Any pair of equal and opposite forces acting on the sameobject is called a coupl

Question

Any pair of equal and opposite forces acting on the sameobject is called a couple. Consider the couple in part (a) of thefigure. The retation axis is perpendicular to the page and passesthrough point P. a) Show that the net torque due to this couple is equal to Fd,where d is the distance between the lines of action of the twoforces. Because the distance d is independent of the location ofthe rotation axis, this shows that the torque is the same for anyrotation axis. b) Repeat for the couple in part (b) of the figure. Show thatthe torque is still Fd if d is the perpendicular distance betweenthe lines of action of the forces.

Explanation / Answer

    (a)     Anticlockwise torque, 1 = F ( x1 )     Clockwise torque, 2 = - F ( x2 )     Net torque , = 1 + 2                          = F ( x1 ) - F ( x2 )                          = F ( x1 - x2 )                          = - F ( x2 - x1 )                  But, x2 - x1 = distance between lines of forces = d     Hence, Net torque , = - F d                Magnitude of net torque, = F d (b)     Anticlockwise torque, 1 = F ( x1 )     Clockwise torque, 2 = - F ( x2 )     Net torque , = 1 + 2                          = F ( x1 ) - F ( x2 )                          = F ( x1 - x2 )                          = - F ( x2 - x1 )                  But, x2 - x1 = perpendicular distance between the lines of forces =d     Hence, Net torque , = - F d                Magnitude of net torque, = F d

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