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Centre of Gravity is taught in the note for Forces in Equilibrium. Read it below and look for the section on this topic.

Forces in Equilibrium

12 min read

The moment of a force

A force can turn an object about a point called the pivot. The turning effect is the moment of the force. It is bigger when the force is bigger and when it acts further from the pivot. That is why a long spanner turns a stiff nut more easily.

Moment = force × perpendicular distance from the pivot. The unit is the newton metre (N m).
  • force (N)
  • perpendicular distance from the pivot (m)
Moment of a forceA spanner turning a nut. The pivot is the centre of the nut. A downward force F acts on the handle at a perpendicular distance d from the pivot, so the moment is F times d.Fd (perpendicular distance)pivotspannermoment = F × d
The force stays at 20 N. Watch the moment grow as the force acts further from the pivot.

The principle of moments

Principle of moments
When an object is balanced, the total clockwise moment about any pivot equals the total anticlockwise moment about it.
Try itBalance the beam

Change the weights and their distances. The beam balances when the two moments are equal.

A balanced see-sawA plank balanced on a pivot. A 300 newton weight sits 2 metres to the left and a 400 newton weight sits 1.5 metres to the right. The clockwise and anticlockwise moments are both 600 newton metres.300 N400 N2 m1.5 m300 × 2 = 600 N m400 × 1.5 = 600 N mpivot
Balance: 300 × 2 = 400 × 1.5. Both moments are 600 N m.
Worked exampleA see-saw

A child of weight 300 N sits 2 m from the pivot of a see-saw. Where must a 400 N child sit on the other side to balance it?

  1. Anticlockwise moment.
  2. Clockwise moment must equal this.
  3. Solve.

Answer: The second child sits 1.5 m from the pivot.

Centre of gravity and kinds of equilibrium

The centre of gravity is the point where the whole weight of an object seems to act. An object is in equilibrium when it is balanced and not accelerating.

Three kinds of equilibriumA cone standing on its base is stable, a cone balanced on its tip is unstable, and a ball on a flat table is neutral. The red dot marks the centre of gravity of each.Stabletilt it, it falls backcentre of gravity risesUnstabletilt it, it topplescentre of gravity fallsNeutralroll it, it stays putcentre of gravity stays level
TypeIf you tilt it a little…ExampleCentre of gravity
Stableit returns to its positiona cone on its baserises when tilted
Unstableit falls overa cone balanced on its tipfalls when tilted
Neutralit stays in its new positiona ball on a tablestays at the same height
Check yourself A force of 20 N acts 0.5 m from a pivot. What is its moment?
Check yourself A cone resting on its flat base is in…

Key terms

Moment
The turning effect of a force: force × perpendicular distance.
Pivot
The fixed point an object turns about.
Equilibrium
Balanced: no resultant force and no resultant moment.
Centre of gravity
The point where the weight acts.

Summary

  • Moment = force × perpendicular distance from the pivot.
  • Balanced: clockwise moments = anticlockwise moments.
  • Stable, unstable and neutral equilibrium depend on how the centre of gravity moves when tilted.
Moment of a Force Types of Equilibrium