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A force couple is the term used for a sy...

A force couple is the term used for a system of two equal antiparallel forces, the arm of the couple is the shortest distance between the forces. Prove that the torque is equal to the product of the magnitude of the force and the arm no matter what is the position of the point with respect to which the torque is determined.

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Hint . Draw the axis of rotation perpendicular to the plane through an arbitrary point in the plane of the forces. Compute the moment of each force about this axis and find their sum.
From an arbitrary point o draw an axis perpendicular tothe plane in which the forces lie (Fig). The moment of the force couple

(the torque) is equal to the algebraic sum of the moments of each force about the axis. We have
`M=F_1a+F_2(a+d)=F_1a+F_2a+F_2d`
However, `F_1=F and F_2 =-F` , so M =-Fd. The minus sign shows that this couple makes a left-hand screw about the axis.
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