What is centrifugal force?
We are all familiar with the effects of centrifugal force, we experience it for example every time we are in a car and take a bend - we feel a force pushing us to the outside of the curve. If, for example, you have placed your sunglasses on the seat next to you it would come as no surprise if, when taking a sharp bend at speed, they slide across the seat.
Centrifugal force is sometimes referred to as a 'fictitious' force, because it is present only for an accelerated object and does not exist in an inertial frame. An inertial frame is where an object moves in a straight line at a constant speed. But Einstein's general theory of relativity allows observers even in a non-inertial frame to regard themselves at rest, and the forces they feel to be real. Centrifugal force is not fictitious, it is a real force.
Centrifugal force arises due to the property of mass known as inertia - the reluctance of a body to change either its speed or direction. A body that is at rest will stay at rest until some force makes it move, and then will continue to move at the same speed and in the same direction unless and until some force changes the way it is moving. This is all neatly summed up by Isaac Newton's three laws of motion.
I. Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it. (This is sometimes referred to as The Law of Inertia)
II. The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma.
III. For every action there is an equal and opposite reaction.
We can illustrate 'inertial frames' by using the example of an astronaut in a space ship. Let's imagine that we have an astronaut aboard a space ship that has no windows, and we are at the controls to which our astronaut has no access to. We ask our astronaut to perform any experiment that he may wish in order to determine if the spaceship is moving or at rest. We start our experiment with the ship at rest and ask our astronaut if we are moving. He replies that he is in zero gravity floating around the ship and is unable to detect any feeling of movement, and that by carrying out various tests - such as measuring a swinging pendulum, he is still unable to detect any movement and concludes that we must be at rest. We then fire up the engine and accelerate through space, and keep accelerating, and again ask if we are moving. This time our astronaut is certain that we are accelerating, he is forced to the back of the ship, by inertia, and the more we accelerate the stronger this force becomes. If he drops an object it will 'fall' to the rear of the ship, which has now - as far as he is concerned - become the 'floor'. If we judge our speed of acceleration just right, we can create a force that is exactly equal to the force of gravity, known as 1G, and this is indistinguishable from gravity in every respect. No matter what experiment our astronaut performs, it would be impossible to tell if he is in a vehicle accelerating at 1G, or stationary on the surface of the Earth. This is the basis of Einstein's general theory of relativity, that the effects of acceleration are indistinguishable from the effects of a uniform gravitational field. This is known as the 'equivalence principle' and results from the equivalence between gravitational mass and inertial mass.
We now start to slow down our space ship, as we can see a speed camera coming up, and again ask our astronaut if we are moving. Again he replies that we are definitely moving, as the sudden slowing down caused him to be thrown forward and collide with the front bulkhead, and he mutters something to the effect that as his nose is bleeding and he is pressed flat against the bulkhead he doesn't feel it necessary to perform any experiments to confirm our movement.
We now stop decelerating and allow the ship to coast along at a uniform speed of 100,000 mph, which is now well within the legal speed limit for this part of space. We ask our astronaut once more if we are moving, and he replies that as far as he is able to tell while freely floating around in a zero gravity environment, that we are not moving.
Our little experiment has demonstrated that if the ship is travelling at a uniform speed in a uniform direction it is not possible, by any means whatsoever, to determine whether or not it is moving, It is only when the ship changes speed, either by accelerating or decelerating that the movement becomes apparent.
So what happens if we change direction instead of changing speed? Let's return to our space ship and find out. We accelerate back to 100,000 mph and maintain this speed and direction, at which point our astronaut with the sore nose is again in 'free fall' - a state of weightlessness - and unable to detect any motion. We now put our space ship into a tight turn to the right and hold the curve, and ask our astronaut if we are moving. He replies that as he is pressed hard against the left side of the ship we must be moving, and adds that as he knows that the space ship is unable to move sideways, it cannot be accelerating in the opposite direction to the force, so it must be turning to the right.
So far so good, all pretty straight forward stuff really, so what's the problem?
The problem is that we have seen that centrifugal force is a result of inertia, an object's resistance to a change in direction. When the space ship turned to the right the astronaut tried to keep going in the original direction, straight ahead, and so was forced to the left side of the ship. That makes sense, it is perfectly understandable according to Newton's first law of motion. But let's consider another movement that we can introduce using our space ship, let's rotate it about its axis.
