The Principle of Moments (Edexcel IGCSE Physics)

The principle of moments

• The principle of moments states that:

  If an object is balanced, the total clockwise moment about a pivot equals the total anticlockwise moment about that pivot

• For a balanced object, the moments on both sides of the pivot are equal 

clockwise moment = anticlockwise moment

Clockwise and anticlockwise moments

Imagine holding the beam about the pivot and applying just one of the forces. If the beam moves clockwise then the force applied is clockwise.

• 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

• Remember that the moment = force × distance from a pivot

• The forces should be perpendicular to the distance from the pivot

  • For example, on a horizontal beam, the forces which will cause a moment are those directed upwards or downwards

Using the principle of moments

The clockwise and anticlockwise moments acting on a beam are balanced

• In the above diagram:

  • Force  causes an anticlockwise moment of about the pivot 

  • Force  causes a clockwise moment of about the pivot 

  • Force  causes an anticlockwise moment of  about the pivot

• Collecting the clockwise and anticlockwise moments:

  • Sum of the clockwise moments = 

  • Sum of the anticlockwise moments = 

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

Sum of the clockwise moments = Sum of the anticlockwise moments

Supporting a beam

• A light beam is one that can be treated as though it has no mass

• The supports, therefore, must exert upward forces that balance the downward acting weight of any object placed on the beam

F₁ and F₂ upwards balance the weight of the beam downwards

• As the mass in the above diagram is moved from the left-hand side to the right-hand side of the beam, force F₁ will decrease and force F₂ will increase

F₁ decreases F₂ increases keep the beam balanced

• Consider what would happen to the beam if the right-hand support was removed:

  • Force F₂ would be 0

  • The weight of the object would produce a moment about the left-hand support, causing the beam to pivot in a clockwise direction

When F₂ is removed the beam will rotate by the clockwise moment

• Therefore, the force F₂ must therefore supply an anticlockwise moment about the left-hand support, which balances the moment supplied by the object