The moment of a force (also known as torque) provides a measure of the tendency of that force to cause rotation about a given point (or axis).

It is calculated based on the following

The positive direction of the three individual axes is defined as shown. This choice of positive direction for these axes is important because the moment of a force is calculated using vector cross-product multiplication, the mathematics of which is based on this choice of sign convention for

Define the following:

where

The moment of the force

Carrying out the vector cross-product multiplication we get

Now, there are certain problems in which we wish to solve for the moment

where

It is interesting that no matter where point

There are specific problems where force couples occur; such as joint locations, where the distance

The moment due to a force couple pair can be simply expressed as:

For certain problems involving force couples, we can solve for the unknowns

Note that moments due to force couples only show up in the moment (e.g. Euler) equations. But they do not show up in the force equations (Newton’s Second law,

As a result, moments due to force couples contribute only to rotation of a body but not to the translation of a body (due to Newton’s Second Law) – more specifically, this means they do not contribute to the acceleration of the center of mass of a body.

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