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## Monday, December 14, 2009

### Moment and couple

Moment

We have when earlier that a force acting on an object causes work done. Here we are going to see that if a force act on an object the a rotation can occur.

Let us look at some examples. You will see that if the force act on an object in a certain way the object would undergo a rotation about a centre of rotation.

Example 1

In this example a footballer would kick the ball and the ball would rotate about the centre of the ball the centre of rotation.

Example 2

In this example a person is opening a door by exerting a force on the door handle. The door will thus rotate about the hinge of the door.

So we can thus say that the moment is related to the turning effect of a force.

We are now going to have look at how the moment of a force is calculated.

In the diagram above we have the force F that is applied on the door handle.

The force is applied on the handle and the point on the object where the force is applied is called point of application of the force. The distance between the point of application of the force and the pivot is the distance d.

Note that the force must be at right angle to the distance d as shown in the diagram below. If it is not at right angle as shown in the second diagram below then the component of the force that is at right angle to the distance must be determined. In the case of the second diagram below the component of the force that is at right angle to the distance is Fcosθ

We can now return to the diagram shown above, and we can say that the moment can be calculated as shown below.

Moment = Force * perpendicular distance from point of application of the force to the pivot

If the force is at right angle to the distance then

moment = F *d

If the force is not at right angle to the distance then

Moment = Fcosθ*d

= Fd cosθ

Couple

A couple is when two forces of equal magnitude but acting in opposite direction on an object causing a rotation.

The best example is the car steering wheel or the handle of a motorcycle. As the diagram below shows two forces that are equal to each other in magnitude but acting in opposite direction act on an object. The point of applications of the two forces are separated by a distance d.

Hence the couple can be calculated using the equations below.

Couple = Magnitude of one of the two forces * the distance between the point of application of the two forces

couple = F* d

Of course the same principle  will apply to couple if the forces are not at right angle to the distance. Then the component of the force at right angle to the distance must be used. The couple will then be calculated using the equation

couple = Fd Cosθ