If we now rotate our space ship about its axis, give it a spin, what happens to our astronaut? He will again be pressed against the side of the ship, providing he is in contact with it and moving with it. The question is WHY is he pressed against the side of the ship? The ship is not accelerating, nor is it changing direction, and the rate of spin can be kept constant, but centrifugal force will keep our astronaut firmly pinned against the side of the ship for as long as it continues to spin.
We can illustrate the central problem of explaining the nature of centrifugal force by examining how a spin drier removes water from clothes. We put wet clothes in, turn the machine on, and the drum spins around at high speed throwing out the water due to centrifugal force. Simple. The question is how do the clothes 'know' that they are spinning? Easy, you say, the drum is spinning in relation to the drier, and the clothes rotate with the drum. If only it were that simple!
We can imagine an arrangement whereby the drum, and hence the clothes, are kept stationary while the drier rotates rapidly about the drum, the opposite to what normally happens of course. Now if the drum rotating in relation to the drier was all that was required for centrifugal force to draw the water out, then this arrangement would work in exactly the same manner as the more conventional arrangement. You do not, however, need to be a rocket scientist to be able to tell that this arrangement would not dry the clothes! This very effectively destroys the argument that the clothes know they are rotating because of their movement in relation to the drier. The movement must be a movement in relation to something else. The next logical step is to argue that in the last example it was obvious that the drum was not really moving, only the drier was, so let's extend the area. This time we will imagine the drum remaining still, just as before, but this time we will rotate not only the drier, but the entire room, around the drum. Will that make any difference? Again we can see that this arrangement wouldn't work either, because from our vantage point from outside the room we can see that the drum isn't 'really' rotating. This does present a problem though. Imagine that we have constructed a large spin drier and we sit inside the drum and the door is closed behind us. The drum again stays still but the drier, and the entire room rotate about us. The view that we see through the door would make us feel quite dizzy, but we would know that we are not moving because we would feel no forces acting upon us, we would not be pressed against the sides of the drum.
If we now return to our astronaut in the rotating space ship, he was pressed against the sides of the ship, so what is the difference? What in 'empty' space is the space ship rotating in relation to?
Isaac Newton thought about this problem of centrifugal force and came to the conclusion that there must exist a 'preferred frame of reference' in the Universe, defined by absolute space. This is just another way of saying that there must be a special place in the Universe that all motion can be related to. If this is the case, our wet clothes would know they are rotating, and hence fling out the water, because they are rotating in relation to this special fixed point in the Universe. This would also explain why it would not be possible to 'fool' the clothes into thinking they are rotating by rotating the drier instead. It is interesting to note however, that if we kept extending outward our rotating frame about the stationary drum, eventually the water would be thrown out because the entire universe would be rotating in relation to the drum, which is the exactly the same thing as the universe remaining stationary and the drum rotating! It may be that the same effect would happen if the rotating frame was just our galaxy instead of the entire universe, we don't know.
Enter Ernst Mach, an Austrian philosopher and physicist (1838-1916) whose ideas were to later influence Albert Einstein when he was developing his ideas on the general theory of relativity. It was Einstein who gave the name 'Mach's Principle'. It was in honour of Mach's work on shock waves associated with projectiles moving through the air that the Mach numbers of speed were named after him; a speed of Mach 1 is equal to the speed of sound, Mach 2 twice the speed of sound, and so on.
Mach proposed (Mach's principle) that inertia is caused by the interaction of an object with all of the other matter in the Universe. It will be remembered that Newton believed that all motion was relative to some universal preferred frame of reference. Thirty years later, George Berkeley, argued that all motion is relative, and must be measured against something. Since 'absolute space' cannot be perceived, that would not do as a reference point, he said. He argued that if only a single globe existed in the Universe it would be meaningless to talk about any movement of that globe. Even if there were two globes, both perfectly smooth, in orbit around one another, it would not be possible to measure that motion. But 'suppose that the heaven of fixed stars was suddenly created and we shall be in a position to imagine the motions of the globes by their relative position to the different parts of the Universe'. What Berkeley is arguing, is that in effect, it is because the clothes in your spin drier know that they are rotating relative to the distant stars that causes the water to be thrown out. Berkeley also argued that it is the same for acceleration in straight lines; Berkeley's reasoning would be that the push into the back of the seat that you feel when a car accelerates is because your body knows that it is being accelerated relative to the distant stars and galaxies.
