nebularain:Answers: No. No. No. That is just some of the sugar to help the medicine go down.

Espritch & Donnie B.: I was writing about the “universe”, not the universe. The difference between the two is too long a story for a bulletin board. Sample my book THE UNIVERSE ON TRIAL at http://www.theuniverse.andmuchmore.com

Kaptain K & Wiley:
Thanks for the replies that evoked what follows…..

Don't say I didn't warn you about a sinister Centrifugal Force cover-up plot. Here is an exposé of the plotters nefarious methods. Don't listen to their mantra-like chanting. Gird yourself with logic lest lies sufficiently repeated become accepted as truths.

Here is armament given to us more than 2300 years ago by Aristotle.
1) The law of identity: A thing is itself. A is identical to A.
2) The law of excluded middle: A thing either is thus-and-such or it is something else. A or B.
3) The law of non-contradiction: A thing cannot at the same time and in the same context both be and not be thus-and-such. A is not equal to non-A

In one of his barely known works he gave the following as a memory aid for law 1:

Remember this resource
A force is just a force
On that you can rely.
A fundamental fact of logic
Though time goes by.
Look what our children are being taught at http://phun.physics.virginia.edu/top...ntrifugal.html. (Thanks, Wiley!)
Here it is verbatim:

"An object traveling in a circle behaves as if it is experiencing an outward force. This force is known as the centrifugal force. It is important to note that the centrifugal force does not actually exist. Nevertheless, it appears quite real to the object being rotated."

"An object traveling in a circular motion is constantly accelerating and is therefore never in an inertial frame of reference. Since the centrifugal force appears so real, it is often very useful to use as if it were real."

A formula for calculating the magnitude of the 'force that does not actually exist' from things that do actually exist is also presented there.

What a terrible idea that the unreal could appear as if real and affect real things! Think about it! If that were true, we would be living in a nightmare world. What a horrible thing to teach the children we love.

Be careful! If you let one unreal thing into reality, it will open the door for hordes of them, allowing all kinds of havoc and mayhem to prevail. Much blood was spilled pushing them back where they belong. Keep them there!

Let’s focus on the pleasant side of reality. I had a personal and unforgettable experience with the 'force that does not actually exist.' When I was a boy I broke a smooth, rounded quartzite rock so I could tie a rope around it. When it broke, a sharp edge cut the fourth finger of my right hand, which bears the scar to this day. I tied the rope to the rock and swung it around me in a circle on our front lawn. I felt the pull on the rope. I saw that the rope was taut. I knew, probably from tug-of-war games, that a rope was only taut when pulled from both ends. I deduced that the rock was somehow pulling the other end of the rope. Incidentally, I noticed that when I let go of the rope the rock, instead of flying off in the direction pointed to by the taut rope, flew in a quite different direction. I repeated the experiment many times that wonderful summer afternoon.

Many years later I was taught that pulls and pushes were called forces and that the pull of the rock was called centrifugal force. I learned that centrifugal force had many useful applications including washing machines, centrifuges, and speed governors for steam engines. Later still, I learned Newton's laws of motion, the third of which includes the idea that for every force there is an equal and opposite force, whether those forces are static or moving.

Now we know that appearances can be deceptive. But only with respect to creatures capable of perception can the notion of appearance be meaningful. The notion of 'reality' is an abstract concept. Only thinking creatures can form abstract concepts. Rocks, ropes, and even the Moon are not perceptive, thinking creatures. The statement "Nevertheless, it appears quite real to the object being rotated", worse than being poor metaphor, carries no meaning at all; it is meaningless. The author of that sentence erred by mixing universes of discourse. I do not believe the error to be innocent.

I suppose that the author of that first quotation, if he is consistent, would also say that although there is no such thing as centrifugal force, to the rope it appears as if there were such a force, so it stretches itself accordingly. However, that author dares not take the next step. If he says that the non-existent force in the rope only appears to be real to the proprioceptive sensors in muscles and tendons, he commits epistemological suicide. Without a properly operating (i.e., healthy) nervous system (which includes sensors, nerves, and brain) he would have no means for obtaining any knowledge of reality; he would thus have to deny himself, and that is the ultimate self-contradiction.

There is another error in dismissing the very existence of centrifugal force. If centrifugal force does not exist then no force opposes the gravitational force of attraction between the Earth and the Moon and those two are somehow evading both Newton's third law of motion and his law of universal gravitation in one fell swoop.

Let us next investigate the portion of the quoted passages that reads:
"An object traveling in a circular motion is constantly accelerating and is therefore never in an inertial frame of reference."

