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What is a couple?

What is a couple? Is it (A) a pair of forces with equal magnitude? (B) A pair of forces with the same magnitude and direction. (C) A pair of parallel forces with equal magnitude and the same line of action. Or (D) a pair of parallel forces with equal magnitude and opposite direction which do not lie on the same line of action.

One of these four options is the direct definition of a couple. It is option (D). A couple is a pair of parallel forces with equal magnitude and opposite direction which do not lie on the same line of action. We can demonstrate this on the rod 𝐴𝐵. If the force 𝐅 sub one acts perpendicular to the rod vertically upwards and 𝐅 sub two acts perpendicular to the rod vertically downwards, then we have a pair of parallel forces which act in the opposite direction. And from the diagram, we see that they do not lie on the same line of action.

If the magnitude of these two forces are also equal, then we can conclude that 𝐅 sub one and 𝐅 sub two are a couple. They are a pair of parallel forces with equal magnitude and opposite direction which do not lie on the same line of action.

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