Calculating Moments & Principle of Moments

(c) make calculations using moment of a force = force × perpendicular distance from the pivot and the principle of moments.

We have already covered that the moment of a force = force applied * perpendicular distance from the pivot. In this post, we will solve a few more questions to further clarify this topic.

The weight of person A is 1000 N. His distance from the pivot is 1m. Therefore, the moment due to his weight, that is the clockwise moment is equal to force * perpendicular distance from the pivot i.e 1000 * 1
= 1000 Nm.

Person B weighs 500 N. Now, you might think that as person B weighs lesser than person A, the moment due to his weight would be lesser than person A. This can not be decided until we see the distance from the pivot, that is 2 m. Calculating the moment, 500 * 2 = 1000 Nm, we see that the anticlockwise moment due to person B is equal to the clockwise moment due to the weight of person A.

Therefore, we must always keep in mind that force and perpendicular distance from the pivot both play an important role in determining the moment of a force.

Principle of Moments 

The principle of moments state that the total moment produced by several different forces applied at the same point, is equal to the the moment produced by the sum of those forces. 

Let's say we apply three forces of 3, 5 and 10 N at a distance of 1 m from the pivot. Now, the moment produced by these forces would be (3 * 1) +  (5 * 1) + (10 * 1) = 18 Nm

Now according to the principle of moments, this moment should always be equal to the moment produced by the sum of these forces, if applied at the same point. The sum of these forces is 10 + 5 + 3 = 18 N. Now calculating the moment, 18 * 1 = 18 Nm, which is equal to our value in the first place.