I believe that the author of that sentence would not object to my including elliptical motion along with circular motion. If rotation precludes being in an inertial frame of reference, then such a frame of reference has no counterpart in reality. I have noted in my original post above that everything is spinning: electrons, planets, stars, galaxies, etc. Space cannot be considered independent of matter. Matter gives space its meaning. All matter is spinning in one way or another. Therefore, no real thing is in an 'inertial' frame of reference. A frame of reference devoid of rotation is a purely imaginary construct. However, the behaviors of stones, ropes, and the Moon are real.

Now let us investigate the validity of the idea that "An object traveling in a circular motion is constantly accelerating." Let us first review the ideas leading to, and implicit in, the notion of 'acceleration.'

Forces can be static and forces can move. Motion is a change of position (ds). Velocity (v) is the time rate of change of position (v=ds/dt). Acceleration (a) is the time rate of change of velocity, or the time rate of change of the time rate of change of position (a=d(ds/dt)/dt). The acceleration of a mass (m) by a force (f) is a=f/m. The change of position (S) of a body having mass (m), initially at rest, and accelerated by a constant force (f) during a time interval (t) is S=½at². The work (w) performed (or energy expended) by the source of force during that acceleration is, w=½ma²t², since work is the product of the force and the distance through which the force moves. If a force does not move, no work is done, and no acceleration is produced.

All of us who drive automobiles know that to accelerate we depress the gas pedal. That allows more fuel and air to be drawn into the engine, which accelerates the rotational motion of the wheels. More fuel (a.k.a energy) is consumed per second when accelerating than when moving at the newly achieved higher speed, when only frictional losses must be overcome. By the way, don't turn sharp corners at high speed or you will enter a ‘non-inertial’ frame of reference (the Twilight Zone?) and the force that doesn't exist will flip your car over.

Let us now consider an object in circular motion with a constant angular velocity. The object's velocity in its circular path is constant. There is no acceleration in that respect. Its distance from the center of rotation remains constant. It moves neither closer toward that center nor farther from it. It neither accelerates nor decelerates along the line through it and the center of rotation. So far all is well, and in a loss-free environment it would spin forever.

However, the author of the quote claims that the object is "constantly accelerating." As noted above, any real acceleration implies both motion in the direction of the acceleration and transfer of energy to (or from) the rotating object. Both are absent in the case we are considering. Only a moving force produces acceleration. In the case we are considering there is no moving force.

The author has things in reverse. It seems that centrifugal force is real and that the acceleration of which he writes is imaginary. If I remember correctly, here is how that mistake was born.

There once was a man who tried to understand why the moon doesn't fall down. He said to himself "If I turn off the force of gravity when the Moon is exactly overhead, it will move in a straight line tangent to, and away from, its orbit. If I next stop the motion of the moon and at the same time turn on gravity, the moon will fall down. Its motion will accelerate while it falls. As soon as it falls to its proper orbit position, I will start its motion again and immediately begin to repeat this process. Then I will speed up that process until it is effectively a continuous process. Aha! I just got a great idea! If the process is continuous it means that the Moon is continuously falling toward the Earth and, therefore, it is constantly accelerating.”

Chicken Little overheard that man and ran around the barnyard cackling “See! I was right! It is falling down after all, and even worse, it is constantly accelerating! Oh! Oh!” Soon everyone was following C. L. saying, “It is constantly accelerating.”

That man made the mistake of incautiously entering the Land of Zero. Strange things can happen in that land. For example, when volumes, areas, and lines enter that land they lose all identity; they all become points. You can no longer tell which is which. In that land geometry and many other things and their identities disappear. It can swallow up things better than any black hole. But I digress.

What really happened was that as that man speeded up the process the Moon fell less and less. Its Earthward acceleration became smaller and smaller. Finally, when the process was continuous, the Moon fell not at all and the earthward velocity and acceleration vanished into the Land of Zero. Goodbye, Constantly Accelerating.

Yes Virginia(.edu), there is a Centrifugal Force, and she is so strong and so real that she doesn’t even need to say, “I think I can. I think I can.” Don’t be afraid that the moon will fall on your head. All that talk about the moon continuously falling is just pretend stuff some mean grown-ups say to scare children.

Some of the confusion in the present subject arises from an incomplete understanding of the nature of inertia. Ernst Mach (remembered in the Mach number) ascribed inertia of a local object to its interaction with all the matter in the ‘universe.’ If that were so we would expect the inertia of a local object to be affected more strongly by much closer objects. But here on Earth we do not find inertial effects to be stronger in line with the Moon or Sun. We find them to be quite independent of direction. Mach's approach covertly assumes the highly questionable uniformity hypothesis.

In my book A JOURNEY BEYOND THE UNIVERSE I disclose an unheard of source of inertia. That source of inertia allows inertial reference frames to rotate. It also ensures that rotating, self-gravitating mass spheroids will be oblate. It de-claws all kinds of hither-to thorny problems.