Why is the centrifugal force excluded from the full equations of motion?
a. it is the result of an imbalance of forces already included in the equation.
b. its inclusion leads to imaginary numbers as a result.
c. it applied only to the northern hemisphere.
d. it has a value of zero in this frame of reference.

Centrifugal force is a force caused due to the inertia of the earth, its directed away from the centre from the axis passing through the coordinates of the rotation. Thus is a result of an imbalance of forces already included in the equation

Explanation:

As it's not a real force its due to the tendency of the objects of the circular path to leave the path in a straight line. As finally, the tangent velocity remains constant hence the path perpendicular to object running from the center. For an equation of motion, uniform acceleration has to be taken place, is described in terms of displacement and velocity the instead the centripetal force keeps the object together, as the centripetal force is guided by gravity and two-body problems apply to the spinning of less angular speeds.