Dimensional Formula of Torque

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.

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.

Dimensional Formula of Torque – FAQs

1. What is Dimensional Formula?

Dimensional Formula is a representation of any quantity in terms of 7 fundamental quantities.

2. Define Torque.

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

3. What are the SI unit of Torque?

We can derive the SI units of potential energy from its dimensional formula. The formula is ML²T^-2 so its SI unit is kg m²s^-2. It is also N-m

4. What is Energy?

Energy is defined as the ability to do work.

5. What is the Dimensional Formula of Energy?

The dimensional formula of Energy is ML²T^-2.

6. Is Dimension of Torque and Energy same?

Yes the dimensional formula of Torque and energy is same as both are physically the same thing.

7. Is Dimensional Formula of Torque and Work Same?

Yes, Dimensional Formula of Torque and Work is same and is equal to ML²T^-2.