# 5.4.2 The Principle of Moments

### The Principle of Moments

• The principle of moments states that:

If an object is balanced, the total clockwise moment about a pivot equals the total anticlockwise moment about that pivot

• Remember that the moment = force × distance from a pivot
• The forces should be perpendicular to the distance from the pivot
• For example, on a horizontal beam, the forces which will cause a moment are those directed upwards or downwards Moments on a balanced beam

• In the above diagram:
• Force F2 is supplying a clockwise moment;
• Forces F1 and F3 are supplying anticlockwise moments
• Due to the principle of moments, if the beam is balanced

Total clockwise moments = Total anticlockwise moments

• Hence:

F2 × d2 = (F1 × d1) + (F3 × d3)

#### Worked Example

A parent and child are at opposite ends of a playground see-saw. The parent weighs 690 N and the child weighs 140 N. The adult sits 0.3 m from the pivot. Calculate the distance the child must sit from the pivot for the see-saw to be balanced. Step 1: List the know quantities

• Clockwise force (child), Fchild = 140 N

Step 2: Write down the relevant equation

Moment = force × distance from pivot

• For the see-saw to balance, the principle of moments states that

Total clockwise moments = Total anticlockwise moments

Step 3: Calculate the total clockwise moments

• The clockwise moment is from the child

Momentchild = Fchild × dchild = 140 × dchild

Step 4: Calculate the total anticlockwise moments

• The anticlockwise moment is from the adult

Step 5: Substitute into the principle of moments equation

140 × dchild = 207

Step 6: Rearrange for the distance of the child from the pivot

dchild = 207 ÷ 140 = 1.48 m

#### Exam Tip

Make sure that all the distances are in the same units and you’re considering the correct forces as clockwise or anticlockwise, as seen in the diagram below Clockwise is defined as the direction the hands of a clock move (and anticlockwise as the opposite)  ### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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