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Finding the Moment of a Force About a Point in Three Dimensions

The torque or moment of a forceabout a point is the cross product of the vectorfrom the point in question to point of application of the force with the force, that is

For example, the moment ofacting atabout the pointis

Properties:

The moment is at right angles to bothandThis is a consequence of the cross product. In the above diagram the moment is directed out of the paper, since the cross product defines a right handed coordinate system.

If a force acts at a point, the moment of the force about that point is zero.

The total moment of a system of forces is equal to the sum of the moments:

The Total Moment is a vector, with magnitude given bywhereis the acute angle betweenand

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