Couples
Every couple has its moment!
This quotation may help
you remember something about the turning effect of a pair of forces.
If two equal and opposite forces whose
lines of action are not the same act on a body then they produce only a turning effect on the
body - such an effect is called a couple and the size of this couple is called the moment of
the couple or torque. (See Figure 1) If these two forces are both equal and opposite the
object will simply rotate but if they are not then the object will translate as well.
DEFINITION OF A COUPLE
A couple is composed of two forces that:
(a)
are equal
(b) are anti-parallel (parallel but in opposite directions)
(c) do not pass
through the same point
The moment of a couple is called a torque. The size of the
torque is given by :
Torque = [Fxd/2]x2 = Fd
(Torques are measured in
Nm).
A space station may be rotated by two rockets placed at opposite ends of a
diagonal. They produce a couple which makes the space station spin. Two hands rotating
the steering wheel of a car is a further example of a couple.
Example problems1.
Two forces of 20 N is applied to a car steering wheeel that has a diameter 40 cm. If the two forces act tangentially to the steering wheel and in antiparallel directions calculate the torque applied.
Torque = [Fxd/2]x2 = 20x0.2x2 = 8 Nm
2. Explain carefully what would happen if the two rockets in Figure 2 were not of equal thrust.
Another look at couples
The diagram shows that the distance
between the lines of action of the forces is vital. As the forces are applied at different angles
so the torque changes.
Torque = Fd
Think of trying to open a door by pulling on the handle so
that your arm makes a very small angle with the door itself.
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