The Principle of Moments in IGCSE Physics — How to Balance a Seesaw

Two students sit on opposite ends of a seesaw. One student is heavier, so their side goes down. Then the heavier student slides closer to the middle, and the seesaw balances. Their weight stayed the same. What changed was its turning effect.

In Cambridge IGCSE Physics, that turning effect is called the moment of a force. The same idea explains why a long spanner makes a tight nut easier to turn and why a door handle is placed far from the hinges. Cambridge IGCSE Physics syllabus, Section 1.5.2

How do you calculate the moment of a force?

Moment = force × perpendicular distance from the pivot to the force’s line of action

The pivot is the point about which the object turns. Measure the force in newtons (N) and the distance in metres (m). The moment is measured in newton metres (N m).

On a level seesaw, the students’ weights act vertically downwards. The perpendicular distance is the horizontal distance from the pivot to where each weight acts. A downward force on the left tends to turn the seesaw anticlockwise. A downward force on the right tends to turn it clockwise.

Worked example — where should the heavier student sit?

A student weighing 240 N sits 1.5 m to the left of the pivot. A second student weighing 360 N sits on the right. The seesaw is symmetrical, so its own weight acts through the pivot and produces no moment about it.

1. Calculate the anticlockwise moment.

240 N × 1.5 m = 360 N m

2. Use the principle of moments.

When the seesaw balances, the total clockwise moment equals the total anticlockwise moment. The heavier student must therefore produce a clockwise moment of 360 N m.

3. Find the distance from the pivot.

Distance = moment ÷ force = 360 N m ÷ 360 N = 1.0 m

The heavier student should sit 1.0 m to the right of the pivot. Their greater weight acts over a shorter distance, so both students produce the same turning effect.

What happens if the heavier student moves farther out?

Suppose the heavier student moves to 1.2 m from the pivot. Their clockwise moment becomes 360 × 1.2 = 432 N m. The other student still produces 360 N m anticlockwise.

The resultant moment is 432 − 360 = 72 N m clockwise, so the right side goes down. If an exam asks for the resultant moment, give both its size and direction.

Try it yourself

A 150 N downward force acts 80 cm to the left of a pivot. What downward force must act 0.5 m to the right to balance it?

Answer — Convert 80 cm to 0.80 m. The anticlockwise moment is 150 × 0.80 = 120 N m. To match it, the force on the right must be 120 ÷ 0.5 = 240 N.

Frequently asked questions

Does a force acting through the pivot produce a moment?

Its moment about that pivot is zero because the perpendicular distance is zero.

What if the force acts at an angle?

Use the shortest distance from the pivot to the line along which the force acts. That distance must meet the force’s line of action at a right angle.

If your child can calculate moments but gets stuck identifying the direction or the perpendicular distance, bring a recent question to a free TheTuitionE demo class.