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.