VOOZH about

URL: https://www.geeksforgeeks.org/physics/dimensional-formula-of-torque/

⇱ Dimensional Formula of Torque - GeeksforGeeks

  • Courses
  • Tutorials
  • Interview Prep

Dimensional Formula of Torque

Last Updated : 23 Jul, 2025

What is the Dimensional Formula of Torque?

Dimensional Formula of torque is [ML2T -2]

Dimensional Formula represents a physical quantity in terms of its fundamental unit with suitable dimensions. Every physical quantity is represented in terms of some fundamental quantities.

In this article, we study what is dimensional formula of torque, how to derive the dimensional formula of Torque.

Dimensional Formula is the representation of physical quantity in terms of the combination of seven fundamental physical quantities.

Torque Definition

Torque is a measure of the force that can cause an object to rotate about an axis.

Torque is what causes angular acceleration in an object about an axis. Hence, torque can be defined as the rotational equivalent of linear force.

Torque Formula

Mathematically torque is represented as

τ = Fr sin(θ)

Where,

  • r is the length of the lever arm
  • θ is the angle between the force vector and the lever arm.

👁 torque

Derivation of Dimensional Formula of Torque

We derive dimensional formula of torque. Since we have seen that torque of an object at a distance r and having angle θ with lever arm is

Torque= Force × distance × sin(θ)

Dimensional formula of τ = dimensional formula of F × r × sin(θ) .....(1)

Now we calculate the dimensional formula of each quantity individually

Dimensional formula of F = [MLT-2]

Dimensional formula of r = [M0L1T0]

Dimensional formula of sin(θ) = [M0L0T0]

Putting all the above three dimensional formulas in Equation (1) we get

Dimensional Formula of Torque = [MLT-2] × [M0L1T0] × [M0L0T0]

Dimensional Formula of Torque = [ML2T-2]

Hence the dimensional formula of Torque is [ML2T-2]

Advantages of Dimensional Formula

There are various advantages of representing a physical quantity through its dimensional formula like:

  • Dimensional Formula can be used to check the consistency of a dimensional equation.
  • It can be used to derive the relation between physical quantities in physical phenomena. Like in equation v = u + at, we can relate acceleration and time.
  • It can be used to change units from one system to another conveniently.
  • It can be used to find the dimension of constants in a given relation.

Also, Check

Comment

Explore