Moment of a force about a point

a vector whose magnitude is determined as a product of

the force magnitude and its arm. The arm is the shortest distance (perpendicular) between the center and the force’s line of action. The vector of moment is perpendicular to the plane of the force and position vector and is directed so that the shortest rotation is counter-clockwise when viewed from the end of the vector.

axis that passes through the point is called the moment

of force about the axis

force about the axis Ox

Moment of a force about the

axis Oy

Moment of a force about the axis Oz

the center lying on the axis, the result is independent

of the choice of the center on the axis.

obtained in the following steps:
Project the force onto plane that

is perpendicular to axis.
Determine the arm h of the force projection with respect to the point of intersection of the axis and plane.
Calculate the moment of the force about the axis as a positive or negative product of the magnitude of the force projection and its arm.

zero if
the force and axis lie in the same plane:

the force is parallel to the axis,
the line of force action intersects the axis.

resultant of several concurrent forces is equal to the sum

of the moments of the various forces about the same point O.

of opposite sense is called a couple. The plane containing

these two forces is called the couple plane.

applied at any point without changing its magnitude and direction

be changed provided the couple moment remains constant.
An effect of

a couple on the rigid body will remain unchanged if the couple is translated (is shifted by parallel translation).
An effect of a couple on the rigid body will remain unchanged if the couple is revolved an orbit angle in couple plane.

rigid body and having the same vector moment are equivalent.

be replaced by a single couple with vector moment equal

to the sum of vector moments of the two original couples.

n couples applied to a rigid body is equivalent to

a single couple with vector moment equal to the geometrical sum of original couples vector moments

The second problem of statics – conditions of equilibrium: a system of n couples applied to a rigid body is balanced if a single couple to which the original system may be reduced is equivalent to zero .