5. MOMENT AND ITS PRINCIPLE

Another parameter used to complete the formulas for equilibrium is Moment. Moment is defined as the turning effect brought about by a force with reference to a certain point. By formula, this is defined as the product of the force by its moment arm, whereby moment arm is the shortest distance between the point of reference from the line of action of the force.

                                

THE PRINCIPLE OF MOMENTS

The principle of moments is also known as Varignon's theorem, which states 

"The moment of a force about a point is equal to the sum of the moments of its components about that point."

By this, the adopted signs for each component are the rotating motions instead of the direction in the Cartesian plane. The most adopted conventional sign convention for moments are

• clockwise - positive moment
• counterclockwise - negative moment

Simply stated the principle of moment of force F about point O (where perpendicular distance from O to line of action R is d) is as follows:

                                                 

COPLANAR APPLICATIONS

 Determining moments from vertical and horizontal forces is easy because the distances can be computed directly. However, it is not the case for inclined forces. It is often easier to solve for the moment of an inclined force by breaking it down first into components and taking the moment instead of directly solving the moment from the force itself. This is due to the fact that distances can be easily solved using the vertical and horizontal axes.

Moments in two dimensional planes can be computed by Vector solution using cross product and Scalar solution using resultant of moments.


EXAMPLE 1: COPLANAR MOMENTS
EXAMPLE 2: COPLANAR MOMENTS
EXAMPLE 3: COPLANAR MOMENTS

EXAMPLE 5.0.4. MOMENT OF COPLANAR FORCES

EXAMPLE 5.0.5: RESULTANT MOMENT OF COPLANAR FORCES
EXAMPLE 5.0.6: APPLICATION OF MOMENT OF COPLANAR FORCES

SPATIAL APPLICATIONS

We can simplify the determination of moment of a force in space by taking the i-, j-, and k- components of the force and the position vector of the point in consideration. These procedures have already been discussed in spatial forces. 

                        

                       

With these two parameters identified, the moment of the force can be solved using the principle of cross product

                       

And also remember Varignon's theorem

                

It would be easier to compute the moment of a force in space using the determinant form after identifying the components.


EXAMPLE 6: SPATIAL MOMENT
EXAMPLE 7: SPATIAL MOMENT
EXAMPLE 8: RESULTANT MOMENT OF SPATIAL FORCES