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ECS221L9

# ECS221L9 - Couples A system of 2 forces of equal magnitude...

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Couples A system of 2 forces of equal magnitude parallel lines of action and opposite sense. The Couple -F F

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Moment of a Couple M O = r A × F + r B × (-F ) = (r A - r B ) × F = r × F Moment of a couple: M = r × F r -F F O r A r B
… more M = r × F , M = rF sin θ = Fd   Magnitude: Fd Sense: right hand rule -F r θ d

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… more “Strength” of a couple is independent of point about which moment is taken! Depends only on F and d.   d F d/2 2F strength equal to Fd
Force Systems Definition. Two force systems are equivalent (have the same effect on a rigid body) if they can be transformed into one another by (i) resolving vectors, (ii) canceling equal and opposite vectors, (iii) sliding vectors (transmissibility).

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… more Theorem. Two couples that have the same moment are equivalent. It does not matter where couple acts on a rigid body, or what the forces or

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ECS221L9 - Couples A system of 2 forces of equal magnitude...

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