| There is such a thing as centrifugal force, but it's a misnomer;
the phenomenon isn't a force at all. Rather, it's a mathematical
fudge factor introduced by physicists when they want to use
Newton's laws of motion in a rotating, non-inertial reference
frame. Newtonian mechanics is only valid in frames of reference that
are either stationary or moving with constant velocity (according
to relativity theory, there's no difference between the two anyway).
Imagine a marble on a rotating platform on a table. In attempting to
describe this situation, one traditionally chooses a coordinate axis
attached to the table, which is not accellerating, and compares the
marble's movement-resisting inertia with the centripetal force of
friction between the marble and the platform to determine where the
marble will go. Unfortunately, this can be conceptually difficult. The
alternative, often discouraged in introductory physics courses but
allowed later on, is to choose a coordinate axis rotating relative to
the table, and attached to the platform. Newton's classic equations
will not work in this reference frame because it is
accellerating, but they can be made to work by treating it as if
it weren't. To do this we have to introducing a virtual
outward-pointing force, the centrifugal force. A derivation of the
centrifugal force using vector calculus follows.
F=mAi
Newton's Second Law in an inertial reference frame.
(d/dt)i=(d/dt)r+(w
x r)
Apply this coordinate transformation...
Vi=Vr+(w x r)
...to the radius vector.
(d/dt)i=(d/dt)r+(w
x r)
And again...
Ai=Ar+2(w x
Vr)+(w x (w x r))
...to the velocity vector.
Fi-2m(w x Vr)-m(w x
(w x r))=mAr
Substitute into the initial Second Law equation...
Feff=Fi-2m(w x
Vr)-m(w x (w x r))
...and get the effective force.
The third term on the right, -m(w x (w x r)) is the
centrifugal force.
The second term on the right is the icing on the cake. -2m(w x
Vr) is the Coriolis force. | 
