Dimensional Formula of Coefficient of Friction

The dimensional formula of coefficient of friction is given by,

[M⁰ L⁰ T⁰]

Where,

• M = Mass
• L = Length
• T = Time

Derivation

Coefficient of friction (μ) = Frictional Force × [Normal Force]^-1 . . . . (1)

Since, Force (F) = Mass × acceleration = Mass × velocity × [Time]^-1

And, velocity = Displacement × [Time]^-1

∴ The dimensions of Force = [M] × [LT^-1] × [T]^-1 = [M¹ L¹ T^-2] . . . . (2)

On substituting equation (2) in equation (1) we get,

Coefficient of friction (μ) = Frictional Force × [Normal Force]^-1

Or, μ = [M¹ L¹ T^-2] × [M¹ L¹ T^-2]^-1 = [M⁰ L⁰ T⁰].

Therefore, the coefficient of friction is dimensionally represented as [M⁰ L⁰ T⁰].

⇒ Check Other Dimensional Formulas:

• Dimensions of Linear Density
• Dimensions of Impedance
• Dimensions of Energy Density
• Dimensions of Universal Gas Constant
• Dimensions of Gravitational Potential Energy