Dimensions and Derivation of Torque - Testbook

The Dimensional Formula of Torque Explained

To fully comprehend the concept of torque, let's delve into its dimensional formula.

M ¹ L ² T ^-2

In this formula, the symbols represent:

• M = Mass
• L = Length
• T = Time

Understanding the Derivation

The formula for torque (T) is derived from Moment of Inertia and Angular Acceleration. Let's represent this as equation (1):

Torque (T) = Moment of Inertia × Angular Acceleration

The Moment of Inertia (M.O.I) is calculated as the product of the square of the Radius of Gyration and Mass.

Hence, the dimensional formula of Moment of Inertia is M ¹ L ² T ⁰ , which we can denote as equation (2).

Furthermore, Angular Acceleration is the product of Angular velocity and the inverse of Time.

Consequently, the dimensional formula of Angular Acceleration is M ⁰ L ⁰ T ^-2 . Let's denote this as equation (3).

By substituting equations (2) and (3) into equation (1), we can derive the formula for Torque.

Torque = Moment of Inertia × Angular Acceleration

Or, I = [M ¹ L ² T ⁰ ] × [M ⁰ L ⁰ T ^-2 ] = [M L ² T ^-2 ].

As a result, we can state that the dimensional representation of torque is [M L ² T ^-2 ].

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