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Moments, couples and the principles of moments
The moment of a force about any point is the product of the force and the perpendicular distance from the point to the line of action of the force.
Thus the moment of a force of ION about a point whose shortest distance from the line of action is 3 m (Fig. 1.11) is 10 X 3 = 30 N-m. Notice that, though both are measured by force X distance, there is a subtle but important distinction between a moment (unit N-m) and the work done by a force (unit Nm, or joules).
The distance in the moment is merely a leverage and no movement is involved; moments cannot be measured in joules.
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Fig 1.11 Moment of a force (Anti-clockwise)
A moment is normally taken to be positive if it is in a clockwise direction, and negative if it is in an anti-clockwise direction.
If a body is in equilibrium under the influence of several forces in the same plane, the sum of the clockwise moments about any point is equal to the sum of the anti-clockwise moments about that point, or, what amounts to the same thing and is much shorter to express, the total moment is zero. This is called the principle of moments, and applies whether the forces are parallel or not.
When considering the forces acting on a body, the weight of the body itself is often one of the most important forces to be considered. The weight may be taken as acting through the centre of gravity, which is defined as the point through which the resultant weight acts whatever position the body may be in.
Two equal and opposite parallel forces are called a couple. The moment of a couple is one of the forces multiplied by the distance between the two, i. e. by the arm of the couple. Notice that the moment is the same about any point (Fig. 1.12), and a couple has no resultant.
Moments about O. P10Xl = 10 clock, Q10Xl = 10 clock,
Total 20 clock.
Moments about A. P zero, Q 10 X 2 = 20 clock,
Total 20 clock.
Moments about В. P 10 X 2 = 20 clock, Q zero,
Total 20 clock.
Moments about С. P 10 X 6 = 60 clock, Q 10 X 4 = 40 anti,
Total 20 clock.
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P 10 newtons
Q 10 newtons
