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Factors affecting moments

When you push a door closed, it doesn't travel in a straight line - it turns around the hinges. This is an example of a moment (or torque).

So there are three things that are important:

  • The size of the force.
  • The direction of the force.
  • The distance from the force to the hinge.

"A moment is defined as a force multiplied by the perpendicular distance from the line of action of the force to the pivot."

Units: Nm. Symbol, M (or sometimes T)

For equilibrium:

The sum of the clockwise moments about a point = sum of the anticlockwise moments about that point.

If you have two forces (for instance, a couple of forces) acting on an object and the forces are:

  • parallel
  • in opposite directions
  • of equal size
  • not along the same line of action

...you have got a couple.

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You need to check that two conditions are satisfied before you can say that something is in equilibrium.

  • The sum of the forces in any direction = 0. If this is satisfied, the object will have no linear acceleration (for instance, it won't accelerate in any direction).
  • The sum of the moments about any point (not just the pivot point) = 0. If this is satisfied, there is no angular (or circular) acceleration (for instance, the object won't rotate faster or slower.)

We write these two in short hand as:

Σ F = 0

Σ M = 0

This is a quick way of finding out if the forces acting on an object are in equilibrium.

This object experiences three forces.

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If it is in equilibrium then drawing accurate vector diagrams of each force one after the other will produce a closed triangle.

Why is it useful?

When doing moment calculations you can say that all the weight of an object acts through the Centre of Gravity.

Centre of Gravity = the point where all the weight seems to be concentrated.

Centre of Mass = the point where all the mass seems to be concentrated.

For regular shapes it is the geometrical centre of the object - for example, the centre of a cube or a sphere.

For irregular shapes, hang the object from a point on its edge and the Centre of Gravity will end up vertically below the point you are hanging it from.