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Law of Moments & Stability (Oxford AQA IGCSE Physics)

Revision Note

Leander Oates

Written by: Leander Oates

Reviewed by: Caroline Carroll

Law of Moments

  • The law of moments states that

For an object that is not turning, the total clockwise moment must be equally balanced by the total anticlockwise moment about any pivot

  • A moment is clockwise if the force applied causes the object to move in a clockwise rotation and vice versa

Clockwise and anticlockwise moments

Clockwise and anticlockwise moments for IGCSE & GCSE Physics revision notes
Imagine holding the beam about the pivot and applying just one of the forces. If the beam moves clockwise then the force applied is clockwise.

  • In the example below, the forces and distances of the objects on the beam are different, but they are arranged in a way that balances the whole system

Using the law of moments

On the left-hand side of the pivot force 1 acts at a distance of d1 in a downward direction. On the right-hand side of the pivot, force 2 acts a distance of d2 in the downward direction and force 3 acts at a distance of d3 in the upward direction. The moments are balanced.
The clockwise and anticlockwise moments acting on a beam are balanced

  • In the above diagram:

    • Force F subscript 1 causes an anticlockwise moment of F subscript 1 cross times d subscript 1 about the pivot 

    • Force F subscript 2 causes a clockwise moment of F subscript 2 cross times d subscript 2 about the pivot 

    • Force F subscript 3 causes an anticlockwise moment of F subscript 3 cross times d subscript 3 about the pivot

  • Collecting the clockwise and anticlockwise moments:

    • Sum of the clockwise moments = F subscript 2 cross times d subscript 2

    • Sum of the anticlockwise moments = open parentheses F subscript 1 cross times d subscript 1 close parentheses space plus space open parentheses F subscript 3 cross times d subscript 3 close parentheses

  • Using the principle of moments, the beam is balanced when:

Sum of the clockwise moments = Sum of the anticlockwise moments

F subscript 2 cross times d subscript 2 space equals space open parentheses F subscript 1 cross times d subscript 1 close parentheses space plus space open parentheses F subscript 3 cross times d subscript 3 close parentheses

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.

A see-saw with an adult and a child sitting on it. The adult has a weight of 690 N at 0.3 m from the pivot, the child has a weight of 140 N

Calculate the distance the child must sit from the pivot for the see-saw to be balanced.

Answer:

Step 1: List the known quantities

  • Clockwise force (child), F subscript c h i l d end subscript space equals space 140 space straight N

  • Anticlockwise force (adult), F subscript a d u l t end subscript space equals space 690 space straight N

  • Distance of adult from the pivot, d subscript a d u l t end subscript space equals space 0.3 space straight m

Step 2: Write down the relevant equation

  • Moments are calculated using:

M space equals space F space cross times space d

  • 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

M subscript c h i l d end subscript space equals space F subscript c h i l d end subscript space cross times space d subscript c h i l d end subscript

M subscript c h i l d end subscript space equals space 140 space cross times space d subscript c h i l d end subscript

Step 4: Calculate the total anticlockwise moments

  • The anticlockwise moment is from the adult

M subscript a d u l t end subscript space equals space F subscript a d u l t end subscript space cross times space d subscript a d u l t end subscript

M subscript a d u l t end subscript space equals space 690 space cross times space 0.3

M subscript a d u l t end subscript space equals space 207 space straight N space straight m

Step 5: Substitute into the principle of moments equation

Moment of child (clockwise) = Moment of adult (anticlockwise)

140 space cross times space d subscript c h i l d end subscript space equals space 207

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

d subscript c h i l d end subscript space equals fraction numerator space 207 over denominator 140 end fraction

d subscript c h i l d end subscript space equals space 1.5 space straight m

  • The child must sit 1.5 m from the pivot to balance the see-saw

Examiner Tips and Tricks

Make sure that all the distances are in the same units and that you’re considering the correct forces as clockwise or anticlockwise.

Moments & Stability

  • If the line of action of the weight of an object lies outside the base of the object, there will be a resultant moment and the body will topple

Car and bus on varying inclines

A car on various inclined planes up to 60 degrees without toppling because the line of action of its weight still lies within its base. A bus is tilted to 45 degrees before the line of action of its weight lies outside its base.
The car can be titled to 60° without toppling, but the bus will topple at 45°

  • Tall objects with a narrow base will topple easily

    • Ten-pin bowling pins are designed specifically to topple easily

  • The stability of objects can be increased by widening the base

    • High chairs are designed with a wide base so that they do not topple

    • Bunsen burners have a wide base to ensure they do not topple

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    Author
    Reviewer
    Leander Oates

    Author: Leander Oates

    Expertise: Physics

    Leander graduated with First-class honours in Science and Education from Sheffield Hallam University. She won the prestigious Lord Robert Winston Solomon Lipson Prize in recognition of her dedication to science and teaching excellence. After teaching and tutoring both science and maths students, Leander now brings this passion for helping young people reach their potential to her work at SME.

    Caroline Carroll

    Author: Caroline Carroll

    Expertise: Physics Subject Lead

    Caroline graduated from the University of Nottingham with a degree in Chemistry and Molecular Physics. She spent several years working as an Industrial Chemist in the automotive industry before retraining to teach. Caroline has over 12 years of experience teaching GCSE and A-level chemistry and physics. She is passionate about creating high-quality resources to help students achieve their full potential.