Ah, Erik, you are the 27,567,233th victim of the Pseudoforce Conspiracy, a secret society whose aim is to prevent hapless students from understanding Classical Mechanics by leading them down a tempting but treacherous path to what looks like an innocent shortcut but is in fact a dead end trap.
There is no such thing as a "centrifugal force".
Newton's 2nd Law means what it says: a mass accelerates only under the influence of a force. But acceleration is the rate of change of velocity, so they are both VECTOR quantities, which means the velocity can change DIRECTION without any speeding up or slowing down, and this is what will happen if a vector force is applied perpendicular to the direction of motion (i.e. the velocity). This is exactly the situation in uniform circular motion, where the "centrifugal force" nonsense always slips in. A mass moving in a circle at constant speed is constantly being accelerated toward the centre of the circle, so there must be a REAL force acting in that direction (toward the center); this force is called "centripetal" meaning "pointing toward the centre of the circle". Doh! For the Moon going around the Earth (almost a circular orbit) the force is supplied by gravity; for a tetherball going around a pole it is supplied by the rope as a tension. There are lots of other examples.
The avowed purpose of making up fictional pseudoforces is to allow you to pretend that the mass in question isn't really accelerating toward the centre of the circle, but has a "centrifugal" force balancing out the (real) centripetal force; the claim is that you are too stupid to understand anything as hard as Newton's 2nd Law and vectors too. Don't you believe it. You are plenty smart enough to get it right in the first place and not have to dismantle a whole bogus misunderstanding when you get to First Year Physics at UBC or other equivalent universities. I have some material about this;check out Chapters 8-10 of my Skeptic's Guide to Physics.
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