Centrifugal force does not exist. Collins Concise Dictionary defines it as 'a fictitious force that can be thought of as acting outwards on any body that rotates or moves on a curved path'. The crucial word in that definition is fictitious. So why have we all heard of it? Indeed, why have we all felt it, on fairground rides, roundabouts and bicycles on corners?
There are many complex phenomena in the universe. Many of them are so complex that to teach them as they really are would be impossible, so instead teachers use convenient fictions. A simple example is this: 'An atom is like a tiny solar system. The nucleus, like the Sun, is in the centre. Around it, orbiting like tiny planets, are the electrons.' This is called the Bohr model, after its originator, Niels Bohr. Real atoms are nothing like that at all, but it is convenient and permissible to pretend that they are until you need to know better.
Another example of a convenient fiction is this: 'The Moon revolves around the Earth.' Actually, the earth-moon system revolves around a point several miles away from the centre of the earth. For most practical purposes, the convenient fiction is true enough, without being 100% accurate.
So it is with centrifugal force. Common sense and observation suggest that when standing on a playground roundabout, if you don't hang on then some 'force' will throw you off. As is often the case, common sense is wrong. So what is going on?
Please refer to the entry on Newton's Laws. The one we're mainly interested in is the first law:
Any object in a state of rest or of uniform linear motion will remain in such a state unless acted upon by an unbalanced external force.
So if a body is moving at all, its natural tendency is to continue moving, in that direction, in a straight line, forever. Physicists usually consider 'ideal systems' because it makes doing the sums easier. No external force is required to keep it moving in that straight line at that speed. In fact, only the application of some force can change the speed or direction of movement.
At any given instant, standing on that rotating playground roundabout, the natural tendency is to continue moving in a straight line at a tangent to the roundabout. The only thing stopping this from happening is the tension in the arms as the passenger holds on - a force pulling them inwards!
This force - the one acting inwards - is called centripetal force, and it most definitely does exist. The centripetal force holding a child on a roundabout is the tension in their arm. The centripetal force holding a satellite in orbit is gravity (see below).
Rotating Frames of Reference
Newton's laws apply to inertial frames of reference. This can be thought of as a hypothetical, non-moving outside observer. In the example above for instance, someone over by the swings. If you are actually on the roundabout, a curious thing happens. Because your frame of reference is not inertial but rotating, Newton's laws appear to you to change. For a fuller discussion, see the entry on Coriolis Force. Suffice to say that from a point of view inside a rotating frame of reference, centrifugal force appears to exist. However, if you do your calculation from the point of view of the outside of observer1 you find that the fudge factors you need to introduce in a rotating frame of reference2 are not required.
What Holds It Down?
Another example is that of artificial satellites. A common misconception is that satellites are somehow 'held up' by centrifugal force. This is a case of asking the wrong question. The correct question is not 'What holds that object up there?', but rather 'Now it's up there, what stops it just flying off?' The answer of course, is gravity (a centripetal force in this context), but people have an ingrained sense that gravity makes things hit the ground. This is not unreasonable given that it seems to have that effect most of the time. However, the question here is one of scale.
Throwing Something Really Hard
If you throw an object the size of a cricket ball across a pitch (50m, say), it describes a curve through the air - a parabola. It rises, peaks, and falls. Eventually, the curve intersects with the surface of the Earth. How far away it intersects depends on many things, including the angle you threw the ball, the wind direction, and how hard you threw it. The point is that the curve intersects the surface of the Earth. It is very obvious that the fundamental forces involved were the initial throw and gravity.
If the object was thrown very hard (over a distance of, say, 50km) it will again rise, peak and fall, still describing a parabolic arc near enough, although the point where it would intersect with the Earth may be over the horizon. This is because at that kind of scale the curvature of the Earth starts to become a factor. Still, very obviously no main forces involved except for that initial throw, plus gravity.
Now for the tricky part. The object is thrown really, really hard (a distance of over 5000km). As before, it rises, peaks, and starts to fall. But if the throw is just right, or the projectile has the ability to correct its course, the path of its fall will be parallel to the surface of the Earth. Your object will now continue to fall around the Earth forever. Exactly as before, no forces are at work here at all except the initial throw, and gravity.
What makes your washing stick to the outside of the drum on 'spin'? Why must you lean into corners on a motorbike? Why do you get flung off a moving merry-go-round? 'The tendency of a body to continue in uniform motion in a straight line unless acted upon by a resultant external force' is the correct answer. 'Centrifugal force' is much easier to say, and conforms to common sense, especially when viewed from a rotating frame of reference. It is important to remember, however, that just because it's easy to say doesn't mean it's right.