Finding the Moment of a Force About a Point in Three Dimensions
The torque or moment of a force
about a point is the cross product of the vector
from the point in question to point of application of the force with the force, that is
For example, the moment of
acting at
about the point
is
Properties:
The moment is at right angles to both
and
This 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 by
where
is the acute angle betweenand