ECAT Interactive Study Tool: Physical Quantities & SI Units

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Physical Quantities & SI Units

ECAT Interactive Study Tool


1. Core Theory

Base vs. Derived Quantities

Base Quantities are the fundamental physical quantities that are not defined in terms of other physical quantities (e.g., Length, Mass, Time).

Derived Quantities are those whose definitions are based on other physical quantities (e.g., Velocity, Force, Volume).

The International System of Units (SI) is built upon 7 base units: meter (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), and candela (cd).

Scientific Notation & Prefixes

In physics, we often deal with very large or very small numbers. Scientific notation expresses numbers as a product of a number between 1 and 10 and a power of 10.

Prefixes are used to denote these powers of 10, making it easier to write and say.

  • Micro ((mu)) = (10^{-6})
  • Milli (m) = (10^{-3})
  • Kilo (k) = (10^3)
  • Mega (M) = (10^6)
Dimensions of Physical Quantities

Dimension describes the qualitative nature of a physical quantity. We use square brackets ([ ]) to denote dimensions. The fundamental dimensions are Length ([L]), Mass ([M]), and Time ([T]).

For example, Velocity ((v)) is distance over time, so its dimension is ([L T^{-1}]).

[L] Width
[L] Height
[L] Depth
Volume = [L] × [L] × [L] = [L³]

Force = Mass × Acceleration

([F] = [M] times [L T^{-2}] = [M L T^{-2}])

2. Concept Check

1. True or False: A light-year is a unit of time.


2. True or False: The dimensional formula for work and energy is exactly the same.



3. Solved Examples

Example 1: Unit Conversion

Convert a speed of (72 , km/h) into SI units ((m/s)).

Step 1: Identify the conversion factors.

(1 , km = 1000 , m) and (1 , hour = 3600 , s).

Step 2: Set up the multiplier.

(72 , km/h = 72 times left( frac{1000 , m}{3600 , s} right))

Step 3: Calculate.

(72 times frac{5}{18} = 4 times 5 = 20 , m/s)

Conclusion: (72 , km/h) is equal to (20 , m/s).

Example 2: Deriving Dimensions

Find the dimensions of Kinetic Energy ((K.E = frac{1}{2}mv^2)).

Step 1: Write down the formula and remove dimensionless constants.

The constant (frac{1}{2}) has no dimensions. We only need to find the dimensions of (m) (mass) and (v^2) (velocity squared).

Step 2: Insert base dimensions.

Dimension of mass (m = [M])

Dimension of velocity (v = [L T^{-1}]), therefore (v^2 = [L^2 T^{-2}])

Step 3: Multiply them together.

([K.E] = [M] times [L^2 T^{-2}] = [M L^2 T^{-2}])

Conclusion: The dimensional formula for Kinetic Energy is ([M L^2 T^{-2}]).

4. MCQ Practice

1. Which of the following is NOT a base SI unit?




2. What is the SI unit of solid angle?




3. The prefix “pico” represents which power of ten?




4. What is the dimensional formula for Work?




5. The number of significant figures in the measurement 0.005020 is:





5. Summary Table (Base SI Units)

Base Quantity Unit Name Unit Symbol Dimension
Length meter m [L]
Mass kilogram kg [M]
Time second s [T]
Electric Current ampere A [I] or [A]
Thermodynamic Temp. kelvin K [(Theta)] or [K]
Amount of Substance mole mol [N]
Luminous Intensity candela cd [J]
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