Dimensional Formula of Torque

The dimensional formula of torque is given by,

M¹ L² T^-2

Where,

• M = Mass
• L = Length
• T = Time

Derivation

Torque (T) = Moment of Inertia × Angular Acceleration . . . . (1)

Since, Moment of Inertia (M.O.I) = Radius of Gyration² × Mass

∴ The dimensional formula of Moment of Inertia = M¹ L² T⁰ . . . (2)

And, Angular Acceleration = Angular velocity × Time^-1

∴ The dimensional formula of Angular Acceleration = M⁰ L⁰ T^-2 . . . (3)

On substituting equation (2) and (3) in equation (1) we get,

Torque = Moment of Inertia × Angular Acceleration

Or, I = [M¹ L² T⁰] × [M⁰ L⁰ T^-2] = [M L² T^-2].

Therefore, the torque is dimensionally represented as [M L² T^-2].

⇒ Check Other Dimensional Formulas:

• Dimensions of Linear Momentum
• Dimensions of Light Year
• Dimensions of Time Period
• Dimensions of Boltzmann Constant
• Dimensions of Universal Gas Constant