Moment vector 2d9/5/2023 We can think of this as taking moments about point □ in the first case, and taking momentsĪ useful way to evaluate the cross product, is by considering the determinant of 3 × 3 matrix. Note that for the above equation for the moment of a couple, ⃑ □ has been substituted by the vector between the points □ = ⃑ □ × ⃑ □įor a couple formed of two forces ⃑ □ acting at point □ and ⃑ □ actingĪt point □, the moment of the couple is given by, Vector from the point about which a moment is being taken to any point on the line of action of the force. The moment of a force ⃑ □ about a point can be found using the cross product. Two points of application of both forces of the couple, and the moments of the two forces in the couple have opposite signs as theyĭefinition: Moment of a Couple using the Cross Product Point B is outside the region between the Points of application of the forces, and the forces produce a rotation in the same sense. It is worth noting the difference between points A and B. It is general: the moment of a couple is the same aboutĪny point on the body that the couple acts on. We observe that the moment of the couple has the same value in both cases. The net moment about □ of the couple is given by Hence, the moment is given byīy contrast, the moment of ⃑ □ about □ is positive since ⃑ □ producesĪ counterclockwise (positive) rotation about □. ⃑ □ produces a clockwise (negative) rotation about □. The moment about □ of ⃑ □ is negative because Let us now find the net moment of ⃑ □ and ⃑ □ about □. The clockwise moment about □ of ⃑ □ is therefore given by The moment is positive when the force produces a counterclockwiseīoth forces produce clockwise (negative) rotation, and their points of application are both at a perpendicular distance of □ 2 from If the force produces a clockwise rotation, the moment is negative. Where □ is the magnitude of the force and □ ⟂ is the perpendicular distance between the force and the point about Recall that the moment of a force about a point is given by Let us find the moments of forces ⃑ □ and ⃑ □ about point
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