Physics

5.8 - Moments - Seesaws

8 min

How levers work

Lever calculation

How gears workOutside your course

note 1 of 5

The principle of moments

When an object is balanced about a pivot, it doesn't turn.
The turning effect of a force is its moment:

$M = F d$

where $d$ is the perpendicular distance from the pivot to the line of action of the force.

The principle of moments: for a balanced object, the total clockwise moment equals the total anticlockwise moment.

note 2 of 5

Balancing with multiple forces

If more than one force acts on the same side of a pivot, calculate the moment of each force separately and add them together to get the total moment for that side.
For the system to balance:

Total clockwise moment = total anticlockwise moment

note 3 of 5

Worked example - Balancing a seesaw

A child of weight 400 N sits 2.0 m from the pivot of a seesaw. A second child of weight 500 N sits on the other side. How far from the pivot must the second child sit for the seesaw to balance?

A seesaw on a triangular pivot with a child at each end, downward arrows labelled 400 N and 500 N, the left distance marked 2.0 m and the right a question mark.

Step 1 - Write down the balance condition

For the seesaw to balance, the total clockwise moment equals the total anticlockwise moment:

$F_{1} d_{1} = F_{2} d_{2}$

Step 2 - Substitution

The first child gives the anticlockwise moment, the second child the clockwise moment:

$400 \times 2.0 = 500 \times d_{2}$

$800 = 500 \times d_{2}$

Step 3 - Solve for the unknown distance

$d_{2} = \frac{800}{500} = 1.6 m$

The heavier child must sit 1.6 m from the pivot - closer than the lighter child, because a larger force needs a shorter distance to give the same moment.

note 4 of 5

Parallel forces on a supported beam

When a beam or rod is supported at both ends, the support closer to a downward load carries the larger upward force.
The upward forces from the supports balance the total downward force:

Total upward force = total downward force

Finding the support forces

Take moments about one support (treating it as the pivot) to calculate the upward force at the other support.
Subtract that force from the total downward load to find the remaining support force.
If the beam is described as light, its own weight is ignored.

A beam labelled light rod rests on two supports with a weight nearer the right one, upward arrows reading support force and greater support force, and a downward arrow reading weight.

note 5 of 5

Resultant moments

If the clockwise and anticlockwise moments about a pivot are not equal, they don't cancel out.
There's a resultant moment, and the object turns in the direction of the larger moment:

Resultant moment = larger moment - smaller moment

A three-bladed propeller seen face on, with a pink curved arrow down its left side labelled 20 Nm and a longer blue curved arrow down its right side labelled 40 Nm.

key terms

TermDefinition

MomentThe turning effect of a force, equal to the force multiplied by the perpendicular distance from the pivot to the line of the force.

Principle of momentsWhen an object is balanced, the total clockwise moment about a pivot equals the total anticlockwise moment.

Resultant momentThe overall turning effect when the clockwise and anticlockwise moments about a pivot are not equal.

end of notes

Key points to remember

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