What is a Moment?

A moment, sometimes called torque, measures the rotational impact made by a force applied at a distance from a pivot point or axis of rotation. It measures to what extent a force acting on an object makes that object revolve around a given point. The moment is calculated by multiplying the magnitude of the applied force by the perpendicular distance from the line of action of that force to the pivot point. It plays a key role in almost all fields, such as physics and engineering, because it can help one study the behavior of structures, mechanisms, or machines under variable load conditions. Understanding moments: predicts how forces will cause objects to turn, bend, or shift, so it is useful for designing stable structures and efficient mechanical systems.

Formula 

The formula for the moment is expressed as

 Moment of force = F x d

Where,

•  F is the force applied,

•  d is the distance from the fixed axis,

 The moment of force is measured in Newton meter (Nm).

The moment of force formula can be utilized to calculate the moment of force when forces are balanced or unbalanced.

Solved Problems

Problem 1: A 200 cm meter rule is pivoted at the middle point (at 50 cm point). If the weight of 10 N is hung from the 30 cm mark and a weight of 20 N is hung from its 60 cm mark, identify whether the meter rule will remain balanced over its pivot or not.

Solution:

According to the principle of moments, when an object is in rotational equilibrium, then

Total anticlockwise moments = Total clockwise moments

Total anticlockwise moments:

Length of lever arm = (50 – 30) 

= 20 cm

= 0.20 m

Since the length of the lever arm is the distance from its mid-point, where its balanced force applied = 10 N

Anticlockwise moment = Lever arm x Force applied

= 0.20 x 10 

= 2 Nm

Clockwise moment: Length of lever arm = (60 – 50)

= 10 cm

= 0.10 m.

Being that the length of the lever arm is the distance from the mid-point, about which balanced Force applied = 20 N

Clockwise moment = lever arm x force applied

= 0.10 × 20 

= 2 Nm

So

The total anti-clockwise moment = total clockwise moment = 2 Nm. According to the principle of moments, it is in rotational equilibrium ie, the meter rule remains balanced about its pivot.

Problem 2: A meter rule is pivoted at its middle point. If a weight of 2 N is allowed to hang from the 20 cm point, calculate the amount of weight required to be applied at the 80 cm mark to keep it in a balanced position.

Solution:

According to the principle of moments, To keep an object in rotational equilibrium, the sum of anticlockwise moments and clockwise moments acting should be equal. Thus, the weight to be hanged from the 80 cm mark should be such that it produces a clockwise moment equal to the anticlockwise moment produced by the weight hanged on the left hand side of the meter rule.

Anticlockwise moment:

Length of lever arm = (50 – 20)

= 30 cm

= 0.30 m

As length of lever arm is distance from mid-point, it is balanced there

Force applied = 2 N

Anticlockwise moment = lever arm x force applied

= 0.30 x 2 N

= 0.6 Nm

Clockwise moment:

length of lever arm = (80 – 50)

= 30 cm

= 0.30 m

Since the length of the lever arm is the distance from its Force applied.

Let it be 'F'.

So, the clockwise moment = F x 0.30

 = 0.30 F Nm

Clockwise moment = Anticlockwise moment

0.30 F = 0.6

 F = 2 N

A weight of 2 N must be hanged from an 80 cm point to keep the meter rule balanced.