Edexcel A Level Maths: Mechanics:复习笔记4.1.1 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 you decide 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