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Moment

MOMENT

The action of a force may tend to rotate a body about an axis. This axis is a line which neither intersects nor is parallel to the line of action of the force.

Fig. 3.3 shows a body acted upon by force F in the plane. (0-0) is an axis normal to the plane of the body. d is the distance of the line of action of the force from the axis. The magnitude of moment is the product of the force and perpendicular distance.

M = F d

Let us use sign convention of a moment. An anticlockwise moment is taken as positive and clockwise moment is taken as negative. Here M is positive.

Now we will use vector notation for moment of a force. The moment of F about point A (or about the z axis passing through point A) is represented by cross-product of with

Where r  is a position vector which runs from the moment reference point A to any point on the line of action of F. The magnitude | M | = M = F r sin  = F r  sin  θ   =f= r sin θ does not depend on the particular point on the line of action of F to which the vector -; is directed. The direction and sense of M are determined by the right hand screw rule to the sequence.