analysis is a technique used to check the consistency of equations and to derive relationships between physical quantities.
It involves treating physical quantities as having dimensions.
The dimensions of a quantity are represented by the powers of the fundamental units involved.
Example: velocity has the dimension of length divided by time (L/T).
In dimensional analysis, one equates the dimensions of quantities on both sides of an equation, ensuring that the exponents for corresponding fundamental units are equal on both sides.
Important notes for dimensional analysis:
- Dimensional analysis helps verify the correctness of mathematical formulas.
- Dimensional analysis cannot provide the numerical value of a constant in a formula.
- This analysis is crucial when dealing with complex formulas and equations, ensuring they are consistent in their units.
Example:
- Consider the equation for the area of a circle (A = πr²).
- The dimension of area is length squared (L²).
- The dimension of the radius 'r' is length (L).
- The dimension of π is dimensionless (1).
- The dimensional consistency in this formula is confirmed as both sides have the dimensions L².
Using dimensional analysis one can also derive formulas:
- If a quantity (Q) is related to other quantities (A, B, C...) then we can determine the pattern by assuming certain powers of A, B, and C affecting Q.
- For instance, if Q = k A^x B^y C^z (where k is a constant), if the dimensions of A, B, C and Q are known, setting the dimensions equal enables solving for x, y and z.
Limitations of Dimensional Analysis:
- It cannot determine dimensionless coefficients present in equations.

Description

This quiz explores the fundamental physical units and the International System of Units (SI). You'll learn about the base units for various measurements and how derived units are formed. Test your knowledge on length, mass, time, and more with this engaging quiz.