Moments Diagrams (Edexcel A Level Maths: Mechanics): Revision Note

Moments diagrams

When an object is modelled as a particle we do not need to consider the rotation of the object due to forces. When we model an object as a rigid body then we need to consider the rotation of the object.

What is a moment?

• The moment of a force is the measure of its ability to cause a body to rotate about a specific point (usually called the pivot)

• The units for moments are newton metres (N m)

• A force can cause a body to rotate clockwise or anti-clockwise

• The moment of a force about a point is calculated by multiplying the magnitude of the force by the perpendicular distance from the line of action of the force to the point

  • We can choose the positive direction to be clockwise or anti-clockwise and the negative direction is the opposite

  • A zero moment will not cause a body to rotate

• The moment of a force about a point is zero if the line of action of the force goes through the point

• If the force is not acting perpendicular to the distance given you will need to use right-angled trigonometry to find the perpendicular distance

How do I know if a moment is clockwise or anti-clockwise?

•  A clockwise moment will cause a body to rotate in the clockwise direction

• To visualise this:

  • Imagine that the perpendicular line from the point to the force is the radius of a circle

  • The direction of the force tells you which way the circle goes round

What is the resultant moment?

• The resultant moment is the sum of all the moments acting on a body (both positive and negative)

• To find the resultant moment:

  • Define the positive direction (clockwise or anti-clockwise)

  • Add together all the moments in that direction

  • Subtract all the moments in the opposite direction

  • The overall value is the resultant moment

• The sign of the resultant moment indicates which direction the body will rotate

  • Positive will be the direction chosen as positive

  • Negative will be the opposite direction