Dimensions and Dimensional Formula

Definition of Dimension

• The dimension of a unit is the power to which the fundamental units of measurement (length, mass, time, etc.) are raised to express the unit.

Dimensional Formula

• A dimensional formula is an expression that shows the powers to which the fundamental units are raised to express a derived unit.
• It is written in the form: [L]^a [M]^b [T]^c [I]^d [θ]^e [N]^f
  • L: length, M: mass, T: time, I: electric current, θ: thermodynamic temperature, N: amount of substance
  • a, b, c, d, e, f: exponents that are integers or fractions

Examples of Dimensional Formulae

• Velocity: [L]^1 [T]^-1
• Force: [L]^1 [M]^1 [T]^-2
• Energy: [L]^2 [M]^1 [T]^-2
• Pressure: [L]^-1 [M]^1 [T]^-2

Importance of Dimension

• Checking the dimension of a physical quantity is essential in physics and engineering to ensure that the units are consistent and correct.
• Dimensional analysis is used to:
  • Derive equations and formulas
  • Check the correctness of derived equations
  • Identify the type of physical quantity being measured

Dimension and Dimensional Formula

• Dimension is the power to which fundamental units of measurement (length, mass, time, etc.) are raised to express a unit.
• A dimensional formula is an expression that shows the powers to which the fundamental units are raised to express a derived unit.

Dimensional Formula Notation

• Written in the form: [L]^a [M]^b [T]^c [I]^d [θ]^e [N]^f
• L: length, M: mass, T: time, I: electric current, θ: thermodynamic temperature, N: amount of substance
• a, b, c, d, e, f: exponents that are integers or fractions

Examples of Dimensional Formulae

• Velocity: [L]^1 [T]^-1
• Force: [L]^1 [M]^1 [T]^-2
• Energy: [L]^2 [M]^1 [T]^-2
• Pressure: [L]^-1 [M]^1 [T]^-2

Importance of Dimension

• Checking the dimension of a physical quantity is essential in physics and engineering to ensure units are consistent and correct.
• Dimensional analysis is used to:
  • Derive equations and formulas
  • Check the correctness of derived equations
  • Identify the type of physical quantity being measured

Learn about the concept of dimension, dimensional formula, and how it's expressed in terms of fundamental units of measurement. Understand the powers to which the units are raised to express a derived unit.