Introduction

Force is a physical quantity or an external factor that starts the motion. Force is not only responsible for the movement of the body but also an important factor in the rotation of the body. To study in detail the effect of force on a rotating body, the concept of a physical quantity was brought into existence called the Moment of force. Let us explore in detail this moment of force.

Definition

It is a basic term in rotatory mechanics that if a body is rotating then there would be its moment of force. We can define it as:

Moment of force is the capability of force to rotate a body.

This means if we apply some amount of force on a body, then it will decide whether the body will rotate or not.

It is also known as Torque which is the turning effect of a force of a rotating body.

• It is denoted by τ.
• Its SI unit is Newton-meter (N-m) and C.G.S. unit is Dyne-centimeter.
• The dimensional formula is [M¹L²T⁻²].
• It is a vector quantity. So it has magnitude and direction both.

Formula

It is the product of the force applied to rotate the body and the perpendicular distance between the axis of rotation and the line of action where force is applied. The distance between the line of action of this force and the axis of rotation is also called the force arm. If the applied force is F and the perpendicular distance is d then we can write the formula of torque as:

Direction

It is an axial vector. Hence the direction is always along the axis of rotation. This orientation is perpendicular upward or downward to the plane surface of the rotating body. Its direction is determined by the right-hand thumb rule or screw rule.

Right hand thumb rule

We can use the right hand thumb rule to find the direction of the moment of force on a body, which can be found by following these steps (1).

1. First of all, we keep our right hand along the vector of the force arm and keep the thumb standing according to the hand in position as shown in the picture.
2. Then we bend our fingers along the direction of the force.

Here the direction of the thumb tells us the direction of the moment of force.

• If we bend the fingers in an anti-clockwise direction then the direction of the moment of force will be upward along the axis of rotation.
• When the direction of bending of fingers is clockwise, the direction of the moment of force will be down along the axis of rotation.

Difference cases

Examples

Q&A

(1) What is the moment of force?

It is the capability of force to rotate a body. Also known as Torque. It can be defined as the product of the force arm (perpendicular distance between the line of action of force and rotational axis) and applied force.

(2) How to calculate the moment of force?

Ans. We have to find the perpendicular distance between the rotational axis and the point where the force is applied. After multiplying the distance, the magnitude of force, and the sine of the angle between the position vector of force arm and force, we will get the torque. We can calculate the  by using this formula

τ = |d||F| sinθ

(3) When will the torque be maximum?

Ans. When the angle between the position vector of the distance between the line of action of force and the rotational axis and the force is 90°, then the torque will be maximum.

  τ = |d||F| sinθ

θ = 90°

_{τ max}  = d.F

(4) What are examples of moment of force?

Ans. We can consider this one real-life example. To run the hand pump, we apply force on the long pipe attached to it. When we apply force on that pipe, it starts rotating, due to the same force, the moment of force is generated on that pipe.

(5) Are torque and moment of force the same?

Ans. A physical quantity that can measure the capability of force, whether it can rotate a body or not is called torque. But a torque that is generated by a force is also called the moment of force.

Reference

Written by: Amber Soni