centrifugal force

If you want to have fun with someone who is pedantic about these things, do what I do and call it by a more correct name: Centrifugal Effect.

Nine times out of ten the person you used this term on will begin their rant about there being no such thing as centrifugal force anyway.

Occasionally, what you actually said will dawn on him or her during the rant, but you will more often have to to interrupt the rant and point it out.

Interrupting a rant makes me feel all warm and mooshey inside.

Centrifugal force occurs when inertia acts upon an object. As in the case of whirling a bucket of water on a string:

Bucket at rest:
\=============/
|=============|
|=============|
|=============|
|=============|
|=============|
|~~~~~~~~~~~~~|
|=============|
\_____________/

(Down is here)
(So is gravity)

Bucket starts moving:

\=============/
|=============|
|============~|
|=========~=~=|
|======~=~====|
|===~=~=======|
|~=~==========|
|=============|
\_____________/
(Down is over here now)
(Same with gravity)

Bucket attains full speed:

\=============/
|=============|
|=============|
|=============|
|=============|(Gravity)
|=============|
|~~~~~~~~~~~~~|
|=============|
\_____________/
(Down)

Centrifugal force relies a great deal upon one's point of view. To the spectator inside the bucket, there's a slight difference in weight, accompanied with some nausea by seeing everything outside the bucket twirling wildly.

However, to the person rotating the bucket, the water 'sticks' to the inside of the bucket, refusing to fall out.

Curious.

The phenomenon relates, as I stated earlier, to inertia.
Take, for example, a car rounding a curve, and you're pushed against the wall. This happens because you and the car are seperate objects, both affected by inertia. Initally, both you and the car are moving in a straight-line path. As the car turns, you continue to move in a straight line, as per Newton's First Law.
This straight-line motion pushes you into the wall of the car, while the car is turning, producing what we call centrifugal force.

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=mA_i
Newton's Second Law in an inertial reference frame.

(d/dt)_i=(d/dt)_r+(w x r)
Apply this coordinate transformation...

V_i=V_r+(w x r)
...to the radius vector.

(d/dt)_i=(d/dt)_r+(w x r)
And again...

A_i=A_r+2(w x V_r)+(w x (w x r))
...to the velocity vector.

F_i-2m(w x V_r)-m(w x (w x r))=mA_r
Substitute into the initial Second Law equation...

F_eff=F_i-2m(w x V_r)-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 V_r) is the Coriolis force.