Statics/Newton's Laws and Equilibrium

Newton's first law states that

    "An object at rest will remain at rest unless acted
     upon by an outside, external net force."  

This also applies to an object in motion. An object in motion will continue to move in the same direction at the same velocity unless some net external force is applied.

When more than one force acts upon an object, the vector sum of these forces is the resultant force.

When the resultant force on an object is zero, it will remain at rest if it is at rest, or continue to move in a straight line at a constant velocity if it is in motion. There is no change in either the magnitude or direction of its velocity. That is, there is zero acceleration.

The above concept can also be applied to motion in any selected direction.

Consider an object moving along the x-axis. If no net force is applied to the object along the x-axis, it will continue to move along the x-axis at a constant velocity with no acceleration.

We can extend this to the y- and z- axes.

In any system, unless the applied forces cancel each other out, that is, the resultant force is zero, there will be acceleration in the direction of the resultant force.

In static systems, where motion does not occur, the sum of the forces must always equal zero (otherwise, it's a dynamics problem).

That is,

    $\sum F_x=0$, 

    $\sum F_y=0$

and,

    $\sum F_z=0$

The concept also applies to rotational motion.

If the resultant moment about an axis is zero, the object will have no rotational acceleration about the axis. If the object is not spinning, it will not start to spin. If the object is spinning, it will continue to spin at the same constant angular velocity.

Again, we can extend this to moments about the y-axis and the z-axis.

For equillibrium about all three axes

    $\sum M_x=0$, 

    $\sum M_y=0$

and

    $\sum M_z=0$

What happens if the sum of forces or moments is not zero?

If the object has a net moment not equal to zero, it will spin about whichever axes are not zero. If the object is acted upon by a net force not equal to zero, it will accelerate in whatever direction the net force is. Once the object moves it cannot be analyzed with statics, instead the rules of dynamics take control. The acceleration of the object is governed by Newtons second law,

$\sum F=m*a$

You will never need this equation in Statics