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1.4.2Forces and Motion

The Principle of Moments

5 min read 5 parts Lesson 22 of 23 Unit quiz

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Section 1 of 5The Principle

1.4.2 The Principle of Moments
Statement
  • For an object in equilibrium, the total clockwise moment about any pivot equals the total anticlockwise moment about it.
Balanced
  • When the clockwise and anticlockwise moments are equal, there is no resultant turning effect, so the object does not rotate.
Unbalanced
  • If one total moment is larger, the object turns in that direction until a new balance is reached.
Any pivot
  • The principle can be applied about any chosen point, and choosing the pivot well can make calculations simpler.

Section 2 of 5Solving Problems

Use the same routine for see-saws, beams and levers.

1
Mark the pivot and list every force acting on the object, including its weight at the centre of a uniform beam.
2
Separate the forces into those turning clockwise and those turning anticlockwise.
3
Calculate each moment as force × perpendicular distance from the pivot.
4
Add the clockwise moments and add the anticlockwise moments.
5
Set the two totals equal and rearrange to find the unknown force or distance.

Section 3 of 5Forces on a Balanced Beam

Forces on a Balanced Beam
Upward force
  • The pivot pushes up with a force equal to the total downward force when the beam is balanced and stationary.
Two conditions
  • A balanced object has no resultant force and no resultant moment.
Uniform beam
  • The weight of a uniform beam acts at its midpoint, so it produces a moment if the pivot is off-centre.
Lever advantage
  • A small force far from the pivot can balance a large force close to the pivot.
SideForce (N)Distance (m)Moment (N m)
Anticlockwise (child)3001.5450
Clockwise (adult)4501.0450

Section 4 of 5Worked Example

Question

  • A child weighing 300 N sits 1.5 m from the pivot of a see-saw.
  • At what distance from the pivot must an adult weighing 450 N sit on the other side for the see-saw to balance?

  1. Anticlockwise moment = 300 × 1.5 = 450 N m.
  2. For balance, clockwise moment = 450 N m.
  3. 450 × d = 450.
  4. d = 450 ÷ 450 = 1.0 m.

Answer 1.0 m from the pivot.

Section 5 of 5Exam Checklist & Tips

1.4.2 – Key Points for the Exam

  • Principle of moments Total clockwise moment equals total anticlockwise moment for a balanced object.
  • Equilibrium The state in which there is no resultant force and no resultant moment on an object.
  • Lever A rigid bar that turns about a pivot to make a force easier to apply.
  • Uniform Having the same mass distribution throughout, so the weight acts at the geometric centre.
  • Reaction force The upward push of the pivot or support on the object.

Common Mistakes

  • Using the distance from the end of the beam instead of from the pivot.
  • Adding clockwise and anticlockwise moments together instead of comparing them.
  • Leaving out the weight of the beam when the pivot is not at the centre.
  • Forgetting that the pivot supports the whole weight, so its upward force equals the total downward force.
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