The Principle of Moments (WJEC GCSE Physics)

Forces and Rotation

• Forces can cause the rotation of an object about a fixed pivot
• This rotation can be clockwise or anticlockwise

Clockwise and Anti-clockwise Rotation

Consider the hands of a clock when deciding if an object will rotate in a clockwise or anti-clockwise direction

• A force applied on one side of the pivot will cause the object to rotate

An Object Rotating Clockwise About a Pivot

The force will cause the object to rotate clockwise about the pivot

• Examples of the rotation caused by a force are:
  • A child on a see-saw
  • Turning the handle of a spanner
  • A door opening and closing
  • Using a crane to move building supplies
  • Using a screwdriver to open a tin of paint
  • Turning a tap on and off
  • Picking up a wheelbarrow
  • Using scissors

Moments

• A moment is defined as:

A turning force about a pivot

• The size of a moment is defined by the equation:

M = F × d

• Where:
  • M = moment in newton metres (N m)
  • F = force in newtons (N)
  • d = distance perpendicular to the direction of the force in metres (m)
• 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

The Moments on a Spanner

The moment depends on the force and perpendicular distance to the pivot

• Increasing the distance a force is applied from a pivot decreases the force required
  
  • If you try to push open a door right next to the hinge it is very difficult, as it requires a lot of force
  • If you push the door open at the side furthest from the hinge then it is much easier, as less force is required

Forces Required to Open a Door

A greater force is required to push open a door next to the hinges than at the door handle

The Principle of Moments

• The principle of moments states that:

For a body in equilibrium, the sum of the clockwise moments equals the sum of the anticlockwise moments about the same pivot

• A body in equilibrium means the moments on both sides of the pivot are equal and balanced

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

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