Law of Moments & Stability (Oxford AQA IGCSE Physics)

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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

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 $F_{1}$ causes an anticlockwise moment of $F_{1} \times d_{1}$ about the pivot
- Force $F_{2}$ causes a clockwise moment of $F_{2} \times d_{2}$ about the pivot
- Force $F_{3}$ causes an anticlockwise moment of $F_{3} \times d_{3}$ about the pivot

Collecting the clockwise and anticlockwise moments:
- Sum of the clockwise moments = $F_{2} \times d_{2}$
- Sum of the anticlockwise moments = $(F_{1} \times d_{1}) + (F_{3} \times d_{3})$

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

Sum of the clockwise moments = Sum of the anticlockwise moments

$F_{2} \times d_{2} = (F_{1} \times d_{1}) + (F_{3} \times d_{3})$

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), $F_{c h i l d} = 140 N$
Anticlockwise force (adult), $F_{a d u l t} = 690 N$
Distance of adult from the pivot, $d_{a d u l t} = 0.3 m$

Step 2: Write down the relevant equation

Moments are calculated using:

$M = F \times d$

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

$M_{c h i l d} = F_{c h i l d} \times d_{c h i l d}$

$M_{c h i l d} = 140 \times d_{c h i l d}$

Step 4: Calculate the total anticlockwise moments

The anticlockwise moment is from the adult

$M_{a d u l t} = F_{a d u l t} \times d_{a d u l t}$

$M_{a d u l t} = 690 \times 0.3$

$M_{a d u l t} = 207 N m$

Step 5: Substitute into the principle of moments equation

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

$140 \times d_{c h i l d} = 207$

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

$d_{c h i l d} = \frac{207}{140}$

$d_{c h i l d} = 1.5 m$

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

Exam 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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