Law of Moments & Stability (Oxford AQA IGCSE Physics)

Revision Note

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 Tip

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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