Mach did not add a great deal to the ideas put forward by Berkeley, but did put forward the suggestion that if we want to explain the equatorial bulge of the Earth as due to centrifugal forces, 'it does not matter if we think of the Earth as turning round on its axis, or at rest while the fixed stars revolve around it'. It is the relative motion that is responsible for the bulge.'
What Berkeley and Mach suggest, that it is the 'fixed stars' which provide a frame of reference, raises another question. The 'fixed stars', as we are well aware today, are not in fact 'fixed', but are actually part of a system that is itself rotating - our own Milky Way galaxy. Even before Mach was born, William Herschel and other astronomers had provided good evidence that the Milky Way is a flattened disc of stars, its shape clearly determined by rotation and centrifugal force. Mach might well have argued that there was only two ways in which the whole galaxy could be seen to be under the influence of centrifugal force. Either Newton was right, and the whole system of 'fixed stars' is rotating relative to absolute, empty space; or Berkeley and Mach were right, and there must be some distribution of matter, far across the Universe, that enables a frame of reference against which the rotation of our Galaxy is measured.
Another example of centrifugal force that is well known to us is demonstrated by objects in orbit, such as satellites or the International Space Station (ISS), or indeed the Moon. The difference here is that astronauts aboard the ISS do not experience the effects of centrifugal force as they orbit around the Earth, they are not pushed away from the direction of the Earth. Why not? To begin, let's examine how an object gets into Earth orbit and stays there, 'unsupported'.
Imagine having a large and powerful cannon, the more gunpowder packed behind the cannon ball the further it will travel. Now imagine setting up our super powerful cannon and firing it so that the cannon ball lands say 1,000 miles away. Now pack in more gunpowder and fire again, this time it will have travelled further, say 2,000 miles, before falling to the ground. Keep repeating the exercise and adding more gunpowder every time, and every time the cannon ball is fired it will travel further before it falls to the ground. Eventually, with enough power behind it, it will go all the way around the world before falling to the ground, and will have almost reached its starting point - it will land just behind you. Now, by packing in even more gun-powder, and getting just the right trajectory, it will over-shoot you and keep on going, it will not land. What the cannon ball is now doing is permanently arcing back down towards the Earth, but the curve of the Earth is falling away at the same rate, the cannon ball never 'catches up' with it. This is known as being in "free fall', the cannon ball is in orbit.
Our astronaut aboard the ISS is in free fall, just like the cannon ball. The ISS - and the astronauts - are prevented from being thrown out of orbit (like the water thrown out of the clothes in the spin drier) by the force of gravity. This balancing force is called centripetal force, and keeps the ISS in a closed orbit. Because the centrifugal force is exactly balanced by the centripetal force of gravity the astronauts aboard the ISS will not feel any sensation of centrifugal force. This is another example of the equivalence principle, which says that the effects of gravity and acceleration are indistinguishable from one another, and in this particular case they exactly cancel each other out.
If you were in a lift that was at the top of a very tall building and the cable snapped, as it hurtled towards the ground you would be in free fall just as the astronauts are aboard the ISS. You would be able to freely float about inside the lift and enjoy the sensation of being weightless, until you reached the ground. It was by employing this trick that the directors of the film 'Apollo 13' were able to film the 'astronauts' in a weightless environment. They just hired a plane, fitted out the interior to look like the the Apollo module, and after having climbed to a suitable altitude nosed the plane down and allowed it to 'fall' towards the ground. Hey presto, 'look mum, I'm floating in space!'
We can create a weightless condition while still on Earth, we just have to fall. We can duplicate the force of gravity in a gravity free environment by acceleration. We can rotate an object and create centrifugal force, but we are unable to explain how centrifugal force works. Is it Newton's preferred frame of reference of absolute space? Or Mach's and Berkeley's idea that it is the average distribution of matter across the Universe? There has to be some way that an object knows that it is rotating in relation to something.
We do not really know how it works. General relativity and Mach's Principle seem to suggest that it is connected to the average density of matter in the Universe, but is unable to explain how this could be done. Recently, a group of physicists have speculated that inertia arises from charged matter (electrons, atoms etc) moving through the physical vacuum which acts differently along the direction of motion and behind the particle so that inertia is actually a quantum mechanical effect produced locally, not by distant matter. Doesn't help much though does it?
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