Two equal and unlike opposite and parallel forces acting along different lines on a body constitute a couple.
When a force is applied on a rigid body which can pivot on a point or fulcrum, in this point appears a reaction force that constitutes a couple with the original applied force. The couple is formed between the applied and the reaction forces.
The turning effect of the couple is called its moment and is calculated by the product of either of the forces and the perpendicular distance 'd' between them (i.e., between their lines of action). The unit of moment of force is newton metre (N m).
M = F d
It there is a body that can pivot on a fulcrum, the torque is, consequently, measured by the product of the applied force and the perpendicular distance of the pivot from the line of action of the force.
A body acted upon by a couple will rotate. If the two forces acting on the body have the same line of action (d =0), then the moment becomes zero.
There are many examples around us where we use the principle of moments. The principle of moment is applied in simple machines like the lever. A beam balance also works on the principle of moments.
If a body is in equilibrium under the action of a number of forces, then the algebraic sum of the moments of the forces about any point is equal to zero. In other words, the sum of the clockwise moments equals sum of the anticlockwise moments when the body is in equilibrium.
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| A son can balance a much heavier father on a see-saw by sitting at a greater distance from the fulcrum F. Moments of weights of the father and the son about the fulcrum F are equal. |
What is the significance of this concept in our everyday life?
To increase the turning effect of force, it is not necessary to increase the magnitude of the force itself. We may increase the turning effect of the force by changing the point of application of force and by changing the direction of force.
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Let us take the case of a heavy door. If a force is applied at a
point, which is close to the hinges of the door, we may find it quite
difficult to open or close the door. However, if the same force is
applied at a point, which is at the maximum distance from hinges, we
can easily close or open the door. The task is made easier if the
force is applied at right angles to the plane of the door.
acts
on a particle P, then the torque acting on the particle with respect
to the origin O is given by
where
gives the position of the particle with reference to the origin O.
If both
and
lie
in the XY plane then,
Generalising, the results to three dimensions
Also t can be written in terms of its components
Equating (1) and (2)
